Modification de The costs of production

Based on a course by Federica Sbergami<ref>[https://www.unige.ch/gsem/en/research/faculty/all/federica-sbergami/ Page personnelle de Federica Sbergami sur le site de l'Université de Genève]</ref><ref>[https://www.unine.ch/irene/home/equipe/federica_sbergami.html Page personnelle de Federica Sbergami sur le site de l'Université de Neuchâtel]</ref><ref>[https://www.researchgate.net/scientific-contributions/14836393_Federica_Sbergami Page personnelle de Federica Sbergami sur Research Gate]</ref> 

{{Translations
| fr = Les coûts de production‎‎
| es = Los costos de producción
| it = Costi di produzione
| pt = Custos de produção 
| de = Die Produktionskosten 
}}

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|[[Introduction to microeconomics]]
|[[Microeconomics Principles and Concept]] ● [[Supply and demand: How markets work]] ● [[Elasticity and its application]] ● [[Supply, demand and government policies]] ● [[Consumer and producer surplus]]  ● [[Externalities and the role of government]] ● [[Principles and Dilemmas of Public Goods in the Market Economy]] ● [[The costs of production]] ● [[Firms in competitive markets]] ● [[Monopoly]] ● [[Oligopoly]] ● [[Monopolisitc competition]]
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The analysis of production costs is a fundamental aspect of industrial organisation in microeconomics. This analysis is crucial because the main objective of any economic agent, particularly firms, is to maximise profits. The study of production costs helps to understand the behaviour of firms in different market contexts, including perfect competition and various forms of imperfect competition.

Production costs are key factors influencing production decisions and prices. In other words, a company's strategies and programmes depend heavily on its choices regarding production factors. The ultimate objective of companies is to maximise their profits, and production costs, which directly affect the supply function, play a significant role in determining profits.

This analysis enables companies to make informed decisions about how much to produce, what technologies to use, and what prices to charge in order to remain competitive while maximising their profits. Costs can include items such as raw materials, labour, energy and equipment depreciation. By understanding these costs and managing them effectively, companies can optimise their production and strengthen their market position.

= Analysis of production costs =

The formula for company profit is quite simple in theory. Profit (π) is calculated by subtracting total cost (TC) from total revenue (TR). In mathematical terms, this is written :

π = RT - CT

Here, π represents profit, RT total revenue and TC total cost.

Total revenue (RT) is calculated by multiplying the unit price of a good or service by the quantity sold. In other words :

RT= Price × Quantity sold

This formula highlights the importance of price and sales volume in generating revenue for a business. A high price or a large quantity sold can both increase total revenue, while effective cost management can reduce total cost, thereby increasing profit. However, it is important to note that this simplified formula does not take into account other factors that can influence profit, such as fixed and variable costs, economies of scale, market conditions, and pricing strategy. In practice, maximising profit is often more complex and requires a detailed analysis of all these factors.

The analysis of production costs is central to understanding the market supply function in microeconomics. This supply function is traditionally seen as an increasing relationship between price and quantity offered. This relationship is explained by the fact that, when prices rise, companies have an incentive to produce more in order to make higher profits. Production costs play a crucial role in this dynamic. They include both variable costs, which change with the level of production, and fixed costs, which remain constant regardless of the quantity produced. Understanding these costs enables companies to determine the quantity of production that maximises their profits at different price levels.

In parallel, consumer theory examines the factors influencing the demand function, which indicates the quantity of a good or service that consumers are prepared to buy at different prices. This demand is shaped by factors such as consumers' incomes, their preferences, the prices of substitute and complementary goods, and their future expectations. Analysis of these factors is essential to understanding how consumer choices influence overall market demand.

Thus, production cost analysis and consumption theory are two pillars of microeconomics that complement each other in explaining market dynamics. On the one hand, companies evaluate their production costs to define their supply, and on the other, consumers make their purchasing decisions based on various factors that influence their demand. The meeting of supply and demand determines market equilibrium, influencing price formation and the quantity of goods traded. This integrated understanding of supply and demand is crucial for analysing market economics, consumer trends and corporate strategies.

[[Fichier:Une entreprise simplifiée 1.png|400px|vignette|centré|A simplified business.]]

This chart provides a visual representation of the basic structure of a company's production and economy. In this model, inputs or factors of production such as labour and capital are acquired on the relevant markets and form the basis of any production process. These inputs are then transformed into finished products or services (outputs) using technology, which can include production methods, equipment and specialised knowledge.

Once the technology has been used to transform the inputs into outputs, the latter are sold on the market, generating revenue for the company. This revenue is a function of the price at which the goods or services are sold and the quantity of them purchased by consumers. The diagram suggests that revenues and costs are intrinsically linked, with costs being a necessary consequence of production. These costs include everything required to produce the output, including but not limited to wages, material costs, and depreciation of capital.

Profits are represented to illustrate their derived nature, being the residual result once costs have been subtracted from revenues. This is the figure that companies are most interested in, as it measures the efficiency with which they have transformed their inputs into profitable outputs. Profits are essential not only for the survival and growth of the business, but also for strategic decisions about investing in new technologies or expanding into new markets.

This schematic model also highlights the importance of input markets, which are key elements of a company's external environment. These markets determine the availability and cost of essential inputs, thereby influencing production costs. Companies therefore need to monitor these markets closely to optimise their cost decisions.

However, it is important to note that this diagram is a simplification of the real economic process. In reality, companies are faced with much more complex decisions, involving a variety of external factors such as changes in regulation, fluctuations in market demand, and rapidly evolving technology. In addition, companies must also manage fixed and variable costs, economies of scale, and differentiated pricing strategies to remain competitive. In summary, although the diagram captures the essence of the business process, it does not capture all the nuances and complexities of the real business world.

= Production function and total costs =

== What is the cost of production ==

=== Opportunity cost ===

The second economic principle deals with a fundamental concept in microeconomics: opportunity cost. This principle highlights the fact that the real cost of any action, investment or acquisition is not measured solely by the amount of money spent to obtain it. In addition to financial transactions, the opportunity cost also includes the value of the best alternative given up in order to make the choice. To illustrate, let's consider an individual who decides to spend an hour studying instead of working, where he could earn 20 euros. The opportunity cost of this hour's study is not just the effort or energy spent on learning, but also the 20 euros he did not earn by working. In this way, opportunity cost provides a more complete and accurate view of economic choices.

In economics, this concept is crucial because it highlights the fact that every choice involves a potential hidden cost associated with the non-selection of an alternative. Companies and individuals use the notion of opportunity cost to make informed and rational decisions, by comparing the expected benefits of an option with those of the best alternative not chosen. Taking opportunity cost into account is therefore essential for understanding incentives and behaviour in economics. It forces decision-makers to consider not only the immediate benefits but also the potential benefits that must be abandoned. This ensures that scarce resources are allocated in the most efficient way to maximise value and welfare.

=== Explicit vs implicit costs ===

In the context of a company producing a good, costs are often classified into two categories: explicit and implicit, reflecting different aspects of the economic sacrifices involved in the production process.

Explicit costs are the direct monetary payments that the firm must make to acquire the necessary factors of production. These payments can include salaries paid to employees, purchase prices for raw materials, rents for plant or equipment, interest on loans, and any other cash expenditure that can be recorded and accounted for. They are often easily quantifiable and are recorded in the company's accounting books, playing a key role in the calculation of net profit in the financial statements.

On the other hand, implicit costs represent the value of resources that the company has chosen not to use for another potentially profitable opportunity. These costs are often non-monetary and may not be evident in a company's traditional balance sheet. For example, if a business owner uses a building they own for their business rather than renting it out to a third party, the implicit cost is the potential rent lost, or the income it could have generated. Similarly, if the owner devotes his own time to the business, the implicit cost may be the salary he could have earned by working elsewhere.

The economic approach recognises that implicit costs, like explicit costs, are real and affect the economic profit of the business. By taking into account implicit costs, it is possible to calculate economic profit, which is often lower than accounting profit because of the inclusion of these non-monetary costs. Economic profit is a more complete measure of profitability, as it reflects the total cost of the opportunities sacrificed to produce a good or service.

To maximise its economic profit, a company must therefore consider both explicit and implicit costs, ensuring that it uses its resources in the most efficient way in relation to all available options. It is this overall analysis that informs strategic decisions and contributes to the judicious management of the company's resources.

=== Illustration by Examples of Implicit Costs ===

Implicit costs, often referred to as unrecorded costs or opportunity costs, are essential elements in assessing a company's real profitability. The following examples perfectly illustrate the nature of implicit costs:

# The cost of equity capital invested in the business: When an entrepreneur invests equity capital in his business, he forgoes the interest or return he could have obtained by investing this money elsewhere, such as in a savings account, bonds, shares, or any other investment opportunity. The implicit cost here is the lost financial return. For a complete economic analysis, this opportunity cost must be considered as a real expense, because it represents the real cost of capital that is not available for other uses. 
# The salary that the entrepreneur would receive as an employee in another activity: If the entrepreneur devotes his time and effort to his business, he or she cannot allocate them to paid employment elsewhere. The implicit cost is therefore the salary that the entrepreneur could have earned by working for someone else or by engaging in another professional activity. This cost must be taken into account when assessing the profitability of the business, as it represents potential income that has not been realised.

These implicit costs are often difficult to quantify precisely, as they involve estimates of what a 'better' alternative might be. Nevertheless, they are crucial to economic decisions because they provide a more realistic measure of a company's economic performance. Ignoring implicit costs could lead to an overstated assessment of the company's financial health and success, as the accounting profit might appear higher than the actual economic profit after taking these costs into account. In short, implicit costs play a vital role in making informed economic decisions. They help to assess whether the company's resources are being used in the most advantageous way possible and whether the company is generating a sufficient return to justify these opportunity costs.

=== Accountant vs. economist analysis in assessing a company's costs and profits ===

The role of the accountant and the economist in assessing the costs and profits of a business differs significantly because of their respective approaches to implicit costs.

The accountant focuses on concrete financial transactions and cash flows. He calculates the accounting profit by subtracting explicit costs, which are the monetary payments made for the company's operations, from the income generated by the sale of goods or services. Explicit costs are therefore all costs that come directly out of the company's cash flow and are recorded in the accounting books: salaries paid, rents, cost of raw materials, interest on loans, etc. Implicit costs, being non-monetary, are recorded in the profit and loss account. Implicit costs, being non-monetary and not representing a real cash flow, are not taken into account in traditional financial statements.

Economists, on the other hand, include both explicit and implicit costs in their calculations to obtain what is known as economic profit. This approach is broader because it recognises that resources have a value beyond their direct monetary cost. By incorporating opportunity costs, the economist measures the real cost of production and the financial success of the business in terms of maximising value rather than simply maximising cash flow. Economic profit is thus defined as revenues minus the sum of explicit costs and implicit costs.

This distinction is crucial because it can lead to very different interpretations of a company's financial performance. A positive accounting profit does not necessarily mean that the company is economically viable if, once the implicit costs have been taken into account, the economic profit turns out to be zero or negative. Consequently, decisions based solely on accounting data can sometimes be misleading if the opportunity costs of the resources employed are not also taken into account.

== Economic profit and accounting profit ===

The distinction between economic profit and accounting profit is fundamental to the analysis of a company's performance.

Accounting profit is the financial result that remains after subtracting explicit costs from total revenues. It is the figure that is usually reported in a company's financial statements and the one on which business decisions are often based. It is an indicator of the company's immediate operating profitability.

Economic profit, on the other hand, takes into account both explicit and implicit costs. Economic profit is calculated by subtracting from total revenue not only explicit costs, but also the value of the opportunity costs of the resources used in the production process. This includes elements such as the cost of own capital and the alternative wage that the entrepreneur could earn elsewhere. Economic profit is therefore a measure of profitability that reflects the overall efficiency with which a company uses all its resources, including those for which it makes no direct monetary payment.

Given that economic profit includes additional costs that accounting profit does not (opportunity costs), it is logical that economic profit can never exceed accounting profit. If all opportunity costs were zero, then economic profit and accounting profit would be equal. However, in reality, there are almost always opportunity costs, so the economic profit is often lower than the book profit.

It is quite possible for a company to show a positive accounting profit while having an economic profit of zero. This can happen when the opportunity costs consumed by the company are exactly equivalent to the book profit. In such a situation, although the company appears profitable from an accounting point of view, economically it is merely covering all its costs, including its opportunity costs, without generating any real return on its resources. This is a state of "normal profit", where the company just covers its implicit and explicit costs, but does not obtain any surplus or real economic gain.

[[Fichier:Profit économique et profit comptable 1.png|400px|vignette|centré]]

Cette comparaison visuelle met en contraste deux méthodes d'évaluation de la performance financière d'une entreprise : l'une selon le point de vue économique et l'autre selon le point de vue comptable.

On the one hand, the economic point of view takes a broader view of profitability. This model breaks down total revenue into three segments. Starting from the bottom, explicit costs are direct payments for resources such as labour, materials and rent. Above these are the implicit costs, which represent the value of what the business has given up by using its resources in the current way rather than the best available alternative. This could include, for example, the potential income from an investment that the company's own capital could have earned elsewhere, or the salary that an owner could earn by working in another business. The top section, coloured green, shows economic profit, also known as 'overprofit'. This is the amount left after all costs, explicit and implicit, have been subtracted from the total revenue. This economic profit is often much smaller than the accounting profit, because it takes into account a wider range of costs.

On the other hand, the accounting view focuses solely on tangible transactions and cash flows. The explicit costs are subtracted from the total revenue to determine the accounting profit, represented in the upper part of the graph. This profit ignores opportunity costs and therefore tends to present a more optimistic picture of the company's financial health.

The graph highlights an important concept: a positive book profit does not necessarily mean that the company is economically profitable. It is possible that, even if a company shows an accounting profit, it may have an economic profit of zero or even negative once opportunity costs are taken into account. This can lead to a misunderstanding of the company's true performance, because the book profit overstates its profitability by ignoring opportunity costs.

This image illustrates the need for companies to take into account not only their immediate costs and revenues but also the opportunity costs associated with their economic decisions. This enables a more accurate assessment of financial performance and helps to ensure that resources are allocated in the most efficient way. For decision-makers and analysts, this distinction is essential for making informed choices that take into account the total value that the business creates or could create.

== The production function and total costs ==

The production function and the total cost function are two closely related concepts in the economic analysis of a company's production. The production function establishes a technical link between the quantities of inputs used and the quantity of outputs produced. It reflects the efficiency with which a company transforms inputs, such as labour, raw materials and capital, into finished products or services. This relationship is often represented graphically and can take different forms depending on the technologies and production processes used by the company.

The total cost function, on the other hand, relates the quantity produced to the corresponding production costs. Production costs include all the explicit and implicit costs associated with the manufacture of goods or services. Total costs generally increase with the quantity produced, but not always in a linear fashion due to the existence of fixed costs that do not change with production and variable costs that do.

The interaction between the production function and the total cost function is fundamental. The technical constraints of the production function, such as the laws of diminishing returns, have a direct influence on total costs. For example, if a company increases the quantity of an input, output may initially increase at an increasing rate. However, after a certain point, adding more inputs may lead to a less than proportional increase in output due to saturation of the efficiency of the additional inputs.

Economists use the total cost function to understand how costs vary with changes in the level of output and to identify the level of output where average costs are minimised. This is crucial for pricing and production decisions. By identifying the marginal cost of production - the cost of producing an additional unit - companies can determine the optimal selling price and quantity of output to maximise profits.

The production and total cost functions therefore provide an overview of a company's production efficiency and cost structure. Understanding their interdependence is essential for economic analysis and for the strategic planning of a company.

[[Fichier:Fonction de production et les coûts totaux 1.png|400px|vignette|centré]]

These two separate graphs represent a different concept in production economics.

The graph on the left describes a production function with the quantity produced on the vertical axis and the number of workers (which is a production input) on the horizontal axis. The green curve represents the production function and shows how the quantity produced increases with the number of workers. The slope of the curve at a specific point is represented by PmL, which stands for marginal labour productivity. This is the additional contribution to output from the addition of an extra unit of labour. Initially, the curve shows that marginal productivity is increasing, which is indicated by the upward slope of the production curve. However, as the number of workers continues to increase, the curve flattens, indicating a decrease in the marginal productivity of labour. This may be due to diminishing returns, where the addition of extra workers leads to a less than proportional increase in output as other factors (such as machinery or capital) become limiting.

The graph on the right represents the total cost function with total cost on the vertical axis and quantity produced on the horizontal axis. The red curve indicates that total costs increase with the quantity produced. Initially, the curve rises slowly, reflecting fixed costs that do not change with production. As production increases, the curve becomes steeper, reflecting the increase in variable costs. Total cost comprises fixed costs plus variable costs multiplied by the quantity produced. As the curve is in the shape of an inverted J, this suggests that the company is experiencing increasing returns to scale up to a certain point, after which it experiences decreasing returns to scale.

Analysing these graphs is crucial for business management. The production function shows how labour efficiency affects the quantity of goods or services that can be produced, while the total cost function shows how these production levels translate into costs. Understanding these relationships helps companies optimise their production levels to maximise profits. For example, a company might seek to produce at a level where marginal productivity is high before diminishing returns begin to manifest themselves, while monitoring total costs to ensure that variable costs do not begin to rise disproportionately to output.

== Marginal and average product of labour ==

The marginal product of labour (MPL) is a fundamental concept in economics that describes the additional impact on total output of adding an extra worker, assuming that all other factors of production remain constant. It is a measure of the marginal efficiency of labour in the production process.

Mathematically, for small increases, the marginal product of labour can be expressed as the ratio of the change in quantity produced (<math>\Delta q</math>) to the change in labour (<math>\Delta L</math>), giving the formula:

<math>PmL = \frac{\Delta q}{\Delta L}</math>

This formula represents the rate of change in output relative to the change in the amount of labour used, i.e. the slope of the production function on the graph. In a more detailed and precise analysis, especially when we are interested in infinitesimally small changes, the marginal product of labour is represented by the partial derivative of the quantity produced with respect to labour, noted as :
<math>PmL = \frac{\partial q}{\partial L}</math>

This partial derivative gives the exact slope of the production function at a given point and reflects the increase in output resulting from the addition of an infinitesimal unit of labour.

The concept of marginal product is crucial to understanding how companies make decisions about the amount of labour to employ. Theoretically, a firm increases the quantity of labour up to the point where the marginal product of labour equals the real wage, i.e. the cost of this additional unit of labour. At this point, the firm maximises its profit, because hiring an extra worker would not produce enough extra output to cover the cost of his wage.

In practice, the firm seeks the level of output where the marginal cost of production (which includes the marginal product of labour) equals the marginal revenue in order to maximise profits. However, various factors such as technological changes, labour market adjustments and regulations can influence the marginal product of labour and, consequently, the firm's optimal labour strategy.

The production function illustrated suggests that the marginal product of labour (MPL) is decreasing, implying that the addition of extra workers increases output but in ever smaller proportions. This is a manifestation of the principle of diminishing returns, where the efficiency of each additional worker decreases as the quantity of labour increases, keeping the other factors of production constant.

In mathematical terms, this means that the first derivative of the production function with respect to labour, <math>\frac {\partial q}{\partial L}</math>, decreases as L increases. Graphically, the slope of the production curve, which represents the AMP, decreases as you move along the curve to the right, indicating that each additional worker contributes less to total output than the previous worker.

Average labour product (ALP), on the other hand, is a different measure that indicates the average output per worker. It is calculated by dividing total output (q) by the total number of workers (L), given by the formula <math>\frac {q}{L}</math>. On a graph of the production function, the PML is represented by the slope of a ray starting from the origin and going to a specific point on the production curve. This radius indicates the average output for all levels of labour employed up to that point.

When the number of workers is low, the LMP can increase as additional workers are hired, as they contribute significantly to the increase in output. However, under diminishing returns, there will come a point where the addition of new workers will start to decrease the LMP, because the total increase in output will be less than the increase in the number of workers. This happens when the PML is lower than the PML.

Understanding these indicators is crucial for companies when making decisions about employing additional workers. Companies will seek to balance the cost of adding workers with the benefits of additional output to maximise efficiency and profitability.

== Diminishing returns ==

The Law of Diminishing Marginal Returns is a fundamental principle in economics that describes how, after a certain point, each additional unit of a factor of production (in this case, labour) contributes less to total output than the previous one, when all other factors of production are held constant. It's a law that has important implications for productivity and production decision-making.

The intuition behind this law can be understood by a simple example: imagine a kitchen with a single oven and several cooks. Initially, adding more cooks may increase meal production because there is enough work for everyone and the oven is used optimally. However, once you have reached the optimum number of cooks in the kitchen, adding more staff will not cook the meals any faster because the oven becomes a bottleneck. The extra cooks may even get in each other's way, which can lead to a reduction in overall efficiency.

Applied to the wider context of economic production, this means that if a company continues to add labour to a fixed quantity of other resources (such as machinery, buildings or technology), the additional contribution of each new worker will decrease. The first workers can make efficient use of the machines and space available, but subsequent workers will have fewer machines to use and less space to work in, reducing their marginal productivity.

This law explains why companies cannot simply increase their production indefinitely by adding more workers. Instead, they have to find a balance between the number of workers and the amount of other resources at their disposal. To increase production beyond a certain point, a company will need to invest in other factors of production, such as purchasing additional machinery or expanding facilities, rather than relying solely on adding labour.

When workers find themselves having to share limited resources such as computers or photocopiers, individual efficiency begins to decline. This decline initially manifests itself in small inefficiencies, such as waiting to use equipment, but can quickly escalate into more significant coordination and communication problems as more workers are added. Delays pile up, workers spend more time waiting than producing, and frustration can lead to low morale, further affecting productivity.

Graphically, this translates into a production function which, after a certain point, flattens out as the quantity of work increases, reflecting a decrease in marginal productivity. Each additional worker adds less to total output than the worker who preceded him. The graph of the total cost function reveals the financial impact of this law: as output increases, marginal costs - the cost of producing an additional unit - also begin to rise. This is because, if production requires more labour for each additional unit due to resource congestion, then the cost of producing that additional unit will inevitably rise.

In reality, companies can encounter this problem when their size reaches a point where resources start to become scarce in relation to the number of employees. The solution to avoiding this pitfall is not always to add more resources, but may also involve better management of existing resources, improving work processes or investing in technologies that improve efficiency.

The intuition behind the law of diminishing marginal returns and its impact on costs is that efficiency and profitability can suffer if a company fails to properly balance its use of labour with the other resources at its disposal. This highlights the importance of strategic resource management to optimise production and control costs in a given production environment.

== Case Study: Production Function and Total Cost ==

The example below shows the production function and cost structure of a pizza producer as a function of the number of workers employed. When the pizza shop employs no workers, there is naturally no production, and the total cost is made up purely of the fixed cost of the shop, which amounts to 30. This sum is probably representative of costs such as rent, utilities and equipment depreciation, which are invariable whatever the level of activity.

[[Fichier:Exemple fonction de production et coût total 1.png|450px|vignette|centré|Production and total cost function of a pizza producer.]]

By introducing the first worker, production starts at 50 pizzas, indicating a significant contribution to the business from this single worker. The total cost rises modestly to 40, incorporating the fixed cost of the workshop plus an additional variable cost of 10 for the labour. This additional cost represents the wage or salary of the worker.

With each additional worker added, the production of pizzas increases, but it is interesting to note that the increase in production decreases each time, from 40 extra pizzas with the first worker to only 10 extra pizzas with the fourth worker. This illustrates the law of diminishing marginal returns, where each additional worker makes a smaller and smaller contribution to overall production, probably due to the limitation of shared resources such as workspace or kitchen equipment.

At the same time, although the fixed cost of the workshop remains constant, the total cost of labour increases linearly with the addition of each new worker. This linear increase is the result of adding the cost of labour for each new worker, assuming that each worker costs the same amount, regardless of the output produced.

Finally, the total cost of production, which is the sum of fixed and variable costs, rises with each addition of workers, reflecting the increase in production costs. However, given the fall in marginal productivity, the cost of producing an additional unit also rises, meaning that the company has to spend more for each additional pizza produced beyond a certain point. This suggests that, although adding labour may increase output, it does so at an increasing marginal cost, a factor that businesses need to manage carefully to maintain profitability.

This analysis highlights the importance of optimising the number of workers in production. A pizza producer, or any business, needs to identify the optimal number of workers to maximise production without incurring disproportionate costs due to diminishing marginal returns. This requires a careful understanding of fixed and variable costs and their impact on the total cost and profitability of the business.

[[Fichier:Exemple fonction de production et coût total 2.png|450px|vignette|centré|Production function.]]

This graph represents the production function that shows the relationship between the number of workers hired and the quantity of pizzas produced per hour by a pizza producer. The graph shows a typical production curve that initially rises rapidly as workers are added, but begins to flatten out after a certain number of workers have been hired, indicating a decrease in marginal productivity.

Initially, with the addition of the first workers, the increase in output is substantial for each additional worker, illustrating high marginal productivity. This may be due to a more efficient use of equipment and a specialisation of work that allows a significant increase in output.

However, the graph also shows that, after the addition of a few workers, output continues to grow but at a slower rate. This happens because each additional worker contributes less to overall output than the previous one, a phenomenon that reflects the Law of Diminishing Marginal Returns. This law suggests that there is an optimal point of work beyond which the efficiency of each additional worker begins to decline, often due to the sharing of limited resources or congestion.

The graph shows that hiring the fourth and fifth workers, for example, increases output but at a decreasing rate relative to the first workers. This can be interpreted as a sign that workspace, pizza ovens or other equipment are becoming a constraint, and that the addition of extra workers cannot be fully exploited.

For the pizza producer, this graph is essential in determining the optimal number of workers to hire in order to maximise production without incurring unnecessary costs for marginal production gains. By analysing where the curve starts to flatten, the producer can identify the point of diminishing returns and make informed decisions about the size of the workforce to maintain for optimum efficiency.

[[Fichier:Exemple fonction de production et coût total 3.png|450px|vignette|centré|Total cost curve.]]

The total cost curve shown in the image represents the relationship between the quantity produced (pizzas per hour) and the total cost in euros. The curve shows an upward progression that intensifies as output increases, which is typical of total cost functions where costs vary with output.

The initial part of the curve rises relatively slowly, suggesting that fixed costs dominate when output is low. Fixed costs are expenses that do not change with the level of production, such as shop rent, the cost of equipment, and perhaps a basic salary for employees. Therefore, when the number of pizzas produced is low, the increase in total cost is moderate because variable costs (such as pizza ingredients and marginal labour costs) are still minimal.

As production increases, the curve rises more steeply. This indicates that variable costs are beginning to have a significant impact on total costs. Variable costs can include extra spending on ingredients, energy used to bake more pizzas, and extra wages for workers hired to increase production. This aspect of the curve is consistent with the law of diminishing marginal returns; as output increases, the marginal costs of producing each additional pizza increase due to the less efficient use of resources as the shop approaches or exceeds its optimal production capacity.

The shape of the curve suggests that each additional pizza costs more to produce than the previous one, indicating diminishing returns to scale in this production range. This is an important consideration for the pizza producer when planning production expansion. If he continues to increase production, the cost per unit will continue to rise, which could ultimately reduce profits.

To maximise profitability, the producer needs to find the level of production where the total cost per unit produced is lowest. This involves achieving a balance between fixed and variable costs and avoiding production beyond the point where marginal costs begin to exceed marginal revenues. The total cost curve is an essential tool for identifying this point and making informed decisions about how much to produce.

= Different cost measures =

== Different cost measures ==

=== Fixed costs ===

Fixed costs (FC) represent the expenses that a company must cover independently of its production. These costs remain constant over a given period even if the quantity of goods or services produced varies. Fixed costs are often associated with investments in physical capital, such as the purchase or rental of equipment and buildings, which do not change according to the company's production or sales.

In the case of a pizza producer, fixed costs might include the rental of commercial space, the purchase or depreciation of pizza ovens and kitchen equipment, employee salaries that are guaranteed regardless of the number of pizzas sold, insurance, and perhaps some utilities such as water or internet subscription. For example, whether the pizza producer makes 10 pizzas or 100 pizzas, the rent for the premises will remain the same for the period in question. Similarly, the purchase of a pizza oven is an initial cost that does not change, whether the oven is used to cook one pizza or is used continuously.

It is crucial for businesses to understand and manage their fixed costs, as they form an important part of the total cost structure and can influence decisions on pricing, production strategy and long-term viability. A high level of fixed costs can also increase a company's financial risk, as these costs must be covered independently of revenues. Companies must therefore generate enough revenue to cover not only variable costs but also these fixed costs in order to avoid losses.

=== Variable costs ===

Variable costs (VCs) in the context of a company's production are those that fluctuate according to the volume of activity or output. Unlike fixed costs, which remain constant whatever the level of production, variable costs change directly with the quantity of goods or services produced.

In the example of a pizza producer, variable costs include the ingredients needed to make the pizzas, such as flour, tomato sauce, cheese and toppings, as well as the cost of the energy consumed to run the ovens and other kitchen equipment. In addition, if workers are paid by the hour or by the piece, then their wages are also variable costs, as the total labour required will vary according to the number of pizzas produced.

If the producer makes more pizzas, he'll need more ingredients and possibly more hours of work, which will increase his variable costs. Conversely, if he decides to reduce production, his variable costs will fall because he will use fewer ingredients and less labour.

Variable costs are essential to business management because they directly affect the profit margin per unit sold. A clear understanding of variable costs is necessary to establish effective pricing strategies and to make decisions about optimal production levels. By controlling and reducing variable costs, a company can increase its margin on each product sold, which is crucial to overall profitability. Similarly, when assessing the profitability of a new product or service, a thorough analysis of the associated variable costs is fundamental to ensuring that the selling price covers these costs and makes a positive contribution to overall profit.

=== Total cost ===

Total cost (TC) is the sum of fixed cost (FC) and variable cost (VC). This relationship is fundamental to understanding a company's cost structure and is expressed mathematically as follows:

TC = FC + VC

This equation illustrates that for each level of production, the total cost is made up of a part that does not change, represented by fixed costs, and a part that fluctuates with the level of production, represented by variable costs. Fixed costs are expenses that must be paid regardless of the volume of production, such as rent, permanent employee salaries, loan payments and equipment depreciation. Variable costs vary according to production, such as raw materials, supplies, and hours of work paid for production.

For example, if a pizza producer has monthly fixed costs of 2,000 euros for rent, equipment and fixed wages, and variable costs of 2 euros per pizza for ingredients and energy, the total cost of producing 1,000 pizzas will be calculated by adding the fixed cost to the total variable cost for that production:

TC = CF + (CV per pizza × number of pizzas)

CT = 2000 + (2 × 1000)

CT = 2000 + 2000

TC = 4000 euros

Understanding total cost is crucial for making decisions about pricing and production levels. By knowing total cost, a company can determine the minimum selling price needed to cover all its costs and generate a profit. Furthermore, by analysing how total cost varies with changes in production level, companies can identify the most efficient point of production and maximise profitability.

=== Average cost ===

Average cost (AC), also known as unit cost, is a measure used to understand the cost of production per unit of good or service produced. It is derived by dividing the total cost (TC) by the total quantity produced (q). This relationship is represented by the following formula:

<math> CM = \frac{CT}{q} </math>

Since total cost is the sum of fixed and variable costs, average cost can also be expressed as the sum of average fixed cost (AFC) and average variable cost (AVC), where average fixed cost is the fixed cost per unit produced and average variable cost is the variable cost per unit produced. Thus, average cost is also represented by the formula:

<math> CM = \frac{CF}{q} + \frac{CV}{q} </math>

This means that for each unit produced, a portion of the fixed cost and a portion of the variable cost are allocated. Average cost allows companies to determine the cost of manufacturing each unit of product, which is crucial for setting appropriate selling prices and assessing production efficiency.

For example, if a pizza producer has a fixed cost of €2,000 and produces 1,000 pizzas, the average fixed cost per pizza is €2 (€2,000 / 1,000 pizzas). If the total variable costs for these 1000 pizzas are 2000 euros, the average variable cost per pizza is also 2 euros (2000 euros / 1000 pizzas). The average cost per pizza would therefore be €4 (€2 MVC + €2 MVC), before taking into account the profit margin.

Understanding average cost is particularly important for pricing strategy. If the average cost is lower than the selling price per unit, the company makes a profit on each unit sold. If the average cost is higher than the selling price, the company makes a loss on each unit. So the aim is often to reduce average cost, either by cutting costs or by increasing production to spread fixed costs over a greater number of units, thereby reducing average fixed cost.

=== Marginal cost ===

Marginal cost (MC) plays a crucial role in the economic analysis of production, as it measures the impact on a company's total cost of producing an additional unit of a good or service. It is essentially the slope of the total cost function at a given point, representing the increase in total cost for each unit increase in output.

Mathematically, marginal cost is defined as the ratio between the change in total cost (<math>\Delta CT</math>) and the change in quantity produced (<math>\Delta q</math>). The formula is as follows:

<math>Cm = \frac{\Delta CT}{\Delta q}</math>

When looking at very small changes in the quantity produced, marginal cost can be expressed as the derivative of total cost with respect to quantity. For infinitesimal changes, the formula is:

<math>Cm = \frac{\partial CT}{\partial q}</math>

Marginal cost is particularly important in production and pricing decisions. Firms will seek to produce up to the point where marginal cost equals marginal revenue, which is the additional revenue obtained from the sale of an additional unit. This point is crucial because it corresponds to the level of production where profits are maximised. If marginal cost is lower than the selling price of the additional unit, it is beneficial for the company to increase production. Conversely, if the marginal cost exceeds the selling price, producing more would reduce the company's profit.

In practice, marginal cost analysis helps companies to adjust their level of production in response to changes in market demand, variations in input costs or the introduction of new technologies, while aiming to maximise efficiency and profitability.

== Example ==

This table profiles the production costs of a lemonade producer. It shows the relationship between the number of glasses of lemonade produced per hour and different types of cost: total cost, fixed cost, variable cost, as well as the associated average and marginal costs.

[[Fichier:Exemple mesures de couts 1.png|400px|vignette|centré|Production costs for a lemonade producer.]]

The fixed cost remains constant at €3.00, suggesting that these are costs that do not depend on production volume, such as rent or equipment depreciation. The total cost starts at €3.00 when no glass is produced and increases with production. The difference between the total cost at each stage and the fixed cost gives the variable cost, which increases with the number of glasses produced.

Average fixed costs (AFC) are calculated by dividing the fixed cost by the number of lenses produced. Since the fixed cost is constant, the MFC decreases as the production volume increases. Conversely, the average variable cost (AVC) is obtained by dividing the total variable cost by the number of lenses produced. The total average cost (TC) represents the sum of the MVC and the AVC and initially decreases before increasing slightly, suggesting that there may be an optimal production range where average costs are minimised.

Marginal cost (MC) represents the cost of an additional glass and is obtained by looking at the change in total cost divided by the change in quantity produced. It starts at €0.30 and increases progressively, indicating that each additional glass costs more to produce than the previous one. This reflects diminishing marginal returns, where the extra cost of production increases after a certain point because, for example, equipment is overused or more labour has to be hired at a higher rate to maintain production.

This data set allows the lemonade producer to understand its cost structures and make informed decisions about pricing and production levels. For example, by identifying the point at which average total cost begins to rise, the producer can determine the most efficient amount of production to maximise profits. Furthermore, by understanding marginal cost, the producer can decide how profitable it is to continue increasing production.

== Example: total cost ==

This graph shows a total cost curve plotted against the quantity of pizzas produced per hour. The curve shows a positive relationship between total cost and the number of pizzas produced, indicating that total cost increases with production.

[[Fichier:Exemple cout total 1.png|400px|vignette|centré]]

Initially, the curve appears to increase at a relatively constant rate, which could indicate that variable costs dominate total costs after fixed costs have been covered. This is consistent with the typical behaviour of variable costs, which increase in proportion to the quantity produced. As production increases, we can see that the slope of the curve becomes steeper. This suggests that the cost of producing each additional pizza is increasing, which may be due to a number of factors, such as diminishing marginal returns where adding more labour or other resources does not result in a proportional increase in output.

The increasing slope of the total cost curve may also reflect the fact that the business has reached its optimum production capacity and producing additional pizzas requires disproportionate investment in inputs. For example, if oven capacity is maximised, the production of extra pizzas could require the use of an extra oven or overtime for staff, which would increase the cost per unit.

Analysis of this curve is essential for production management decision-making. It can help the producer identify the most profitable level of production and assess whether current costs are sustainable over the long term. If the trend of the curve continues, the producer may need to reconsider its production process, invest in more efficient equipment, or readjust its pricing strategy to ensure that rising costs do not eat into profits.

== Example: marginal cost ==

Marginal cost reflects the increase in total cost due to the production of an additional unit of a good or service. In a context of decreasing productivity, characteristic of the law of diminishing marginal returns, marginal cost tends to increase as the quantity produced increases. This happens because each additional unit requires more input or effort to produce, due to capacity constraints or the increased inefficiency of the additional factors of production.

Since fixed cost (FC) remains constant regardless of the level of production, any increase in total cost when an additional unit is produced is due to an increase in variable cost (VC). Marginal cost is therefore a direct measure of the variation in variable cost. Mathematically, this can be expressed as follows:
<math> Cm = \frac{\Delta CV}{\Delta q} </math>

This implies that marginal cost is equal to the slope of the variable cost curve in relation to the quantity produced. In practice, this means that if the cost of producing the next pizza (for example) is higher than that of the previous pizza, this is due to increased variable costs, such as the extra labour required or the extra material costs incurred to maintain production.

For businesses, understanding marginal cost is essential to making optimal production and pricing decisions. Producing beyond the point where marginal cost begins to exceed selling price can reduce profitability. Therefore, companies generally aim to adjust their level of production to keep marginal cost as low as possible while satisfying market demand.

[[Fichier:Exemple de cout marginal 1.png|400px|vignette|centré]]

The graph shows an ascending linear curve representing marginal cost (MC) as a function of quantity produced. The vertical axis represents costs in CHF (Swiss francs), while the horizontal axis represents the quantity of goods produced.

The straight line indicates that marginal cost remains constant with each additional unit produced. This suggests that for each additional unit produced, the additional cost incurred by the company remains the same. This type of linear relationship is typical of a situation where variable costs do not increase with output, which could be the case if the company operates in a production area with constant returns.

However, this situation is fairly ideal and is not often observed in reality over long periods of production or on a large scale, as most companies will face diminishing marginal returns at some point. In simple terms, this means that the marginal cost curve is generally U-shaped, starting with a negative slope, reaching a minimum and then becoming positive as output increases.

The situation represented by this graph could occur in a context where the company has sufficient production capacity and resources such as raw materials and labour, which can be easily and uniformly increased to raise output without incurring significant additional costs.

For the company, a constant marginal cost means that production planning can be carried out with a degree of predictability in terms of costs. This facilitates pricing and expansion decisions, as the cost structure does not vary with increases or decreases in production. However, the company should always monitor the situation for any signs of change in the marginal cost trend, as increases could indicate growing inefficiencies or impending capacity constraints.

== Example: Average cost ==

The behaviour of average cost is characteristic of many production structures and is an essential concept in economics. The U-shaped curve of average cost reflects different phases of production and cost efficiency.

In the initial phase of production, average costs tend to fall as the quantity produced increases. This is due to the distribution of fixed costs over an increasing number of units produced. When production is low, each unit produced has to bear a large proportion of the fixed costs, making the average cost per unit relatively high. However, as production increases, these fixed costs are spread over more units, reducing the average cost per unit. This reduction continues until the company reaches what are known as economies of scale.

As production continues to increase beyond this point, the company may encounter diminishing returns to scale. This means that variable costs begin to have a more significant impact on total costs. Average variable costs may increase due to the decreasing marginal productivity of additional inputs. For example, the company may have to pay overtime to workers or face higher input costs due to increased demand. As a result, the average cost starts to rise, giving the average cost curve its characteristic U-shape.

This U-shape implies that there is an optimal level of production where the average cost is minimised. For a company, identifying this level is crucial because it maximises efficiency and profitability. Producing less than this level means that the company is not fully exploiting its production capacity and economies of scale, while producing more means that the company is facing increasing inefficiencies and rising marginal costs. So, understanding where their own production sits in relation to this U-shaped curve is essential for companies when making strategic decisions about production and price levels.

[[Fichier:Exemple de cout moyen 1.png|400px|vignette|centré]]

The graph shows the average cost (AC) curve as a function of quantity produced, in Swiss francs (CHF). As expected, the curve is U-shaped, indicating that the average cost per unit initially decreases as production increases, reaches a minimum point, and then starts to increase as production continues to rise.

Initially, when output is very low, the average cost is high due to the distribution of fixed costs over a small number of units. As production increases, these fixed costs are spread over a greater number of units, which lowers the average cost per unit. The descending part of the curve represents the economies of scale achieved as production increases. It is during this phase that the company becomes more efficient, reducing average costs.

The lowest point on the curve corresponds to the Minimum Efficient Scale (MES), which is the level of production where the average cost is at a minimum. At this point, the company is operating optimally, unable to produce an additional unit at a lower average cost. This is the most efficient level of production for the company.

Beyond the MSE, the average cost begins to rise, suggesting that the company is facing diminishing marginal returns. As output increases beyond this point, each additional unit costs more to produce, partly due to the increase in average variable cost which could be caused by the exhaustion of production capacity, the need to invest in additional or more expensive equipment, or the hiring of additional labour at higher rates.

It is crucial for a company to recognise where its EME is and seek to maximise production around that point to minimise average costs and maximise profits. If a company produces less than its EME, it is not as efficient as it could be. If it produces more, it risks increasing its costs unnecessarily, which could harm its competitiveness in the market.

== Marginal cost and average cost ==

The relationship between marginal cost (MC) and average cost (AC) is a key aspect of the economic theory of production. Marginal cost is the cost of producing an additional unit, and average cost is the total cost divided by the number of units produced. Their interaction determines the dynamics of a company's production and costs.

Marginal cost plays a decisive role in the behaviour of average cost:

* When marginal cost is lower than average cost, each additional unit produced costs less than the current average cost, which has the effect of pulling average cost down. This typically occurs when the company increases production from a low level of output, benefiting from economies of scale and the amortisation of fixed costs over a larger number of units. 
* When marginal cost is higher than average cost, this means that the cost of producing each additional unit is higher than the average cost to date, resulting in an increase in average cost. This can happen when the company has passed its maximum efficiency point and is facing diminishing marginal returns, where increases in production lead to proportionately higher increases in costs.

The point at which marginal cost intersects average cost is particularly significant. This occurs at the minimum of average cost, which is also the Minimum Efficient Scale (MES). At MERS, the company produces at a level where the average cost per unit is as low as possible. If production increases beyond this point, the marginal cost, being higher than the average cost, will increase the average cost.

In practice, a company will seek to produce at a level where the marginal cost is equal to the average cost, i.e. at the EME, because this is where production is most efficient in terms of costs. Producing less than the EME means that the company is not as efficient as it could be, while producing more means that the company is encountering inefficiencies and increasing costs.

[[Fichier:Coût marginal et coût moyen 1.png|400px|vignette|centré]]

The graph shows two distinct curves: the marginal cost curve (Cm) in red and the average cost curve (CM) in green, plotted against the quantity produced, with the cost expressed in Swiss francs (CHF).

The average cost curve has the characteristic U-shape we discussed: it declines rapidly at the beginning, reflecting economies of scale and the amortisation of fixed costs over an increasing number of units. The lowest point on the average cost curve represents the Minimum Efficient Scale (MES), where the average cost per unit is at a minimum. After this point, the curve begins to rise, suggesting that average costs are increasing as the quantity produced continues to increase, which is probably due to decreasing marginal returns and increasing average variable costs.

The marginal cost curve starts above the average cost curve and crosses it precisely at the EME. Before this crossover point, marginal cost is lower than average cost, which means that adding extra production units reduces average cost. After the crossover point, marginal cost becomes higher than average cost, indicating that each additional unit costs more to produce than average cost, leading to an increase in average cost.

This graph illustrates the important economic principle that marginal cost intersects average cost at its minimum point. This means that the company is producing at EME, the most cost-efficient level of production. If production were to increase beyond this point, it would become less efficient, as shown by the increase in average cost.

For a company, understanding the relationship between marginal cost and average cost is vital to optimising production and maximising profits. Managing production to keep costs as close as possible to the EME level can help ensure that the business operates efficiently and profitably.

== Average cost (fixed and variable) ==

Average fixed cost (AFC) and average variable cost (AVC) are two components of average total cost (ATC). Each measures a different part of the total costs per unit produced.

Average Fixed Cost (AFC): The average fixed cost is calculated by dividing the total fixed cost (FC) by the quantity of goods produced (q). Fixed costs are costs that do not change with the quantity produced, such as rent, salaries of employees not directly involved in production, depreciation of machinery, and insurance. The formula for average fixed cost is: <math> AFC = \frac{CF}{q} </math>

As production increases, the AMC decreases because fixed costs are spread over more units. For example, if the rent for a workshop is €1000 per month, and the workshop produces 100 units, the CMF is €10 per unit. If production doubles to 200 units, the CMF falls to 5 euros per unit.

Average variable cost (AVC): The average variable cost is obtained by dividing the total variable cost (CV) by the quantity produced. Variable costs vary directly with the quantity produced and include items such as raw materials, energy consumed in production, and the wages of production workers paid by the hour. The formula for average variable cost is: <math> AVC = \frac{CV}{q} </math>

The AVC can remain constant if the costs per unit of input remain the same as output increases, but it can also vary depending on various factors, such as savings on bulk purchases or the depletion of resources requiring more expensive inputs.

In short, the total average cost, which is the sum of the FPC and the GPC, provides an overview of the cost per unit for the whole of production. Understanding these average costs enables companies to determine the selling price of their products, plan production levels and carry out profitability analyses.

[[Fichier:Coût moyens (fixe et variable).png|400px|vignette|centré]]

== Plus en général ==

La productivité marginale est initialement croissante (spécialisation des travailleurs dans leurs tâches) et décroissante ensuite (car les facteurs fixes doivent être partagés par un nombre croissant de travailleurs)

[[Fichier:Couts moyen (fixe et variable)2.png|400px|vignette|centré]]

Le graphique montre quatre courbes qui illustrent la relation entre les coûts de production et la quantité produite en unités.

# Coûts fixes moyens (CFM): Cette courbe grise montre que le coût fixe moyen diminue constamment avec l'augmentation de la quantité produite. Cela est dû au fait que les coûts fixes (tels que le loyer, les salaires des employés permanents, etc.) sont répartis sur un plus grand nombre d'unités, diminuant ainsi le coût attribué à chaque unité supplémentaire.
# Coûts variables moyens (CVM): La courbe marron représente les coûts variables moyens qui, dans ce cas, semblent initialement baisser avec l'augmentation de la production, atteignant un point minimum, puis augmentent à nouveau. Le point le plus bas représente le point où l'entreprise bénéficie pleinement des économies d'échelle sur les coûts variables. La remontée de la courbe suggère que, après un certain point, l'entreprise commence à subir des rendements marginaux décroissants, ce qui entraîne une augmentation des coûts variables par unité.
# Coût moyen (CM): La courbe verte indique le coût moyen total, qui est la somme du CFM et du CVM. Elle suit la forme classique en U, baissant initialement avec les économies d'échelle puis remontant en raison des rendements marginaux décroissants. Le point le plus bas de cette courbe indique l'efficience productive optimale de l'entreprise, où le coût moyen total par unité est le plus bas.
# Coûts marginaux (Cm): La courbe rouge trace le coût marginal, qui est le coût de production d'une unité supplémentaire. Cette courbe commence sous la courbe des coûts moyens, les croise au point le plus bas de la courbe des coûts moyens (qui est aussi l'Échelle Minimale Efficace ou EME), et continue ensuite à augmenter. Cela confirme la règle que lorsque le coût marginal est inférieur au coût moyen, le coût moyen est décroissant, et lorsque le coût marginal est supérieur au coût moyen, le coût moyen est croissant.

Les observations faites dans le graphique soutiennent les principes économiques standard selon lesquels le coût moyen atteint un minimum lorsque le coût marginal est égal au coût moyen. Le graphique illustre également clairement que le coût variable moyen est toujours inférieur au coût marginal après le point où les coûts moyens commencent à augmenter, ce qui est cohérent avec l'idée que le coût de production d'une unité supplémentaire est plus élevé à mesure que la production augmente. Cela indique également que le coût marginal rencontre le coût moyen au niveau de l'EME, où le coût moyen est au plus bas, ce qui est un point de référence important pour les décisions de production et de tarification.

== Propriétés ==

Les trois propriétés suivantes sont des principes fondamentaux dans la théorie économique des fonctions de coûts, et elles ont des implications directes sur la gestion de la production et la stratégie de tarification des entreprises.

# Augmentation du coût marginal : La propriété selon laquelle le coût marginal finira par augmenter avec la quantité produite est liée à la loi des rendements marginaux décroissants. Cela signifie que, dans la plupart des processus de production, ajouter des unités supplémentaires de facteurs de production (comme le travail ou le capital) à un certain point entraînera une augmentation moins que proportionnelle de la production. Cela peut être dû à des contraintes de capacité, à des inefficacités croissantes ou à des coûts de ressources supplémentaires. Cette augmentation du coût marginal reflète le coût supplémentaire de production d'une unité additionnelle qui augmente au fur et à mesure que la quantité de production s'élève.
# Forme en U du coût moyen : La forme en U du coût moyen découle de la façon dont les coûts fixes et variables se comportent avec les changements dans la production. Lorsque la production commence, les coûts moyens diminuent car les coûts fixes sont répartis sur un nombre croissant d'unités. Cependant, une fois que la production atteint et dépasse l'EME, les coûts variables moyens commencent à peser plus lourdement dans le coût total, entraînant une augmentation du coût moyen. Si le coût marginal était toujours décroissant, cela signifierait que l'entreprise continuerait indéfiniment à gagner en efficacité avec chaque unité supplémentaire produite, ce qui n'est pas réaliste dans la plupart des cas à cause des contraintes physiques et pratiques.
# Intersection du coût marginal et du coût moyen : Le point où le coût marginal croise le coût moyen est critique car il représente le niveau de production où le coût moyen est au plus bas - l'Échelle Minimale Efficace (EME). À ce point, l'ajout d'unités supplémentaires commence à augmenter le coût moyen, ce qui signifie que l'entreprise perd en efficacité au-delà de ce point. Ce croisement est donc un indicateur pour l'entreprise qu'elle a atteint sa capacité de production la plus efficiente.

Ces propriétés ont des conséquences pratiques pour les entreprises. Pour maximiser la rentabilité, une entreprise doit chercher à opérer au niveau de l'EME, où elle peut minimiser les coûts moyens et ainsi maximiser les profits. Cela exige une compréhension approfondie de la structure des coûts et des capacités de production. En outre, les entreprises doivent être attentives à la gestion de la production pour ne pas dépasser le point où les coûts marginaux commencent à augmenter, ce qui pourrait entraîner une production inefficace et des pertes.

== Résumé graphique ==

L'image ci-dessous est un résumé graphique représentant les relations entre le coût marginal (Cm), le coût moyen variable (CVM), le coût moyen total (CTM), et le coût variable (CV(q)), dans deux contextes différents : lorsque les coûts fixes (CF) sont nuls et lorsque les coûts fixes sont positifs.

[[Fichier:Propriétés_des_couts.png|400px|vignette|centré]]

L'image affichée est un résumé graphique représentant les relations entre le coût marginal (Cm), le coût moyen variable (CVM), le coût moyen total (CTM), et le coût variable (CV(q)), dans deux contextes différents : lorsque les coûts fixes (CF) sont nuls et lorsque les coûts fixes sont positifs.

Dans les deux graphiques, les courbes du coût marginal (ligne pointillée orange), du coût moyen variable (ligne marron) et du coût moyen total (ligne verte) présentent les caractéristiques typiques :

# Lorsque CF=0 :
#* La courbe du coût moyen variable (CVM) et la courbe du coût moyen total (CTM) commencent au même point sur l'axe des ordonnées car il n'y a pas de coûts fixes à amortir sur les unités produites.
#* Les courbes CVM et CTM diminuent initialement, atteignent un point minimum, puis commencent à augmenter, formant la classique courbe en U qui représente les économies, puis les déséconomies d'échelle.
#* Le coût marginal (Cm) coupe les courbes CVM et CTM à leur point minimum, ce qui est le point d'inflexion où le coût marginal commence à être supérieur au coût moyen variable et total, indiquant que produire une unité supplémentaire devient plus coûteux que la moyenne.
# Lorsque CF>0 :
#* La courbe CVM commence à partir de l'origine car les coûts variables sont nuls lorsque la production est nulle.
#* La courbe CTM commence au-dessus de l'origine à la hauteur des coûts fixes positifs, car même sans production, l'entreprise doit couvrir ses coûts fixes.
#* Comme précédemment, les courbes CVM et CTM montrent une diminution des coûts moyens avec l'augmentation initiale de la production, suivie d'une augmentation après avoir atteint un minimum.
#* Le coût marginal suit la même trajectoire que dans le premier graphique, mais il est important de noter que le point où le Cm coupe le CTM est plus élevé sur l'axe des coûts à cause de la présence des coûts fixes.

Dans les deux cas, la position où le Cm coupe le CVM et le CTM est cruciale pour la prise de décision en matière de production. C'est là que l'entreprise ne bénéficie plus d'économies d'échelle et doit réévaluer l'augmentation de la production pour éviter des augmentations coûteuses des coûts moyens.

Les graphiques illustrent de manière claire l'importance des coûts fixes dans la détermination du coût moyen total et montrent que les entreprises doivent prendre en compte à la fois les coûts fixes et variables lors de l'analyse de leurs structures de coûts. Ils doivent chercher à maximiser la production là où le coût moyen est minimisé, tout en reconnaissant que l'ajout de capacité de production peut entraîner une hausse des coûts à long terme si les rendements marginaux décroissants se manifestent.

== Exemple numérique ==

L'entreprise manufacturière a une fonction de coût total complexe qui incorpore à la fois des termes linéaires, quadratiques et cubiques, ainsi qu'un coût fixe. Pour cette entreprise, les différentes catégories de coûts peuvent être résumées comme suit :

#Coût Total (CT(q)): C'est la fonction qui représente la somme totale des coûts fixes et variables en fonction de la quantité produite  q. Pour l'entreprise, le coût total est donné par la formule : <math> CT(q) = 100q - 4q^2 + 0.2q^3 + 450 </math>
#Coût Fixe (CF): C'est un coût qui ne varie pas avec la quantité produite et est représenté ici par une valeur de 450.
#Coût Variable (CV(q)): C'est la partie du coût total qui varie avec la quantité produite. La fonction de coût variable est : <math> CV(q) = 100q - 4q^2 + 0.2q^3 </math>
#Coût Marginal (Cm(q)): C'est le coût supplémentaire de la production d'une unité additionnelle. Il est dérivé en prenant la dérivée première de la fonction de coût total par rapport à q : <math> Cm(q) = \frac{\partial CT}{\partial q} = 100 - 8q + 0.6q^2 </math>
#Coût Fixe Moyen (CFM(q)): C'est le coût fixe réparti sur chaque unité produite. Il diminue à mesure que la quantité produite augmente : <math> CFM(q) = \frac{CF}{q} = \frac{450}{q} </math>
#Coût Variable Moyen (CVM(q)): C'est le coût variable par unité produite : <math> CVM(q) = \frac{CV(q)}{q} = 100 - 4q + 0.2q^2 </math>
#Coût Moyen (CM(q)): C'est le coût total par unité produite, et il est égal à la somme du coût fixe moyen et du coût variable moyen : <math> CM(q) = \frac{CT(q)}{q} = 100 - 4q + 0.2q^2 + \frac{450}{q} </math>

Ces formules donnent un aperçu complet de la structure de coûts de l'entreprise et sont essentielles pour évaluer la performance économique et prendre des décisions stratégiques concernant la production et la tarification.

== Lien entre fonction de production et coûts ==

La fonction de coût total peut être vue comme la réflexion de la fonction de production, avec un accent sur les intrants et les coûts plutôt que sur les extrants.

Dans le cadre de cette interprétation :

# Fonction de Production Inversée: Pour une quantité donnée de production q, et avec un stock de capital physique K fixe, la fonction de production inverse indique le nombre d'heures de travail L nécessaires pour produire q. Ceci est basé sur l'hypothèse que la technologie de production et l'efficacité sont déjà établies.
# Masse Salariale et Coût Variable (CV): En multipliant ces heures de travail par le salaire horaire w, on obtient la masse salariale, qui, dans ce cas, serait le coût variable total, supposant que le travail est le seul input variable. La masse salariale est donc une fonction de la quantité produite q et du stock de capital K : Masse salariale = w ⋅ L (K,q)
# Coût Total (CT): Finalement, pour obtenir le coût total, on additionne le coût fixe, qui est le coût engendré par le capital physique (par exemple, amortissement, loyer, entretien), au coût variable (masse salariale) : CT (K, q) = w ⋅ L (K, q) + Coût fixe

Cette façon de concevoir les fonctions de coût total comme inverses des fonctions de production est particulièrement utile lorsque l'on considère la théorie de la firme dans un cadre de production où les décisions de production sont prises en fonction des coûts des inputs et de l'efficacité de leur utilisation. Elle souligne l'importance de la gestion des ressources et la nécessité d'optimiser les intrants pour minimiser les coûts et maximiser les profits.

[[Fichier:Lien entre fonction de production et coûts 1.png|500px|vignette|centré]]

Ces deux graphiques illustrent la relation entre la quantité de travail nécessaire et les coûts variables pour produire différentes quantités d'un bien dans le cadre d'une fonction de production à court terme avec un stock de capital fixe (K).

# Graphique de la fonction de travail : Sur le premier graphique (à gauche), l'axe vertical (L) représente la quantité de travail nécessaire, et l'axe horizontal (q) représente la quantité du bien produite. La courbe montre les phases de rendements croissants et décroissants au travail. Initialement, à mesure que la quantité produite augmente, moins de travail est nécessaire par unité supplémentaire produite, ce qui est caractéristique des rendements croissants. Cependant, après avoir atteint un certain niveau de production (point d'inflexion), la quantité de travail nécessaire pour produire chaque unité supplémentaire commence à augmenter, indiquant des rendements décroissants.
# Graphique de la fonction de coût variable : Sur le second graphique (à droite), l'axe vertical représente le coût variable total (CV), et l'axe horizontal représente également la quantité du bien produite. La courbe montre le coût de production variable associé à chaque niveau de production. Le coût variable est calculé en multipliant la quantité de travail (L) par le salaire horaire (w), ce qui donne la masse salariale. Cette courbe reflète la forme de la courbe de travail, où les coûts variables par unité diminuent initialement en raison des rendements croissants, mais augmentent ensuite à cause des rendements décroissants au travail.

Les deux graphiques illustrent comment la fonction de production peut être "inversée" pour déterminer les coûts variables associés à la production de différents niveaux de sortie. Le concept de rendements décroissants est crucial pour comprendre pourquoi, après un certain point, produire plus devient de plus en plus coûteux pour l'entreprise. Cette information est vitale pour la planification de la production et pour l'établissement des stratégies de tarification, car elle aide à identifier le point de production le plus efficace et le plus rentable.

Dans la pratique, cette analyse peut aider les entreprises à décider combien de travailleurs embaucher et quelle quantité produire pour minimiser les coûts et maximiser les bénéfices. Les entreprises doivent faire attention à ne pas produire au-delà du point où les coûts marginaux dépassent les coûts moyens, car cela pourrait réduire les bénéfices globaux.

[[Fichier:Lien entre fonction de production et coûts 2.png|500px|vignette|centré]]

Ce graphique illustre la structure des coûts dans une entreprise, mettant en évidence la manière dont les coûts totaux sont constitués et comment ils évoluent avec la quantité produite.

Sur le graphique, il y a deux courbes principales :

# La courbe des coûts variables (CV(q, K)) : Cette courbe montre comment les coûts variables changent avec la quantité produite (q). La courbe commence à l'origine, indiquant qu'il n'y a pas de coûts variables si la production est nulle. La courbe présente d'abord une pente ascendante moins raide, puis devient plus abrupte, ce qui indique des rendements d'abord croissants, puis décroissants au travail. Cela signifie que pour chaque unité supplémentaire produite, le coût variable augmente initialement à un rythme décroissant (efficacité croissante), puis à un rythme croissant (efficacité décroissante) en raison de la loi des rendements marginaux décroissants.
# La courbe des coûts totaux (CT(q, K)) : Le coût total est représenté par la somme verticale des coûts fixes (CF) et des coûts variables (CV). La courbe des coûts totaux commence au niveau des coûts fixes, car même sans production, l'entreprise doit supporter ces coûts. La courbe CT a la même forme que la courbe CV, mais elle est déplacée vers le haut de la valeur des coûts fixes.

Les coûts fixes (CF) sont représentés par une ligne horizontale, ce qui est logique puisque les coûts fixes ne changent pas quelle que soit la quantité produite. Le point où la courbe des coûts variables change de pente (le point de rendement décroissant) est également le point où la courbe des coûts totaux change de pente. Ce point est crucial car il indique la quantité de production où l'efficacité commence à diminuer.

Le graphique illustre également que le coût total pour chaque niveau de production est toujours supérieur aux coûts variables en raison de l'addition des coûts fixes. Cela souligne l'importance pour les entreprises de couvrir non seulement leurs coûts variables mais aussi leurs coûts fixes pour atteindre la rentabilité. En résumé, le graphique est un outil utile pour visualiser les coûts de production et pour comprendre comment l'efficacité de la production change avec l'augmentation de la quantité produite. Pour les entreprises, il est crucial de comprendre ces relations pour optimiser la production, fixer les prix et maximiser les profits.

= Short versus long term =

== Short- and long-term production function ==

We need to distinguish between the notion of short-term and long-term production in economics. In the short-term framework, at least one of the factors of production is fixed, which is often capital (K), while the other factors, such as labour (L), can vary. This reflects situations where the company can quickly adjust the amount of labour it uses, but cannot as easily change its capital capacity because of long-term commitments, delivery times for new machinery, or simply because capital adjustments require major investment and strategic decisions.

In a long-term framework, the assumption changes: all factors of production, including capital, are considered to be variable. This allows the company to adjust all its resources to find the most profitable combination that maximises profit. The key difference between short- and long-term analysis is the flexibility with which the company can adjust all its inputs.

Long-term analysis :

# Production choice: In the long run, the firm has the flexibility to adjust the amount of physical capital (K) as well as the amount of labour (L) to produce a certain level of output (q). This means that the firm can choose from a wider set of production combinations to minimise costs or maximise output.
# Isoquantes : The firm can use isoquant graphs to illustrate the different combinations of capital and labour that produce the same level of output. Each isoquant corresponds to a different level of output, and the slope of the isoquant (marginal rate of technical substitution) indicates the rate at which labour can substitute for capital while holding output constant. 
# Profit maximisation : Profit maximisation involves choosing the point on the isoquant where the cost of production is lowest, or, in other words, where the isoquant is tangent to the isocost line. The isocost line shows all the combinations of capital and labour that the company can afford for a certain total cost. The company will adjust its combination of capital and labour until the marginal rate of technical substitution between labour and capital is equal to the ratio of the prices of these factors. 
# Change of scale: In the long term, the company can also carry out changes of scale by proportionally increasing all its inputs. If output increases more than proportionally to inputs, we speak of increasing returns to scale. If output increases less than proportionally, these are known as diminishing returns to scale. If it increases in the same proportion, we speak of constant returns to scale.

Long-term analysis is essential for strategic planning and investment, as it enables the company to position itself optimally for future growth and market competitiveness. It considers the entire production process, taking into account how investment decisions and capacity adjustments affect costs and profits.


The distinction between short-term and long-term time horizons in economic theory is fundamental to understanding companies' production decisions.

Short-term: In the short-term context, companies consider certain resources, particularly physical capital, to be fixed. These resources include buildings, machinery and other equipment that cannot be adjusted quickly or without significant cost. The short-run production function, denoted <math>q = f(\bar{K}, L)</math>, reflects this constraint: capital <math>\bar{K}</math> is a given quantity, while labour L can vary. Fixed costs in this period include capital-related expenses, such as rent or loan payments, which do not change regardless of the level of output. Variable costs, on the other hand, include items such as labour and raw materials, which can be adjusted according to the quantity produced.

Long term: In the long term, the company can adjust all its inputs, including capital. This gives it the flexibility to resize or completely restructure its operations in response to changes in demand, technological innovations or other external factors. The long-run production function, expressed as <math>q = f(K, L)</math>, shows that the firm can choose how much capital K and labour L it will use for production. At this point, distinctions between fixed and variable costs become less relevant, as all costs are considered variable in the long run.

A company's ability to move from short-term production to long-term planning is crucial to its long-term viability and growth. Long-term decisions can include investing in new equipment, expanding or downsizing facilities, or changing the business model to explore new markets or products. By understanding and planning for both horizons, companies can better navigate market conditions and maintain their competitiveness over the long term.

== Production costs in the short and long term ==

The distinction between fixed and variable costs is essential to understanding a company's decision-making in terms of production and investment over different time horizons.

Short term: In the short term, certain expenses cannot be changed quickly or without significant cost. These expenses, such as lease payments or equipment loans, are considered fixed costs because they do not change with the level of production. Physical capital, in this context, is often a fixed cost because the company cannot easily acquire or dispose of major capital assets to adjust production in the short term. Variable costs, on the other hand, can be adjusted more easily and include items such as raw materials and direct labour hours, which vary directly with the quantity produced.

Long-term: In the long term, the company has the flexibility to modify all its production capacities, including physical capital. This means that costs that were fixed in the short term become variable in the long term. Given enough time, companies can make strategic investments or divestments to increase or decrease their production capacity. This includes purchasing new equipment, expanding facilities, or even closing parts of the business. These decisions are guided by long-term cost considerations, where the aim is to align production capacity with anticipated demand and the company's overall strategy.

This ability to make fixed costs variable is fundamental to strategic planning and long-term competitiveness. It enables companies to adapt to changes in their business environment, such as fluctuations in demand, technological advances, and regulatory changes. By understanding these concepts, companies can better forecast their potential costs and benefits and adjust their strategies accordingly to maintain sustainable growth and profitability.

The nature of companies' cost functions varies considerably between the short term and the long term due to the flexibility of adjusting factors of production.

In the short run, the company operates with fixed factors, which means that it must optimise its production by adjusting only its variable factors. The short-run cost function is constrained by these fixed factors (such as equipment and facilities) which cannot be changed quickly or easily. As a result, the company may not be able to achieve the most economically efficient level of production if demand changes rapidly.

In the long term, however, all factors become variable. The company can invest in new technologies, increase or reduce the size of its facilities, and adjust the workforce to exactly match its production needs. This flexibility allows the company to achieve levels of efficiency that the short-term framework does not allow. The long-term cost function therefore offers a more fluid and dynamic view, reflecting the company's ability to adapt to market changes and optimise its production costs.

This implies that, in theory, production costs should be lower in the long term because the company can achieve economies of scale and benefit from better technologies or production methods. However, this also depends on the company's ability to manage these changes effectively and invest wisely so that long-term costs are reduced. Moreover, long-term investments are often accompanied by risks and uncertainties that can influence costs.

Long-term cost analysis is therefore a key element of business strategy, requiring careful planning and assessment of investment opportunities, as well as market conditions that may influence demand for the company's products.

== Average costs in the short and long term ==

Average costs, both short and long term, play a crucial role in a company's financial planning and strategy. However, they differ according to the period under consideration, due to the nature of fixed and variable costs.

Average Short-Term Costs: In the short term, certain costs are considered fixed. This means that regardless of the level of production, these costs do not change. Examples include rent, salaries of permanent employees, and equipment payments. Short-run average costs (SRA) are therefore affected by the amount of production:

* If output is low, average fixed costs (AFC) are high because they are spread over a small number of units. * As output increases, AFC per unit decreases because they are spread over more units. * Average variable costs (AVC) change with output, but to a lesser extent than fixed costs. * Short-run average total costs (SRAC) initially decrease with increasing output (taking advantage of economies of scale) but may increase after reaching the point of diminishing marginal returns.

Long Run Average Cost: In the long run, all costs are considered variable. A company can adjust its production capacity by changing the amount of physical capital and labour used. Long Run Average Costs (LRAAC) offer a more flexible perspective:

* Economies of scale can be achieved by increasing output, which reduces the long-run average cost up to a certain point * Constant returns to scale occur when increasing inputs lead to a proportional increase in output, thus keeping the average cost constant * Decreasing returns to scale occur when increasing inputs lead to a less than proportional increase in output, thus increasing the average cost.

The Long Run Average Cost (LRAEC) curve is often represented as the envelope of the various Short Run Average Cost (SRAEC) curves for various levels of production capacity. It shows the minimum average cost possible for each level of production if the company fully optimises all its inputs.

In practice, companies seek to produce where the long-run average cost is lowest, as this indicates the most efficient and profitable point of production. This is where a company can maximise profits, as it produces at the lowest possible average cost while having the flexibility to adjust to changes in demand over the long term.

[[Fichier:Coûts moyens dans le court et long terme 1.png|400px|vignette|centré]]

The graph shows a comparative analysis of average costs in the short and long term for a company as a function of production quantity. In the short term, we see three distinct curves representing average costs for plants of different sizes - small, medium and large. Each curve shows an average cost that decreases with increasing output up to a certain point, reflecting the economies of scale achieved when fixed costs are spread over an increasing number of units produced. However, after reaching the lowest point, average costs begin to rise again, illustrating diminishing marginal returns where additional costs are incurred for each additional unit produced, often due to over-utilisation of existing capacity or increased inefficiency.

The short-run average cost curve for the small plant reaches its minimum at a relatively low production level, indicating that small production quantities are optimal for such a configuration. The medium plant, with a larger capacity, reaches its lowest average cost point at a higher production level, suggesting that it can more efficiently produce a larger quantity before encountering diminishing marginal returns. The large plant, with the largest capacity, has the lowest average cost at an even higher level of production, indicating that it is best equipped to take advantage of economies of scale on a large scale.

In contrast, the curve in red, representing long-term average costs, is an envelope curve that lies below all the short-term average cost curves. This envelope curve reflects the flexibility of the company to adjust the size of its plant and optimise other factors of production over a longer period. It shows the lowest average cost achievable at each production level if the company perfectly adjusts its production capacity to the desired quantities. This curve also reaches a minimum, indicating the most efficient point of production in the long term, but unlike the short-term curves, it offers a broader perspective of the optimisation options available to the company, including the possibility of choosing between different plant sizes.

The analysis depicted in this graph highlights that companies tend to have greater flexibility and potentially lower costs in the long term, as they can adjust all factors of production, including capital. Decisions taken today with long-term commitments can define the future trajectory of production costs and, as a result, influence a company's competitiveness and profitability. Companies must therefore carefully evaluate their investment and production capacity decisions, taking into account demand forecasts and technological developments, to ensure that they can produce at the most efficient and profitable level possible.

== Economies of scale ==

Economies of scale refer to the reduction in long-run average costs when a company increases its production. The slope of the long-run average cost function (LRAC) is a key indicator of the presence of economies of scale.

If the slope of the LRAEC function is negative, this means that average costs fall as the quantity produced increases. This is the classic sign of economies of scale: producing more becomes less costly per unit because of increased efficiency, the amortisation of fixed costs over greater output, or the acquisition of inputs at lower costs through volume purchases.

When the slope of the CMLT function becomes positive, this indicates diseconomies of scale. This can occur when increased output leads to higher average costs, perhaps due to increased management complexity, exhaustion of efficiency benefits, or operational constraints.

Finally, if the slope of the CMLT function is zero, this means that the company is experiencing constant returns to scale. In this case, average costs do not change as output increases. Each additional unit costs the same to produce, indicating a direct proportionality between costs and output.

Understanding where their company stands in relation to these different phases of economies of scale is crucial for decision-makers. This allows them to plan expansions or adjustments in production capacity with an understanding of how these changes will affect their costs and competitiveness in the market. Economies of scale are often a driving force behind companies' growth strategies, as they can lead to significant competitive advantage.

[[Fichier:Fonction cm Economies d’échelle.png|400px|vignette|centré]]

This graph illustrates the concepts of economies of scale, constant returns to scale and diseconomies of scale through the relationship between average costs and quantity of production.

Three phases can be identified on the graph:

# Economies of scale: On the left-hand side of the graph, the average cost (AC) curve is decreasing, indicating that the increase in production leads to a decrease in average costs per unit. This is generally due to the more efficient distribution of fixed costs over an increasing number of units produced and to greater efficiency in the use of resources. Companies often benefit from economies of scale when they are in a growth phase or when they can purchase inputs at reduced rates through bulk orders. 
# Constant returns to scale : At the centre of the graph, the CM curve stabilises and the average cost per unit remains constant despite an increase in production. This suggests that the company has reached a level of production where the benefits of economies of scale have been fully realised and any further increase in production does not change the average cost. This can occur in situations where the company is operating at its optimum capacity. 
# Diseconomies of scale: On the right-hand side of the graph, the CM curve begins to rise, indicating that average costs per unit increase with additional production. This may be the result of overloaded production capacity, additional management costs, or increased operational complexity that makes production less efficient as scale increases.

The black dots on the curves probably indicate the minimum points of average costs for plants of different sizes, suggesting that each type of plant has an optimal amount of production. The shift from one curve to the other reflects changes in production capacity that could be achieved through long-term investment, allowing the company to move to a higher level of efficient production with a lower average cost.

This graph is a valuable tool for decision-making on investment and production capacity. It highlights the importance for companies to understand not only where they are currently on the average cost curve, but also to predict how changes in production capacity may affect their costs in the future. Companies should aim to operate where they can minimise average costs to maximise profits, while remaining alert to the risks of diseconomies of scale.

== Marginal returns vs. returns to scale ==

=== Marginal returns vs. returns to scale ===

It is crucial not to confuse marginal return with returns to scale, as they apply to different contexts and have distinct implications for production decision-making.

Marginal return, often associated with the law of diminishing marginal returns, refers to the impact of adding an extra unit of a single factor of production, holding all other factors constant. This is a short-term observation because it examines the immediate and direct effect of increasing a single input on total output. In practice, this can be illustrated by adding an extra worker to a factory where equipment and space are fixed constraints. Initially, adding workers can significantly increase output, but as more workers are added, each will contribute less and less to total output due to space and equipment constraints.

On the other hand, returns to scale examine how the proportional variation of all inputs together affects output. This reflects a long-term perspective where the company has the ability to change its production structure, including the size of its facilities, the amount of machinery and the number of employees. Economies of scale occur when doubling all inputs increases output by more than double. Constant returns to scale mean that output increases in the same proportion as inputs, and diminishing returns to scale occur when output increases by less than the proportion by which inputs increase.

Understanding these differences is fundamental for companies when making strategic decisions. In the short term, cost optimisation may involve fine-tuning variable inputs to obtain the best marginal return. In the long term, the company needs to consider investments that can change the overall cost structure and production capacity, and so influence returns to scale. These long-term strategic decisions are essential for sustainable growth and market competitiveness.

=== increasing returns to scale ====

Economies of scale, often associated with increasing returns to scale, are a phenomenon observed when companies increase their production and see their average costs fall as a result. This concept is rooted in several operational and organisational aspects of a company as it expands. In a large factory, for example, it is possible to combine different tasks which, in smaller facilities, would be dispersed and managed less efficiently. This consolidation of tasks can lead to significant efficiency gains.

In addition, a large-scale plant offers the opportunity for greater specialisation of both labour and capital. Workers can concentrate on specific tasks, honing their skills and expertise through repetition and focus on a particular aspect of the production process. This specialisation can lead to an increase in productivity per worker. At the same time, capital can also become more specialised. Equipment and machinery designed for specific functions can be used to optimum effect, increasing capital productivity.

Another advantage of large-scale production is a company's ability to invest in highly skilled labour and advanced technologies. While these investments may be costly and not justified for a small operation, a company operating on a larger scale can spread these costs over a larger output, thereby reducing average costs. In addition, larger companies can often get better prices for their purchases because of bulk orders, and they have a greater ability to invest in research and development, which can lead to innovations that further reduce costs in the long term.

However, it is crucial to bear in mind that these benefits are not unlimited. As companies become too large, they may face diseconomies of scale, such as management difficulties, communication problems and less effective coordination, which can ultimately lead to higher average costs. So, although economies of scale can offer considerable benefits, companies need to carefully assess how far they can grow before the additional management and operating costs start to outweigh the benefits of larger-scale production.

=== diminishing returns to scale ====

Diseconomies of scale occur when, unlike economies of scale, a company's average costs increase as the quantity of production increases. This phenomenon is generally associated with diminishing returns to scale and can be attributed to several factors linked to the growth of the company.

As a plant reaches and exceeds a certain size, the integration and co-ordination of activities can become increasingly complex. Effectively managing a large workforce and harmonising numerous production lines can prove problematic. These operational difficulties can lead to increasing inefficiencies, as communication becomes more cumbersome and processes more error-prone. As a result, the benefits of increasing size can be outweighed, if not outweighed, by these new challenges.

Employee motivation and commitment can also be affected in a large company. In smaller structures, employees may feel more invested and have a clear understanding of the impact of their work on the company's results. However, in a large-scale environment, the sense of personal contribution can diminish, which can lead to lower productivity and overall effectiveness.

In addition, management systems may not evolve at the same pace as the size of the company. Management structures that worked well in a small or medium-sized business may become 'fixed factors' in a large company, limiting its ability to adapt and respond effectively to its growing operational needs. Like physical capital, management may need to be resized or restructured to effectively manage a larger organisation.

Diseconomies of scale illustrate that there is an optimal size for companies, beyond which increasing production can actually reduce efficiency and increase costs. That's why companies need to constantly evaluate their operational performance and remain agile, even as they grow, to avoid the pitfalls of diseconomies of scale.

= Summary =

The fundamental objective of a business is to maximise its profit, which is the difference between its total revenues and its total costs. To achieve this, a firm must not only cover its explicit costs, such as expenditure on raw materials, wages and rents, but also take into account its implicit costs. The latter represent the opportunity costs associated with production, such as the potential returns from alternative investments or the salary that the entrepreneur could earn elsewhere.

The total cost of a business is directly related to its production function, which describes the relationship between the quantities of inputs used and the quantity of output produced. Typically, the production function shows a phase of decreasing marginal productivity, meaning that beyond a certain point, each addition of a factor of production produces less additional output than the previous one. This is often due to capacity constraints or less efficient use of resources as the scale of production increases.

Company costs are divided into fixed costs, which remain constant whatever the quantity produced, and variable costs, which vary with output. Fixed costs can include expenses such as rent and wages for permanent employees, while variable costs can include costs related to raw materials and labour directly assigned to production.

Average cost, which is the total cost divided by the number of units produced, gives a measure of cost per unit. Marginal cost, on the other hand, indicates how much it costs to produce an additional unit. In many cases, marginal cost increases with the quantity produced, especially after a certain level of production has been reached. This increase is generally attributed to decreasing marginal productivity.

The behaviour of average cost and marginal cost is such that average cost follows a U-shaped curve. It initially falls as output increases, due to economies of scale and the spread of fixed costs over a greater number of units, but then starts to rise as diseconomies of scale take hold. The marginal cost curve intersects the average cost curve at the point where the average cost is lowest, which is known as the minimum efficient scale point.

As far as the time horizon is concerned, a company's cost structure varies between the short and long term. Many costs considered fixed in the short term, such as plant and equipment, can become variable in the long term, as the company then has the opportunity to adjust these factors according to its production decisions. This gives the company greater flexibility to optimise its cost structure and therefore its long-term profit potential. A company's ability to adapt and revise its factors of production over the long term is crucial to its ability to maintain sustainable growth and respond effectively to changes in the market.

= Appendices =

= References =

<references/>

[[Catégorie:Économie]]
[[Catégorie:Microéconomie]]
[[Catégorie:Federica Sbergami]]
[[Catégorie:Giovanni Ferro-Luzzi]]
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