FundEcon 2024WS25 Chapter 6 Presentation PDF

6 Behind the Supply Curve Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 1 6.1 Learning Outcomes 1. You understand the concept of the production function. 2. You understand the difference between fixed and variable production factors. You are aware of the impo...

6 Behind the Supply Curve Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 1 6.1 Learning Outcomes 1. You understand the concept of the production function. 2. You understand the difference between fixed and variable production factors. You are aware of the importance of the planning horizon for the differentiation between both types of production factors. 3. You understand the concept of the cost curve and the associated marginal cost curve as well as the average cost curves. 4. You understand the concepts of scale effects and returns to scale. 5. You know the characteristics of a perfectly competitive market. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 2 6.1 Learning Outcomes 6. You are able to determine the profit-maximising output of a price- taking firm. 7. You understand the meaning and relevance of the break-even price and the shut-down price. 8. You understand the difference and relationship between the short-run and the long-run supply curves. 9. You understand what determines the short-run and the long-run industry supply curve. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 3 6.2 Firms´ Goal: Profit Maximisation The goal of a company is to maximise profits. All actions in the firm are subordinated to this goal, including the supply decision. The profit (𝜋𝜋) is formed by Sales/Revenue (𝑇𝑇𝑇𝑇) and Cost (𝑇𝑇𝑇𝑇) and is defined as follows: 𝜋𝜋 = 𝑇𝑇𝑇𝑇 − 𝑇𝑇𝑇𝑇 This should never be forgotten in all the detailed and lengthy derivations below. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 4 6.3 The Production Function A firm is an organization that produces goods and services for sale. In order to fulfill this task, the firm must transform inputs into output. The output (𝑞𝑞) depends on the quantities 𝑥𝑥1 , … , 𝑥𝑥𝑛𝑛 of the inputs/production factors (1, … , 𝑛𝑛) used. The relationship between output and inputs is called a firm´s production function (𝑇𝑇𝑇𝑇): 𝑇𝑇𝑇𝑇 = 𝑞𝑞 𝑥𝑥1 , … , 𝑥𝑥𝑛𝑛 This production function is the base of a firm´s cost functions. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 5 6.3.1 Inputs and Output Classification of inputs: A production factor can again and again generate income from the sale of its output. Thus, it represents a permanent source of income. Examples are: land (provided by nature) labour (provided by people) capital: Asset used by a company to produce its output (physical) capital: consists of produced resources such as buildings or machines human capital: the improvement in the workforce resulting from education, knowledge and experience and linked to employees/workers In contrast, other input factors are consumed by the use in the production process (e.g. energy). Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 6 6.3.1 Inputs and Output The importance of human capital has increased significantly due to technical progress, because this means that a high level of technical skills is indispensable in many areas. It is therefore one of the reasons for the increasing premiums that accrue to employees with higher educational qualifications. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 7 6.3.1 Inputs and Output There are two types of inputs or production factors: Fixed production factors: Quantity is fixed and does not depend on the level of output. Variable production factors: The amount used can be changed by the firm and depends on the output level. In reality, the answer to the question of whether a production factor is fixed or variable depends ONLY on the planning horizon: In the long term, firms can adapt any type of input. Therefore, there are no fixed production factors in the long term. However, this is not possible in the short term. Therefore, there are only short-term fixed production factors. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 8 6.3.1 Inputs and Output The production function is also called the total product function (𝑇𝑇𝑇𝑇) because it indicates the entire production (depending on the use of the variable production factor(s). This production function 𝑇𝑇𝑇𝑇 = 𝑞𝑞 𝑥𝑥1 , … , 𝑥𝑥𝑛𝑛 , which depends on the 𝑛𝑛 production factors, can be represented graphically in a (𝑛𝑛 + 1)- dimensional space. Since this is not possible on the two-dimensional paper or computer screen, the production function is often just shown as a function of one production factor, e.g. the 𝑖𝑖-th, where the other 𝑛𝑛 − 1 production factors are assumed to be constant (ceteris paribus analysis), i.e. 𝑇𝑇𝑇𝑇 = 𝑞𝑞 𝑥𝑥̅1 , … , 𝑥𝑥̅𝑖𝑖−1 , 𝑥𝑥𝑖𝑖 , 𝑥𝑥̅𝑖𝑖+1 , … , 𝑥𝑥̅𝑛𝑛. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 9 6.3.1 Inputs and Output Graph of a typical production function 𝑇𝑇𝑇𝑇 = 𝑞𝑞 𝑥𝑥̅1 , … , 𝑥𝑥̅𝑖𝑖−1 , 𝑥𝑥𝑖𝑖 , 𝑥𝑥̅𝑖𝑖+1 , … , 𝑥𝑥̅𝑛𝑛 : Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 10 6.3.1 Inputs and Output Characteristic properties of a production function (I): The production function always increases in the use of its variable production factors, e.g. the 𝑖𝑖-th production factor. The slope of the production function can be determined using the first derivative: 𝑑𝑑𝑑𝑑 This is positive, i.e. 𝑀𝑀𝑀𝑀𝑖𝑖 = > 0, 𝑑𝑑𝑥𝑥𝑖𝑖 but becomes smaller and smaller as the amount of factor input 𝑥𝑥𝑖𝑖 increases. The first derivative of the production function with respect to the 𝑖𝑖-th production factor is called the marginal product function of the 𝑖𝑖-th production factor 𝑀𝑀𝑀𝑀𝑖𝑖. The marginal product function indicates how much additional output can be achieved (ceteris paribus) if the 𝑖𝑖-th input is increased by one unit. Examples: marginal product of labor Marginal product of capital Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 11 6.3.1 Inputs and Output Characteristic properties of a production function (II): Graph of a marginal-product function 𝑀𝑀𝑀𝑀: Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 12 6.3.1 Inputs and Output Characteristic properties of a production function (III): The slope of the production function decreases over the course of the function, i.e. it is concave. This means that each additional unit of input increases output by less than the previous one. Thus, there is a decreasing marginal product of the underlying production factor. This can be done mathematically 𝑑𝑑𝑀𝑀𝑀𝑀𝑖𝑖 via the first derivative of the marginal product function (which measures the 𝑑𝑑𝑥𝑥𝑖𝑖 change in the marginal product) or 𝑑𝑑 2 𝑞𝑞 the second derivative of the production function : 𝑑𝑑𝑥𝑥𝑖𝑖2 𝑑𝑑𝑀𝑀𝑀𝑀𝑖𝑖 𝑑𝑑 2 𝑞𝑞 = 0 and 𝑏𝑏 < 0 The other cost functions can be derived from this (see next page). Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 37 6.5 Realistic Cost Functions Other for the following analysis important cost functions can be derived from a general s-shaped cost function: Variable cost function: 𝑉𝑉𝑉𝑉 𝑞𝑞 = 𝑎𝑎𝑞𝑞 3 + 𝑏𝑏𝑞𝑞 2 + 𝑐𝑐𝑐𝑐 Fixed cost function: 𝐹𝐹𝐹𝐹 𝑞𝑞 = 𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑 𝑞𝑞 Marginal cost function: 𝑀𝑀𝑀𝑀 𝑞𝑞 = 𝑇𝑇𝑇𝑇 ′ 𝑞𝑞 = = 3𝑎𝑎𝑞𝑞 2 + 2𝑏𝑏𝑞𝑞 + 𝑐𝑐 𝑑𝑑𝑑𝑑 𝑇𝑇𝑇𝑇 𝑞𝑞 𝑑𝑑 Average total cost function: 𝐴𝐴𝐴𝐴𝐴𝐴 𝑞𝑞 = = 𝑎𝑎𝑞𝑞 2 + 𝑏𝑏𝑏𝑏 + 𝑐𝑐 + 𝑞𝑞 𝑞𝑞 𝑉𝑉𝑉𝑉 𝑞𝑞 Average variable cost function: 𝐴𝐴𝐴𝐴𝐴𝐴 𝑞𝑞 = = 𝑎𝑎𝑞𝑞 2 + 𝑏𝑏𝑏𝑏 + 𝑐𝑐 𝑞𝑞 𝐹𝐹𝐹𝐹 𝑞𝑞 𝑑𝑑 Average fixed cost function: 𝐴𝐴𝐴𝐴𝐴𝐴 𝑞𝑞 = = 𝑞𝑞 𝑞𝑞 Please note: Average costs, unit costs and costs per unit are synonyms! Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 38 6.6 Scale Effects and Returns to Scale The term scale always refers to the production quantity 𝑞𝑞. Scale effects are about how changes in output affect costs. There are two types: Internal scale effects: Internal scale effects occur when changes in output of a firm have an impact on the firm´s own costs. External scale effects: External scale effects occur when changes in output of a whole industry affect a firm´s own costs (e.g. agglomeration effects like in Silicon Valley). Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 39 6.6 Scale Effects and Returns to Scale Internal economies of scale are concerned with returns to scale. There are three different types of returns to scale (I): Increasing returns to scale: These occur when the next unit has a lower cost than the previous units, i.e. 𝑀𝑀𝑀𝑀(𝑞𝑞) < 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). This is the case to the left of the minimum average cost 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). Increasing returns to scale are often the result of increasing specialization, which allows higher levels of production. Individual workers can focus more on specialized tasks, allowing them to gain greater skill at those tasks and complete them more efficiently. Increasing returns to scale therefore create incentives for firms to grow. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 40 6.6 Scale Effects and Returns to Scale There are three different types or returns to scale (II): Diminishing returns to scale/decreasing returns to scale: These occur when the next unit has a higher cost than the previous units, i.e. 𝑀𝑀𝑀𝑀(𝑞𝑞) > 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). This is the case to the right of the minimum average cost 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). Decreasing returns to scale typically occur in large companies due to coordination and communication problems: As the size of the company increases, it becomes increasingly difficult and therefore more expensive to communicate and organise activities. Decreasing returns to scale therefore tend to limit the size of a company. With a given technology, firms should no longer grow, but rather shrink. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 41 6.6 Scale Effects and Returns to Scale There are three different types of returns to scale (III): Constant returns to scale: These occur when the next unit costs the same as the previous units, i.e. 𝑀𝑀𝑀𝑀(𝑞𝑞) = 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). This is the case at the minimum average cost 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 42 6.6 Scale Effects and Returns to Scale The returns to scale can be measured using the output elasticity of cost 𝜀𝜀𝑇𝑇𝑇𝑇,𝑞𝑞 : ∆𝑇𝑇𝑇𝑇 ∆𝑇𝑇𝑇𝑇 𝑞𝑞 as arc elasticity: 𝜀𝜀𝑇𝑇𝐶𝐶,𝑞𝑞 = 𝑇𝑇𝑇𝑇 ∆𝑞𝑞 = ∆𝑞𝑞 𝑇𝑇𝑇𝑇 𝑞𝑞 𝑑𝑑𝑑𝑑𝐶𝐶 𝑞𝑞 1 𝑀𝑀𝑀𝑀 as point elasticity: 𝜀𝜀𝑇𝑇𝐶𝐶,𝑞𝑞 = = 𝑀𝑀𝑀𝑀 = 𝑑𝑑𝑑𝑑 𝑇𝑇𝑇𝑇 𝐴𝐴𝐴𝐴𝐴𝐴 𝐴𝐴𝐴𝐴𝐴𝐴 The output elasticity of costs 𝜀𝜀𝑇𝑇𝑇𝑇,𝑞𝑞 measures, by what percentage the costs 𝑇𝑇𝑇𝑇(𝑞𝑞) change if the output 𝑞𝑞 increases by 1 % 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑜𝑜𝑜𝑜 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑇𝑇𝑇𝑇 𝑞𝑞 percent 𝜀𝜀𝑇𝑇𝑇𝑇,𝑞𝑞 =. % 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑜𝑜𝑜𝑜 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑞𝑞 Or in general: It represents cost changes as a result of changes in output (each measured in percent). The output elasticity of cost is also called the elasticity of scale/scale elasticity. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 43 6.6 Scale Effects and Returns to Scale Please note (I): 1. Fixed-cost degression is not responsible for increasing returns to scale! Or better, only to a small extent: This can be seen by the fact that by increasing output 𝑞𝑞 from the first unit on you always have 𝐹𝐹𝐹𝐹 decreasing unit fixed cost 𝐴𝐴𝐴𝐴𝐴𝐴 = ; 𝑞𝑞 However, an s-shaped cost function starts with increasing returns to scale, but from a certain output 𝑞𝑞 on there will always be decreasing returns to scale. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 44 6.6 Scale Effects and Returns to Scale Please note (II): 2. Marginal cost is only identical with unit variable cost if the underlying cost function is linear! s-shaped cost function linear cost function 𝑇𝑇𝑇𝑇 𝑞𝑞 = 𝑎𝑎𝑞𝑞 3 + 𝑏𝑏𝑞𝑞 2 + 𝑐𝑐𝑐𝑐 + 𝑑𝑑 𝑇𝑇𝑇𝑇 𝑞𝑞 = 𝑐𝑐𝑐𝑐 + 𝑑𝑑 𝐴𝐴𝐴𝐴𝐴𝐴 𝑞𝑞 = 𝑎𝑎𝑞𝑞 2 + 𝑏𝑏𝑏𝑏 + 𝑐𝑐 𝐴𝐴𝐴𝐴𝐴𝐴 𝑞𝑞 = 𝑐𝑐 𝑀𝑀𝑀𝑀 𝑞𝑞 = 3𝑎𝑎𝑞𝑞 2 + 2𝑏𝑏𝑏𝑏 + 𝑐𝑐 𝑀𝑀𝑀𝑀 𝑞𝑞 = c 𝑴𝑴𝑴𝑴 𝒒𝒒 ≠ 𝑨𝑨𝑨𝑨𝑨𝑨 𝒒𝒒 𝑀𝑀𝑀𝑀 𝑞𝑞 = 𝐴𝐴𝐴𝐴𝐴𝐴 𝑞𝑞 Thus, in general marginal cost is not identical with unit variable cost! Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 45 6.6 Scale Effects and Returns to Scale Tasks (I): 1. The following s-shaped cost function is given: 𝑇𝑇𝑇𝑇 𝑞𝑞 = 2𝑞𝑞 3 − 4𝑞𝑞2 + 3𝑞𝑞 + 500 a) Calculate the following cost functions: Variable cost function 𝑉𝑉𝑉𝑉(𝑞𝑞) Fixed cost function 𝐹𝐹𝐹𝐹 Marginal cost function 𝑀𝑀𝑀𝑀(𝑞𝑞) Average total cost function 𝐴𝐴𝑇𝑇𝐶𝐶(𝑞𝑞) Average variable cost function 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞) Average fixed cost function 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞) b) Calculate the scale elasticity for the output levels 𝑞𝑞1 = 1 and 𝑞𝑞2 = 10. c) Give an economic interpretation of the values of the scale elasticity. d) Which types of returns to scale do you find at the two output levels? Explain your answers. e) Which firm strategies concerning output do you deduct from the returns to scale? Explain your answers. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 46 6.6 Scale Effects and Returns to Scale Tasks (II): 2. Think about different cost functions and their implications: a) What types of returns to scale can you find in a s-shaped cost function? What does this mean for the firm´s strategy regarding the level of output? b) What types of returns to scale can you find in a linear cost function? What does this mean for the firm´s strategy regarding the level of output? c) Show the fixed cost degression effect for a s-shaped cost function. d) Show the fixed cost degression effect for a linear cost function. e) How do the two fixed cost degression effects differ and why? Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 47 6.7 Perfect Competition and the Supply Function In this section we will derive a firm´s supply function and the market supply function under the assumption of perfect competition. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 48 6.7.1 Perfect Competition Short recap: Assumptions of the market structure of perfect competition (I): atomistic market structure: (infinitely) large number of firms intense competition each company only has a tiny market share no market power price takers (infinitely) large number of consumers no market power price takers In relation to the market size, the firms and consumers are (infinitely) small. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 49 6.7.1 Perfect Competition Short recap: Assumptions of the market structure of perfect competition (II): Homogeneous goods are traded. There are no barriers to entry or barriers to exit the market. There is perfect information, i.e. complete transparency in the market. All market participants react infinitely quickly to all kinds of changes. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 50 6.7.2 Profit Analysis The goal of a firm is profit maximisation. The profit 𝜋𝜋(𝑞𝑞) consists of sales/revenue 𝑇𝑇𝑇𝑇(𝑞𝑞) and costs 𝑇𝑇𝑇𝑇(𝑞𝑞): 𝜋𝜋(𝑞𝑞) = 𝑇𝑇𝑇𝑇(𝑞𝑞) − 𝑇𝑇𝑇𝑇(𝑞𝑞) Mathematically, the maximum profit is calculated by differentiating the profit function twice with respect to output (companies are price takers!). The following applies: Necessary condition for a profit maximum: first derivative equals zero Sufficient condition for a profit maximum: second derivative is negative (i.e. the profit function is concave in the area of the maximum) Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 51 6.7.2 Profit Analysis General calculation of the profit maximum (I): Necessary condition: 𝑑𝑑𝜋𝜋 𝑞𝑞 𝑑𝑑𝑑𝑑𝑑𝑑 𝑞𝑞 𝑑𝑑𝑑𝑑𝑑𝑑 𝑞𝑞 = − = 𝑀𝑀𝑀𝑀 𝑞𝑞 − 𝑀𝑀𝑀𝑀 𝑞𝑞 = 0 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 ⇔ 𝑀𝑀𝑀𝑀 𝑞𝑞 = 𝑀𝑀𝑀𝑀(𝑞𝑞) where 𝑀𝑀𝑀𝑀(𝑞𝑞) represents the marginal revenue, i.e. the additional revenue/sales for an additional unit of output. This necessary condition for a profit maximum is also called the optimal output rule: Profit is maximised when the quantity is produced at which the additional revenue from the last unit exactly covers the additional costs caused by this last unit. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 52 6.7.2 Profit Analysis General calculation of the profit maximum (II): In order to ensure that you are in a profit maximum, it is still necessary to observe the sufficient condition: 𝑑𝑑2 𝜋𝜋 𝑑𝑑𝑑𝑑𝑑𝑑 𝑞𝑞 𝑑𝑑𝑑𝑑𝑑𝑑 𝑞𝑞 = − 0, i.e. 𝑇𝑇𝑇𝑇 𝑞𝑞 > 𝑇𝑇𝑇𝑇 𝑞𝑞 : If the intersection of the 𝐴𝐴𝐴𝐴𝐴𝐴 function with the 𝑀𝑀𝑀𝑀 function is below price 𝑝𝑝1 , the company earns a positive profit. In this case, at the profit-maximizing output 𝑞𝑞1 the contribution margin per unit 𝑝𝑝1 − 𝐴𝐴𝐴𝐴𝐴𝐴1 is positive, the unit costs 𝐴𝐴𝐴𝐴𝐴𝐴1 are smaller than the price 𝑝𝑝1 , resulting in a positive unit profit 𝑝𝑝1 − 𝐴𝐴𝐴𝐴𝐴𝐴1 and thus also in a positive overall profit (red shaded area). Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 58 6.7.2 Profit Analysis In principle, three profit situations are possible for a firm (II): 2. Negative profit 𝜋𝜋 < 0, i.e. 𝑇𝑇𝑇𝑇 𝑞𝑞 < 𝑇𝑇𝑇𝑇 𝑞𝑞 : If the intersection of the 𝐴𝐴𝐴𝐴𝐴𝐴 function with the 𝑀𝑀𝑀𝑀 function is above price 𝑝𝑝2 , the company earns a negative profit. In this case, at the profit-maximizing output 𝑞𝑞2 the contribution margin per unit 𝑝𝑝2 − 𝐴𝐴𝐴𝐴𝐴𝐴2 is negative, the unit costs 𝐴𝐴𝐴𝐴𝐴𝐴2 are larger than the price 𝑝𝑝2 , resulting in a negative unit profit 𝑝𝑝2 − 𝐴𝐴𝐴𝐴𝐴𝐴2 and thus also in a negative overall profit (red shaded area). Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 59 6.7.2 Profit Analysis In principle, three profit situations are possible for a firm (II): 3. Profit 𝜋𝜋 = 0, i.e. 𝑇𝑇𝑇𝑇 𝑞𝑞 = 𝑇𝑇𝑇𝑇 𝑞𝑞 : If the intersection of the 𝐴𝐴𝐴𝐴𝐴𝐴 function with the 𝑀𝑀𝑀𝑀 function is on the 𝑝𝑝3 price line, the company earns zero profit. In this case, at the profit-maximizing output 𝑞𝑞3 the contribution margin per unit 𝑝𝑝3 − 𝐴𝐴𝐴𝐴𝐴𝐴3 is positive, the unit costs 𝐴𝐴𝐴𝐴𝐴𝐴3 correspond to price 𝑝𝑝3 , resulting in a zero unit profit and thus also in a zero overall profit. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 60 6.7.3 Production Decision The following will analyse whether a firm should produce depending on its profit situation. At first glance, one might think that a firm with negative profits should not produce. However, this has to be viewed with more sophistication. The reason for this is that the total costs also include fixed cost, which do not depend on the quantity produced. The illustration on the following page helps to explain this point. Two definitions of terms are important for the following analysis: The price at the minimum of the average total cost 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞) is also called the break-even price 𝑝𝑝𝐵𝐵𝐵𝐵. The price at the minimum average variable cost 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞) is also called the shut-down price 𝑝𝑝𝑆𝑆. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 61 6.7.3 Production Decision Basic figure for analysing firms´ production decisions: The average fixed cost 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞) can be identified as the difference between average total cost 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞) and average variable cost 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 62 6.7.3 Production Decision A firm´s production decision depends on its cost situation and the market price (I): 1. Price below the minimum average variable cost (I): Graph: Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 63 6.7.3 Production Decision A firm´s production decision depends on its cost situation and the market price (II): 1. Price below the minimum average variable cost (II): Costs that must in any case be covered by the price/revenue per unit 𝑝𝑝 are the variable unit costs 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). In this case, this condition is violated. The price per unit does not even cover the variable unit costs of production 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞), not to mention (part of the) unit fixed costs 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). In this case, the following applies: The firm makes a loss (red shaded area; 𝜋𝜋 < 0). The contribution margin per unit 𝑝𝑝2 − 𝐴𝐴𝐴𝐴𝐴𝐴2 is negative. The firm should not produce. If there is no prospect of higher prices, the firm should exit the market as quickly as possible. That´s why the price at the intersection between the 𝑀𝑀𝑀𝑀 and 𝐴𝐴𝐴𝐴𝐴𝐴 curve is also called the shut-down price 𝑝𝑝𝑆𝑆. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 64 6.7.3 Production Decision A firm´s production decision depends on its cost situation and the market price (III): 2. Price between the minimum of the average variable cost and the minimum of the average total cost (I): Graph: Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 65 6.7.3 Production Decision A firm´s production decision depends on its cost situation and the market price (IV): 2. Price between the minimum of the average variable cost and the minimum of the average total cost (II): This means that the price/revenue per unit covers the variable unit costs of production 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞) as well as a part of the average fixed costs 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞). In this case, the following applies: The firm makes a loss (red shaded area; 𝜋𝜋 < 0). The contribution margin per unit 𝑝𝑝4 − 𝐴𝐴𝐴𝐴𝐴𝐴4 is positive. The firm should produce in the short run because its loss when producing is lower than when not producing due to the partial coverage of fixed costs. If there is no prospect of higher prices, the company should exit the market in the long run. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 66 6.7.3 Production Decision A firm´s production decision depends on its cost situation and the market price (V): 3. Price above the minimum average total cost (I): Graph: Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 67 6.7.3 Production Decision A firm´s production decision depends on its cost situation and the market price (VI): 3. Price above the minimum average total cost (II): This means that the price/revenue per unit covers the variable costs of production 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞) as well as the total average fixed costs 𝐴𝐴𝐴𝐴𝐴𝐴(𝑞𝑞) and beyond. In this case, the following applies: The firm makes a positive profit (red shaded area; 𝜋𝜋 > 0). The contribution margin per unit 𝑝𝑝1 − 𝐴𝐴𝐴𝐴𝐴𝐴1 is positive. The company should produce in the short and long run. That´s why the price at the intersection between the 𝑀𝑀𝑀𝑀 and 𝐴𝐴𝐴𝐴𝐴𝐴 curve is also called the break-even price 𝑝𝑝𝐵𝐵𝐵𝐵. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 68 6.7.3 Production Decision A firm´s production decision depends on its cost situation and the market price (VII): 4. Conclusion: The level of the contribution margin shows whether a company should produce in the short term. The Profit situation indicates whether a company should produce in the long term. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 69 6.7.4 Short-run Individual Supply Function of a Firm From the above reasoning, the short-run individual supply function of a firm can be determined (I): The intersection points between price and marginal costs define the quantity supplied in accordance with the optimal output rule. These intersection points are always found on the 𝑀𝑀𝑀𝑀 function. Therefore, the points of the 𝑀𝑀𝑀𝑀 function represent the individual short-run supply function 𝑆𝑆𝑖𝑖 of firm 𝑖𝑖. All points that are equal to or above the shut-down price 𝑝𝑝𝑆𝑆 are relevant for production. No production or supply applies to prices below. The short-run individual supply function shows how the profit-maximizing output depends on the market price. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 70 6.7.4 Short-run Individual Supply Function of a Firm From the above reasoning, the short-run individual supply function of a firm can be determined (II): Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 71 6.7.4 Short-run Individual Supply Function of a Firm Task: The following s-shaped cost function is given (with 𝑞𝑞 ≥ 0): 𝑇𝑇𝑇𝑇 𝑞𝑞 = 𝑞𝑞 3 − 17𝑞𝑞2 + 114𝑞𝑞 + 72 a. Determine the functions of variable cost, fixed cost, marginal cost, as well as variable, fixed, and total unit costs. b. Determine the minima of marginal cost, variable unit cost, and total unit cost. c. Determine the intersection of marginal cost and variable unit cost. d. Determine the firm´s individual supply function. e. Given a market price for the produced good of 𝑝𝑝 = 60, determine the profit-maximising output. f. What are the unit profit, the total profit and the contribution margin when producing the profit-maximising output. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 72 6.7.5 Short-run Industry Supply Function The final step in the supply analysis is from the individual supply function to the industry supply function or market supply function. The latter indicates the relationship between price and output volume of the industry/market under consideration. So far, we have referred to it as the supply function 𝑆𝑆. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 73 6.7.5 Short-run Industry Supply Function A distinction can be made here between short-run and long-run market supply or equilibrium. In the short run, the number of firms in an industry is given. There are no market entries and exits. In this scenario, the short-run market supply function arises. In the long run, the number of firms in an industry is variable. Market entries and exits depend on the profit situation: If profits are positive, market entries occur. If profits are negative, market exits occur. In this scenario, the long-run market supply function arises. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 74 6.7.5 Short-run Industry Supply Function Derivation of the short-run market supply function: The short-run industry supply function is obtained by horizontally adding all the short-run individual supply functions (three in this example: 𝑆𝑆𝑖𝑖𝑖 , 𝑆𝑆𝑖𝑖𝑖 , 𝑆𝑆𝑖𝑖𝑖 ) of the existing producers. As a result, the industry supply function 𝑆𝑆 (using the same scale) is flatter and further to the right than the individual supply functions. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 75 6.7.5 Short-run Industry Supply Function The short-run market equilibrium then lies at the intersection of the short-run market supply function 𝑆𝑆 with the market demand function 𝐷𝐷: Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 76 6.7.6 Long-run Industry Supply Function Derivation of the long-run market supply function (I): In addition to the companies currently on the market, there are usually additional potential competitors. When will these potential competitors enter the market? Whenever a positive profit can be realized in the market, i.e. when the market price is above the break-even price 𝑝𝑝1 > 𝑝𝑝𝐵𝐵𝐵𝐵. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 77 6.7.6 Long-run Industry Supply Function Derivation of the long-run market supply function (II): If more firms then enter the market, the quantity supplied will increase at any given price (I): This has the effect of a shift to the right of the short-run industry supply function (𝑆𝑆1 → 𝑆𝑆2 → 𝑆𝑆3 ; see right-hand graph on the next page). Due to the higher quantity supplied, the equilibrium price falls (𝑝𝑝1 → 𝑝𝑝2 → 𝑝𝑝𝐵𝐵𝐵𝐵 ; see right-hand graph on the next page). The companies already in the market reduce their individual outputs (𝑞𝑞1 → 𝑞𝑞2 → 𝑞𝑞3 ; see left-hand graph on the next page) due to the price decline. The quantity traded in the market will increase at the same time (𝑞𝑞𝑀𝑀𝑀 → 𝑞𝑞𝑀𝑀𝑀 → 𝑞𝑞𝑀𝑀𝑀 ; see right-hand graph on the next page). Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 78 6.7.6 Long-run Industry Supply Function Derivation of the long-run market supply function (III): If more producers then enter the market, the quantity supplied will increase at any given price (II): These market entries only come to an end when the market price has fallen to the break-even price 𝑝𝑝𝐵𝐵𝐵𝐵. Then long-run market equilibrium is reached. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 79 6.7.6 Long-run Industry Supply Function Derivation of the long-run market supply function (IV): For a better understanding of the difference between the short-run and the long-run equilibrium, the effect of an increase in demand is analysed for an industry with free market entry, which is originally in long-term equilibrium, i.e. 𝑝𝑝 = 𝑝𝑝𝐵𝐵𝐵𝐵. This means there is a positive demand shock. The demand curve shifts to the right (𝐷𝐷1 → 𝐷𝐷2 ; see right-hand graph on the next page). Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 80 6.7.6 Long-run Industry Supply Function Derivation of the long-run market supply function (V): Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 81 6.7.6 Long-run Industry Supply Function Derivation of the long-run market supply function (VI): The rightward shift of the demand curve has the following effects: Effects of the positive demand shock (green arrows): The new short-run equilibrium is at the intersection of the new demand function with the short-run supply function (see top of the right-hand graph on the previous page). This increases the market price from 𝑝𝑝𝐵𝐵𝐵𝐵 to 𝑝𝑝.̂ There are positive profits for existing producers. Effects of market entry (red arrows): This leads to market entries of additional firms as long as they can earn positive profits. The short-run supply curve shifts to the right (𝑆𝑆1 → 𝑆𝑆2 ; see right-hand graph on the previous page). The new intersection point between the new demand and new supply curves is at the original price level 𝑝𝑝𝐵𝐵𝐵𝐵. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 82 6.7.6 Long-run Industry Supply Function Derivation of the long-run market supply function (VII): With perfect competition, this results in a long-run industry supply function 𝑆𝑆𝐿𝐿𝐿𝐿 , a horizontal function at the level of the break-even price 𝑝𝑝𝐵𝐵𝐵𝐵. It shows how the quantity supplied by the industry responds to price when firms have enough time to enter or exit the industry. So in the long run, industry supply is perfectly elastic under perfect competition. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 83 6.7.6 Long-run Industry Supply Function Derivation of the long-run market supply function (VIII): But there are also industries in which the long-run industry supply function continues to have a positive slope: Usually this is because firms have to use an input whose supply is limited. Regardless of whether the long-run industry supply function 𝑆𝑆𝐿𝐿𝐿𝐿 is horizontal or rising, with free market entry and exit it is always the case that the long-run price elasticity of supply is larger than the short-run. The long-run industry supply function 𝑆𝑆𝐿𝐿𝐿𝐿 is therefore always flatter than the short-run 𝑆𝑆𝑆𝑆𝑆𝑆. Fundamentals of Economics WS 2013/14 Prof. Dr. Stephan O. Hornig 84