Chapter 7 Costs and Production in the Short Run (Intro Micro, June 2023) PDF

Chapter 7 Costs and Production in the Short Run under Perfect Competition ©1 Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 09/10/2024 2:47 PM In the remainder of the chapters of the lecture notes, we use interchangeably the terms, firm, owner(s) o...

Chapter 7 Costs and Production in the Short Run under Perfect Competition ©1 Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 09/10/2024 2:47 PM In the remainder of the chapters of the lecture notes, we use interchangeably the terms, firm, owner(s) or manager(s). In pursuit of the own self-interest, the owners and/or the managers of a firm would strive to maximize their total economic profit, which is equal to the excess of total revenue over total cost. They maximize total economic profit by adjusting the levels of inputs and that of the output. If they cannot make a profit they may choose inputs and output levels to minimize the total loss or close down the firm. When the firm’s managers are making a loss such as in a recession, they may tolerate it only for a short period of time until market conditions change say until an expansion in economic activity takes place. If the market conditions don't change quick enough they will close down the firm. Most likely, to finance a loss that is expected to be temporary, the managers would borrow from banks or other creditors. If the economic conditions do not change quickly to allow the firm’s manager to improve sales and eliminate the loss, creditors will force it to close down and sell its assets at the highest price possible. It is these forces that ensure that owners and/or managers of firms operating under perfect competition respond to market signals and strive to maintain an efficient allocation of resources. The goal of this chapter is to analyze the responses of a firm’s manager operating under perfect competition to market signals and show that at any quantity supplied the height of the supply curve of such a firm is equal to the firm’s marginal cost or the minimum cost of producing an additional unit of output. As we have argued in earlier chapters, this property of the supply curve of a product is crucial in showing that perfectly competitive markets are production efficient. Classification of Costs Producers combine labour, physical capital, and raw or semi processed material such as steel or iron to produce goods and services that they sell to other producers for further processing or to consumers. Their main objective is to maximize total economic profit. Total economic profit is the difference between total revenue and total costs. While the definition of revenue is straight forward, the definition of costs is not. To gain insight into the nature of costs, economists classify costs in many ways according to the question they wish to study. We discuss two of the most insightful classifications: Implicit vs. Explicit Costs, Fixed vs. Variable Costs. Implicit and Explicit Costs Total cost is the sum of raw material costs, labour costs, capital costs, and taxes. An important way to classify costs is to distinguish two kinds of costs: Explicit costs and implicit costs. Explicit Costs Explicit costs (or accountant’s total cost) are equal to the sum of out of pocket expenditures on inputs. They include raw material costs, labour costs, capital costs, and taxes. An important issue in economics is what constitutes capital costs and total costs. Capital costs include a yearly allowance for depreciation of physical capital, payment of interest on borrowed financial capital, and another implicit component that economists include but accountants do not include in total costs for tax purposes, Economists call this implicit component, normal profit. 1Cartago Research and Development, 10/9/24, 2:47 PM Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 2 Implicit costs or Normal Profit The firm’s owners must contribute a certain amount of physical and financial capital of their own. In some cases, own capital may constitute all the capital that is needed to run and operate the firm. In most cases, own capital is not enough and it is only a small portion of the total capital needed. Investing this capital in own firm involves an opportunity cost to the firm’s owner(s). If they had invested it somewhere else, they could have earned a fair return on it. Hence economists assign to own capital a certain fair remuneration for the services of their own capital. This remuneration is an implicit cost. In addition to a fair remuneration of own capital, implicit costs include a fair wage for own work if the owner is also one of the managers of the firm and/or a worker in the firm. Implicit costs include also a yearly allowance for the depreciation of own capital. The firm’s manager wage if he/she is not the owner of the firm is an explicit cost not an implicit cost. Economists define normal profit as the sum of the fair remuneration for own capital, a yearly allowance for the depreciation of own capital, and a fair wage for the owner(s) of the firm if he/she (they) is (are) also one (some) of the managers of the firm and/or a worker(s) in the firm. The normal profit is an implicit cost. Total Economic Cost and Total economic profit In economics, Total Economic Cost is the sum of explicit costs and implicit costs. Thus, Total Economic Cost includes normal profit. In contrast, economists define Total economic profit as the difference between total revenue and Total Economic Cost. Accordingly, total economic profit is a surplus that is not necessary for a firm’s owner to stay in business. If total economic profit is equal to zero, the revenue is just enough to cover all explicit costs and pay the owners of the firm a fair return on their own capital and a fair remuneration of their own effort. Under perfect competition, economic profit is temporary. The temporary appearance of an economic profit performs an important function as a signal that the invisible hand “uses to achieve and an efficient allocation of resources. Following a long tradition in economics, we will use interchangeably the terms total cost and total economic cost, keeping in mind that it is always the latter not the total accountant cost that we mean. Fixed and Variable Costs Economic activity is subject to all kinds of uncertainties and shocks: some natural, some resulting from errors, some from the errors committed by policy makers and financial institutions managers, and others from the nature of the perfect or imperfect competition itself. Driven by their self-interest and total economic profit maximization, producers, suppliers, and/or managers need to adjust their inputs in response to these shocks. Not all inputs can be adjusted easily in the short run. To understand how the economy behaves in the short and the long run, economists distinguish between short term and long term decision making. In the short term, producers, suppliers and managers react differently than in the long term. For example they might accept to lose some money in the short run but not in the long run. They may have to lose money in the short run because they cannot change the size of their capital stock or the size of their skilled labour force. They cannot sell their enterprise without incurring significant losses or they cannot increase the size of their capital stock quickly enough. Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 3 We call variable costs those costs that are associated with inputs that can be changed quickly. This is the case of unskilled labour, raw materials, or semi-finished materials, and energy. We call fixed costs those costs that are associated with inputs that cannot be changed quickly in the short term. Only in the long run physical capital can be sold or transformed to suit a different line of business or increased. Similarly for skilled labour, start-up costs such as costs of lawyers, licenses and the like. The distinction between variable costs and fixed costs is important for understanding the relationship between the short term and long term behaviour of economic activity and especially for understanding economic instability and how economic policy should deal with it. In the remainder of this chapter, we study the production decisions of the owners and/or managers or producers in the short run in response to changes in economic conditions under perfect competition. In the following chapter, we study their production decisions in the long run when they can change the levels of all their inputs. Short Run Production Analysis In the short run, only variable costs can be changed in response to a change in the desired production level. Unskilled labour is a good example of a variable input that gives rise to variable costs. To understand the behaviour of the firm’s manager in the short run, we need to start with the study of the relationship between labour and output in the short run. We call this relationship the short run production function. Columns (1) and (3) in Table 1 give an example of a short run production function. Table 1 Characteristics of the Short Run Production Function Units of Change Output Change Average Marginal Returns Labour in in Output Productivity: APL Productivity: MPL Labour (1) (2) (3) (4) (5) =(3)/(1) (6) =(4)/(2) (7) 0 0 Increasing 2 30 15 2 30 15.00 Increasing 2 50 25 4 80 20.00 Increasing 2 64 32 6 144 24.00 Decreasing 2 60 30 8 204 25.50 Decreasing 2 56 28 10 260 26.00 Decreasing 2 50 25 12 310 25.83 Decreasing 2 40 20 14 350 25.00 Decreasing 2 30 15 16 380 23.75 Decreasing 2 20 10 18 400 22.25 Decreasing 2 10 5 20 410 20.5 Decreasing Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 4 2 As the amount of labour increases, output increases. Note, however, that the output per unit of labour does not necessarily increase. At low levels of output and labour, producers encounter increasing returns because they can take advantage of ample opportunities for specialization and division of labour without incurring high communication and management costs. Thus at low levels of output and labour the output increases faster than labour input. When output rises faster than labour input, the ratio of output to the labour input must rise. We call this ratio average productivity of labour (APL). That is Output Average Productivity of Labor = Number of units of labor Column 5 of Table (1) gives the average productivity of labour. It shows that at low levels of labour input (less than 6 units) APL is increasing. Figure 1 illustrates this positive relationship between output and labour input. Figure 1 The Production Function Output 250 200 150 100 50 0 0 2 4 6 8 10 12 14 Labor Figure 2 illustrates this positive relationship for levels of the labour input less than or equal to 6 units. If output rises faster than labour input the ratio of the change in output to the change in labour input must be greater than average productivity. This must be the case because if we add one unit of labour and the additional output we get is greater than the current average productivity per worker, the new average productivity of labour including the output of the additional worker must rise. Similarly, when average productivity of labour is falling, the additional unit of labour adds to output less than the current average productivity of labour. We define Marginal productivity of labour (MPL) is the additional output that an additional unit of labour adds to total output In general, MPL is the ratio of additional output to additional units of labour. That is: change in Output Marginal Productivi ty of labor = Change in number of units of labor Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 5 Column (6) of Table 1 describes the behaviour of MPL. MPL is equal to the ratio of the corresponding entries of column (4) (numerator) and column (2) (denominator) of Table 1. At low (higher) levels of labour input MPL is rising (falling). The relative size of MPL with respect to APL determines the behaviour of APL. Figure 2 Average and Marginal Productivity When a firm’s size grows too big the gains from division of labour and specialization decrease because management costs, including communications and organization cost, increase tremendously. Marginal productivity starts falling as output hardly increases in response to the same amount of increase in labour. When marginal productivity becomes less than average productivity, average productivity starts falling. The firm’s manager encounters decreasing returns. Of course when marginal productivity is equal to average productivity, the average productivity ceases to increase. This is illustrated in Table 1 and Figure 2 for levels of labour greater than 10 units. At 10.5 units of labour, the average productivity and marginal productivity are equal. At this level average productivity is at its maximum. For levels of labour input less than that at which APL = MPL, MPL is greater than APL, APL is rising and the firm experiences increasing returns. For levels of labour input greater than 10.5 units of labour at which APL = MPL, the MPL is lower than the APL, APL is falling and the firm experiences decreasing returns. By definition, MPL at a given level of labour input is also the slope of the curve representing the production function at the corresponding labour input output point. In contrast, APL is the slope of the straight line joining the origin to the corresponding labour input output point on the curve representing the production function Short Run Cost Analysis The pattern of returns to increasing labour usage has important implications for unit costs. When APL increases labour costs per unit of output should fall and vice versa. Since we do not consider variable costs other than labour, we can write: Variable Cost VC = Total Labour Cost = Wage x (Number of units of labour input) Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 6 When the wage is equal to $300 per unit of labour, columns (2) and (5) of Table 2 give the variable cost schedule corresponding to the production function described by columns (1) and (2) of Table 2 as calculated according to the previous equation. Table 2 Short Run costs Labour Output APL MPL VC FC TC AVC AFC ATC MC =300 x (1) = (5)+(6) = 5)/(2) = (6)/(2) =(7)/(2) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 0 0 0 500 500 15 20 2 30 15.00 600 500 1100 20.000 16.667 36.667 25 12 4 80 20.00 1200 500 1700 15.000 6.250 21.250 32 9.375 6 144 24.00 1800 500 2300 12.500 3.472 15.972 30 10.00 8 204 25.50 2400 500 2900 11.766 2.500 14.216 28 10.71 10 260 26.00 3000 500 3500 11.538 1.923 13.462 25 12.00 12 310 25.83 3600 500 4100 11.613 1.613 13.226 20 15.00 14 350 25.00 4200 500 4700 12.000 1.429 13.429 15 20.00 16 380 23.75 4800 500 5300 12.632 1.316 13.947 10 30.00 More important is the Average Variable Cost (AVC), which is the variable cost per unit of output. AVC is important since profits will depend on the relationship between unit cost and price. By definition, Variable Cost VC Labour Cost Wage x (Number of Units of Labour) Average Variable Cost AVC = = = Output Output Output Output However, Average Productivi ty of Labour = APL = , Number of Units of Labour It follows that Wage Average Variable Cost = AVC = APL In other words, the AVC behaves like the inverse of APL. When APL increases we have increasing returns but decreasing AVC and vice versa. Thus: Increasing returns are characterized by decreasing AVC and decreasing returns are characterized by increasing AVC. This is illustrated in Table 2. When we compare the two columns (3) and (8) of Table 2, we find that the APL and the AVC vary inversely to each other. APL attains its maximum at the same time that Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 7 AVC attains its minimum. As output increases AVC first falls and then rises. Curve ABC in Figure 3 illustrates this relationship between AVC and output. Corresponding to marginal productivity there is a marginal cost. The relative levels of the marginal cost and the average variable cost determine whether the latter is rising or falling. We define the marginal cost (MC) as: change in Variable Cost Marginal Cost = change in output But Change in Variable Cost = Wage x (change in Number of Units of Labour Input) Therefore Change in Number of Units of Labour Input 1 Marginal Cost = Wage x = Wage x change in output MPL Hence the Marginal cost is proportional to the inverse of MPL. Since the Marginal productivity rises with the level of output and then falls, the marginal cost must first fall with the level of output and then rise. This is illustrated in columns (2), (4) and (11) of Table 2 and Curve DEBF in Figure 3. Figure 3 Average Variable Cost Curve and Marginal Cost Curve A Unit Costs Increasing Returns Decreasing Returns 35 in $ Average F 30 Variable Cost Marginal Cost 25 A 20 D 15 C B 10 E 5 0 0 15 30 55 80 112 144 174 204 232 260 285 310 330 350 365 380 390 Output Another important property of MC is the following: When MC is lower than AVC, then AVC decreases as output increases. The marginal cost is the additional cost of an additional unit of output. If at the current level of output the MC is lower than the AVC, producing an additional unit of output will add an additional cost equal to MC, which is less than AVC at the current level of output. When the firm produces one more unit of output, the AVC decreases. Thus, when the MC is less than AVC, AVC decreases when the output increases, as section AB of the AVC curve in figure 3 illustrates. Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 8 Similarly, when MC is higher than AVC, the AVC is rising as section BC of the AVC curve in figure 3 illustrates... Thus, in the region of falling AVC or increasing returns, the MC is less than the AVC. In contrast, in the region of decreasing returns, the MC is above the AVC. When AVC is equal to MC, AVC must be at its minimum. It follows that the MC curve crosses the AVC curve at the minimum of the latter. This is illustrated by point B in Figure 3. Fixed Cost Define: Average Fixed Cost = AFC = Output As Table 2 shows the fixed cost does not change with the level of output. Thus, The average fixed cost AFC decreases when output increases In Figure 4, curve GHK, which represents the relationship between AFC and output, illustrates this property of the AFC. Fixed Cost + Variable Cost Define: Average Total Cost = ATC = = AFC + AVC Output That is, ATC is the sum of AVC and AFC. For low levels of output, both AVC and AFC decrease as output increases. Therefore, ATC must also decrease as output increases. Figure 4 Unit Cost Functions Unit Costs in $ Increasing Returns Decreasing Returns 40 L 35 Average Variable Marginal Cost G Cost Curve Curve 30 F 25 Average Total Cost Curve 20 A D 15 M N C 10 B Average Fixed E Cost Curve 5 H K 0 0 15 30 55 80 112 144 174 204 232 260 285 310 330 350 365 380 390 Output For higher levels of output higher than the level of output at which the AVC reaches its minimum, AFC is still falling and becomes small relative to AVC but AVC is rising. AVC dominates AFC, causing ATC to rise and behave like AVC. ATC is higher than AVC by an amount equal to AFC and the MC curve Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 9 must cross the ATC curve at the minimum of the latter. In Figure 4, curve LMN represents the relationship between ATC and the level of output and it illustrates these properties. Output Decision in the Short Run In the short run, a firm’s capital stock is fixed and the firm’s manager can adjust only labour or variable inputs in order to adjust output to the ever-changing market conditions. One might think that he/she could also adjust the price of the firm’s product. However, under perfect competition when there is no excess demand, a firm’s manager who raises the firm’s product price above the market equilibrium price will lose immediately all her/his firm’s customers. If he/she lowers her/his firm’s product price below the market equilibrium price when there is no excess supply he/she will lose revenue since he/she can sell at the current market equilibrium price as much as he/she can produce at with current production capacity at an average cost lower than the market equilibrium price. Therefore, Under perfect competition, when there is no excess demand or excess supply, a firm’s manager is a price taker not a price maker. Given the market equilibrium price, a firm’s manager maximizes total economic profit or minimizes total loss by choosing the levels of inputs and output appropriately. Actually, we do not need to consider both input and output decisions. Knowing the output decision is enough. Indeed, given that we know the production function we can derive the optimal level of every input. This is easy when there is only one variable input. When there is more than one variable input, we can derive the optimal level of every input jointly given any fixed level of output and the fact that the firm’s manager must minimize total cost of production in order to maximize total economic profit. In the following chapter, we discuss this question in detail. Our purpose in this section is to show that under perfect competition when there is no excess demand or excess supply, the height of the short run supply curve of a firm at each quantity supplied is the minimum cost of producing an additional unit of output which is the value of the marginal cost at that quantity supplied. This fact will be used later to confirm that perfect competition is overall efficient. There are three steps in the proof according to the relative magnitudes of the price, the minimum ATC, and the minimum AVC. We consider each step in turn. Market Equilibrium Price Greater than Minimum ATC To find the level of output that maximizes total economic profit, the firm’s manager must first determine whether there is any level of output at which he/she can make at least a zero total economic profit. Consider figure 5. Suppose that the market equilibrium price is P0 = $25. That price is greater than the minimum value $10 of ATC. The horizontal line in figure 5 going through P0 = $25 intersects the ATC curve at two points A and B. The corresponding levels of output are respectively Qa = 2 units and Qb = 12 units. At any output level smaller than Qa = 2 units or greater than Qb = 12 units, the market equilibrium price is less than the corresponding ATC and the firm’s manager will make a loss if he/she produces that output. The firm’s manager will not choose to produce at such levels of output because, for levels of output between Qa = 2 units and Qb = 12 units, the market equilibrium price P0 = $25 is greater than the corresponding ATC and at which output levels the firm’s manager can earn an economic profit. Thus, the output that would maximizes the firm’s total economic profit must lie between Qa = 2 units and Qb = 12 units. Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 10 At Qa = 2 units and Qb = 12 units, the total economic profit is zero and the firm’s owners are earning a normal profit. Driven by self-interest, the firm’s manager will consider whether he/she can improve and make the firm earn a positive total economic profit. Obviously, the answer is yes. If produced, all output levels between Qa = 2 units and Qb = 12 units yield a positive economic profit. The pursuit of self-interest suggests that the firm’s manager would choose among these that level which maximizes the total economic profit. To find out which output level would produce the maximum total economic profit, we proceed as follows. Starting at Qa = 2 units in figure 5, where the total economic profit is zero, let the firm’s manager increase the level of output by one unit to 3 units. Total cost would increase by MC and total revenue would increase by P0 = $25. We call the additional revenue obtained from selling an additional unit of output the marginal revenue (MR). In this case of a firm operating under perfect competition, MR = price = P0 = $25 and total economic profit would change by MR - MC = P0 (= $25) - MC. At Qa = 2 units, MC is less than ATC = P0 = $25. Therefore, (MR - MC) is greater than zero. Starting at Qa = 2 units, increasing the output by one unit would increase total economic profit. Similarly at Qa = 2 units + 1, MC is less than P0 = $25. Increasing the output by one unit will change the total economic profit by MR - MC = P0 (= $25) - MC. Since P0 is still greater than MC, the additional unit will raise the total economic profit. As long as P0 = $25 is greater than MC, the firm’s manager would keep increasing output since total economic profit keeps rising. However, sooner or later the firm’s manager will meet with decreasing returns and MC starts rising so the difference between P0 = $25 and MC would eventually start falling until it reaches zero. This happens at C in figure 5 when MC becomes equal to P0 = $25. The corresponding level of output is QC = 8 units. Figure 5 Optimal Output: Price Greater than Minimum ATC. Price, 45 unit costs Marginal Cost 40 Average Total Cost 35 30 A C B 25 20 15 10 Average Variable Cost 5 a Qa Qc Qb 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Output For any level of output greater than QC = 8 units, MC is greater than P0 = $25 and the additional economic profit from producing an additional unit of output is negative. The firm’s manager can increase its profit in this case by lowering output by one unit. This will save the firm’s manager the marginal cost MC. The cost savings is greater than the loss in revenue, which is equal to MR = P0 = $25. Thus, Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 11 When there is no excess demand or excess supply in the market, the output that maximizes total economic profit under perfect competition is such that MR = MC or Market equilibrium price = MR = MC. Next we consider the case when the market equilibrium price is lower than the minimum ATC but higher than the minimum AVC Price between Minimum ATC and Minimum AVC Suppose that the price drops to P1 = $9. This price is lower than the minimum ATC of $10 but higher than the minimum AVC of $7. Figure 6 illustrates this situation. At all levels of output, the total economic profit is negative. However, as we shall argue presently, the firm’s manager should not go out of business in the short run unless her/his bank’s manager refuses to lend him more money in the short run to help the firm’s manager cover losses. The price P1 = $9 is still greater than the minimum AVC = $7. The horizontal line AB at P1 = $9 in figure 6 intersects the AVC at two points A and B at the corresponding output levels of Qa = 4 and Qb = 8. According to figure 6, for levels of output lower than Qa = 4 units or greater than Qb = 6 units, the price is less than AVC. At such levels of output, the firm’s manager cannot cover its variable cost and in addition he/she will have to pay the fixed cost FC = $20. Thus, the firm’s total economic loss is equal to the difference between its VC and its total revenue plus the fixed cost. At such levels of output including a zero output, the total economic loss is thus greater than or equal to the fixed cost FC of $20. Among such levels of output, closing down is the best course of action. The firm’s total loss would be equal to the FC of $20. However, this is not the overall optimal choice. The reason is the following: Figure 6 Optimal Output Level: Price between Minimum AVC and Minimum ATC. Price, 20 Unit Costs 19 Average Total Cost 18 Curve 17 16 Marginal Cost 15 Curve 14 13 Average 12 Variable Cost 11 Curve 10 9 8 A C B 7 6 5 P1 = $9 4 3 2 1 QC Qb 0 2 3 4 Qa 5 6 7 8 9 10 11 12 Output If the firm goes out of business its loss in the short run would be equal to the fixed cost FC = $20. Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 12 According to figure 6, if the firm’s manager produces an output between Qa and Qb, the corresponding AVC is lower than the price P1 = $9. At any output between Qa and Qb, the corresponding total revenue is greater than variable cost VC. By producing an output such as 5 units, the firm’s manager can cover the variable cost VC and he is left with an excess of total revenue over variable cost VC that he/she can use to cover part of the firm’s fixed cost FC = $20. The firm’s total economic loss is therefore less than its total fixed cost FC =$20. Thus, the firm’s manager would reduce total economic loss by producing an output between Qa = 4 and Qb = 8, where price is greater than the minimum of AVC of $7 rather than closing down even though its total economic profit is negative. Among those output levels between Qa = 4 and Qb = 8., the firm’s manager would choose that output that would minimize total economic loss. To find this level of output, we proceed as follows. Start at point A in figure 6 where the price P1 = $9 is exactly equal to AVC = $9 and output Qa = 4 units. At A, the firm’s total economic loss is equal to the fixed cost FC = $20. Let the firm’s manager increase output by one unit. Then total revenue increases by MR = P1 = $9 and the firm’s total cost rises by marginal cost MC. However, figure 6 shows that at Qa = 4, AVC = $9 is greater than MC = $1. Thus, at Qa , MR = P1 = $9 = AVC > MC =$1. By producing one more unit, total revenue would increase more than variable cost. According to figure 6, at an output of Qa = 4+ 1, total revenue exceeds VC by $9 - $1 = $8. This excess can be applied to cover part of the fixed cost and lower the total economic loss. According to figure 6, the production of the additional unit, beyond Qa = 4, produces an excess of revenue over VC equal to $9 - $1 = $8 and the firm’s manager can reduce total economic loss from $20 = FC at Qa to $12 = $20 - $8. The firm’s manager can reduce the total economic loss further and cover more of the firm’s fixed cost by producing still an additional unit of output since at 5 units of output, figure 6 shows that the price P1 = $9 is still greater by $6.5 than MC which is approximately equal to $2.5. The total economic loss would be reduced to $5.5 = $12 -$6.5. The firm’s manager would continue to increase output as long as the price P1 = $9 is greater than MC. Increasing the output to 6 units, he/she can reduce total loss to $3.5 = $5.5 - ($9 - $7) by producing an additional unit. Note that as the firm’s manager continues to increase the level of output one unit at time and reduce the total economic loss, the excess of the price over MC falls until it reaches zero at Qc where MC = $9 = P1. Increasing output beyond this level would increase the total economic loss instead of reducing it because MR = P1 =$9 becomes lower than MC as decreasing returns causes MC to increase above $9. It follows that the optimal level of output that minimizes total economic loss or maximizes total economic profit satisfies the following equation: Marginal revenue = Market equilibrium price = Marginal cost This result is valid for any market equilibrium price between the minimum AVC and the minimum ATC. Pulling together the results for this case and the previous case, we conclude: Regardless whether the price is greater than or smaller than the minimum ATC but provided that it is greater than the minimum AVC, we reach the same conclusion: Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 13 In pursuit of its own self-interest and if there is no excess demand or excess supply in the market, the optimal level of output for a firm operating in a perfectly competitive market is that output at which Marginal Cost MC.= Market equilibrium price = Marginal Revenue MR The difference between the case when the price is greater than ATC and that when it is less than ATC is that in the first case the firm’s manager is maximizing total economic profit and in the second case he/she is minimizing total economic loss. Market Equilibrium Price Lower than Minimum AVC When the price is less than the minimum AVC, total revenue is not enough to cover VC at any level of output. If the firm’s manager produces some output he/she will have to cover the excess of the variable cost VC over total revenue plus the fixed cost. This loss is greater than the fixed cost. If the firm goes out of business the firm’s owners and/or managers will have to cover only a loss equal to the firm’s total fixed cost. Thus, driven by self-interest, the firm’s owners and/or managers would minimize their total economic loss by going out of business and the managers of any bank will not lend them anymore money to cover their losses. Short Run Supply Function The previous analysis shows that, for firms operating under perfect competition, knowledge of a firm’s average total cost curve, average variable cost curve, total fixed cost, and marginal cost curve helps the firm’s manager find the quantity of output that maximizes the firm’s total economic profit or minimize its total economic loss. Given a market equilibrium price greater than or equal to the minimum AVC, the output that will maximize its total economic profit or minimize its total economic loss is that output at which the marginal cost is equal to the market equilibrium price. Put differently, this means that: Given a market equilibrium price greater than the minimum average variable cost, one draws the horizontal line curve at a height equal to the market equilibrium price until one meets the MC curve. The level of output on the output axis directly underneath the intersection point of the two curves is the output that maximizes total economic profit or minimizes total economic loss. Since the quantity that a firm produces is equal to its quantity supplied to the market, it follows that for any market equilibrium price greater than or equal to the minimum average variable cost the short run supply curve is identical to the marginal cost curve. Hence, the portion of the MC curve above the minimum AVC constitutes one section of the short run supply curve of a firm operating under perfect competition when there is no excess supply or excess demand in the firm’s product market. Segment BC of the broken line OABC in Figure 7 represents this portion of the short run supply curve operating under perfect competition when there is no excess supply or excess demand in the firm’s product market. For all prices less than the minimum AVC, the maximum total economic profit is negative, equal to the negative of the total fixed cost, and the quantity of output that maximizes total economic profit or minimize total economic loss is zero. Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 14 Segment OA of broken line OABC in Figure 7 represents this portion of the short run supply curve. Figure 7 Short Run Supply Curve Price, 20 Unit Costs in $ 19 Average Total Cost Curve C 18 17 16 Supply Curve 15 14 13 12 11 Average Variable Cost 10 Curve 9 8 7 6 A B 5 4 Marginal Cost Curve 3 2 1 O 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Output By definition of MC, the fact that the portion of the MC curve above the minimum AVC is the short run supply curve implies that the height of the short run supply curve of a firm operating under perfect competition is equal to the minimum additional cost of producing an additional unit of output. We used this property in chapter 2 to establish that markets operating under perfect competition will produce an overall efficient allocation of resources. Equilibrium of Perfect Competition Markets in the Short Run In the short run, different firms may have different cost functions because they may not have entered the market at the same time. Some of them may be using old technology and they have not had enough time to change their physical capital in response to a change in the conditions of their product market such as a change in technology that lowered unit costs, a change in tastes, or a change in international trade policy of the governments of various countries. In figure 8, we illustrate the case of two groups of firms. At every output, the heights of the AVC, ATC, and MC curves of firms in group A are lower than the heights of the corresponding cost curves of firms in group B. To simplify, suppose that each group of firms is composed of one firm only. The broken curves OABC in figures 8.a and 8.b give respectively the short run supply curve of a firm in group A and group B. The short run supply curves are identical to their respective MC curves for prices greater than their respective minimum AVC. To build the market supply curve we add horizontally the two supply curves. The market supply curve is given by the market supply curve in figure 8.c. (Review chapter 2 to understand how to add the two supply curves). We also draw in figure 8.c the market's demand curve. The equilibrium of the market is reached at point E in figure 8.c. The market equilibrium price is equal to $14.5 and the market equilibrium quantity, supplied and demanded, is equal to 13.33 units. Assume that each firm’s manager equates her/his MC to the market equilibrium price. Points E in panels (a) and (b) of Figure 8 indicate the two firms optimal choices at equilibrium. The quantity of output that firm A will produce is equal to 7 units. The quantity of output that firm B will produce is Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 15 equal to 6.33 units. Of course, the sum of the quantities supplied by the two firms must be equal to 13.3 units, the total quantity supplied to the market. Figure 8 Equilibrium of Perfect Competition Markets in the Short Run Figure 8.a Figure 8.b Figure 8.c Firm A’s Units Costs Firm B’s Units Costs Market 40 40 A T C Curve C Market Supply Curve 35 35 A T C Curve 35 30 Supply Curve, 30 30 Market Demand Curve MC Curve 25 25 25 AV C Supply AVC Curve Curve C 20 20 20 Curve 14 E E 15 15 15 14.5 E 14 A B 10 10 10 A 5 B 5 MC Curve 5 M C Curve 0 c 0b 6.3 0 0 1 2 3 4 5 6 7 8 9 10 11 012 2 3 4 5 6 3 7 5 6 12.66 13.33 14.43 15.52 16 Output Ou Output Market (c) Firm A makes a positive total economic profit since the market equilibrium price of $14.5 is greater than the minimum of its average total cost of $10.33. Firm B makes a negative total economic profit or a total economic loss since the market equilibrium price of $14.5 is lower than its minimum average total cost of $15. However, note that the market equilibrium price of $14.5 is greater than the minimum AVC of $12 of firm B. The loss that firm B makes at the output where MC is equal to the market equilibrium price is less than the loss it would make by closing down. In the long run, either the demand curve would shift upward and to the right or the managers of firm B would lower the firm’s costs by reorganizing and/or adopting the same technology or method of organization as the managers of firm A. Otherwise, firm B may have to close down. We look at this question in the following chapter. Conclusions In this chapter, we have developed a few basic concepts. Economists consider total economic costs as composed of an explicit component and an implicit component. The implicit component includes remuneration of own effort and services provided by own capital. We call this remuneration normal profit. The normal profit is actually an opportunity cost of the firm's own resources. This is the maximum remuneration own resources can earn in other lines of business. By contrast, total economic profit is equal to the excess of total revenue over total economic cost. In the short run, there are fixed and variable costs. Fixed costs are associated with factors of production that cannot be changed on short notice in response to changes in the economic environment such as a recession, technology shocks, or a shift of the market demand curve. Factors that a firm’s managers cannot changed on short notice are: initial set up costs, the location, size and/or technology of physical capital, and the number and know-how of skilled workers. Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 16 Unit costs are inversely related to productivity. Average productivity of a factor of production is the ratio of total output of the product to the number of units of the factor of production the services of which were used in the production of the product. The average variable cost of a variable factor of production such as unskilled labour is the ratio of the total cost paid for the use of the services of that factor to the number of units of the factor the services of which were used in the production of the product. At small output levels, the average productivity of the factor of production labour rises with output and it will eventually fall at relatively much higher output levels. Consequently, the average variable cost first falls with output and then rises. The marginal productivity of a factor of production is the maximum additional output obtained from the use of the services of an additional unit of that factor of production. The marginal cost of a product associated with a variable factor of production, such as labour, is the minimum additional cost of producing an additional unit of the product using the services of that factor of production. The marginal cost of a product associated with a factor of production is inversely related to its marginal productivity. When average productivity of a variable factor of production is rising (falling), its marginal productivity must be higher (lower) than its average productivity. Consequently, when its average variable cost is falling (rising), its marginal cost must be lower (higher) than its average variable cost. Similarly, the marginal cost must be lower (higher) than average total cost when average total cost is falling (rising). Decreasing returns to an increase in one factor of production only are associated with decreasing average productivity of that factor of production. Thus decreasing returns are responsible for increasing average and marginal costs. The short run supply curve of a firm operating under perfect competition has two sections. One section is a vertical line at 0 output for all market equilibrium prices lower than the minimum average variable cost. The second section is identical to the firm’s marginal cost curve for all market equilibrium prices higher than the minimum average variable cost and it is upward sloping. At any given quantity supplied by of any firm producing under perfect competition when there is no excess demand or excess supply of the product the height of its short run supply curve is the minimum additional cost of producing an additional unit of the product and it is its marginal cost. Firms operating in perfect competition markets are small compared to the in the market size where they sell their products in the sense that increasing returns are quickly exhausted. Decreasing returns for these firms occurs at relatively small levels of output and dominate the production process thereafter. We know from chapter 2 that the market short run supply curve under perfect competition is the horizontal sum of the short supply curves of the exiting firms in the industry. Thus, the market short run supply curve is upward sloping and its height at every quantity supplied is equal to the marginal social cost of producing an additional unit of the product In the short run, the market equilibrium price does not guarantee that all firms are earning a total non- negative economic profit. Some firms may be making economic losses that are lower than their total fixed cost. If the following chapter, we show that in the long run either some of these firms will exit or they will change their technology an/or their internal organization.. In the short run, however, costs are not necessarily minimized under perfect competition. It is possible that some producers may be making losses in the short run. Their average total costs and Chapter 7 Costs and Production in the short run, Chapter 7 Costs and Production in the Short Run, Intro Micro, June 2023 10/9/24 2:47 PM 7- 17 marginal costs may be higher than that of other firms in the business because they are not using the best technology available or the best method of organization and management. Some producers are making losses while others are making profits. This is evidence that costs are not minimized. In the long run some of them will reorganize it and adapt their stock of capital, their internal organization, and/or technology. If not they exit their current market. In the following chapter we will analyze this process and we will show that if perfect competition prevails in the market of a product, it will make sure that every producer is operating at the minimum average cost and her/his total economic profit is equal to zero. End