Chapter 8 Long Run Supply & Equilibrium Under Perfect Competition June 2023 PDF

Chapter 8 Long Run Supply and Long Run Equilibrium under Perfect Competition ©1 Chapter 8 Long Run Supply and Long Run Equilibrium under Perfect Competition, Intro Micro, June 2023, 20/08/2024 4:22 PM. In the previous chapter, we have seen that markets operating under perfect competi...

Chapter 8 Long Run Supply and Long Run Equilibrium under Perfect Competition ©1 Chapter 8 Long Run Supply and Long Run Equilibrium under Perfect Competition, Intro Micro, June 2023, 20/08/2024 4:22 PM. In the previous chapter, we have seen that markets operating under perfect competition may not operate efficiently in the short run. However, in the long run they operate efficiently if there are no externalities. By pursuing their self-interest economic agents promote the public interest. One of the reasons that markets operating under perfect competition can be inefficient in the short run is because information about technology is incomplete. In the long run, information is complete and a firm’s managers can adjust all factors of production. We say, in the long urn firms operate on their long run production function. The main goal of this chapter is to demonstrate that, in the absence of externalities to be defined later in this chapter, a market operating under perfect competition achieves an overall efficient allocation of resources. Owners of firms operating in markets under perfect competition cannot earn an economic profit at the long run equilibrium, but they will earn a normal profit. Free entry and exit will force the equilibrium price in the long run to be equal to the minimum long run average cost, which includes the normal profit and it is equal to the marginal cost at the corresponding output. Since in the long run every firm’s marginal cost must be equal to the common minimum average total cost and the equilibrium price must be equal to the willingness to pay and to the marginal benefit of every consumer who wish to buy the product, it follows that the marginal social cost must be equal to the marginal social benefit at the long run equilibrium of a product’s market that operates under perfect competition. That is, in the long run and in the absence of externalities, markets operating under perfect competition will achieve an efficient allocation of resources. As we did in the short run analysis of equilibrium of perfect competition markets, we start with the analysis of the long run production function. The Long Run Production Function In the long run, the managers of a firm can change the output of the firm’s product by changing the levels and combination of the firm’s stock of capital (K), the amount of labour services (L) or that of any other factor of production they use in the firm’s production process. To simplify the process of derivation of the characteristics of the long run equilibrium of a market operating under perfect competition, we assume that the firm’s production process uses the services of only two factors of production, capital and labour. The output of a product is an increasing function of the number of units K of capital input and the number of units L of labour input to product it. We can express this relationship in the form of a table and a figure. Figure 1 gives an example of a table that illustrates the relationship between output, and the number of units K of capital input and the number L of units of labour input. We call this relationship the long run production function. The horizontal axis in figure 1 indicates the number of units L of labour input and the vertical axis indicates the number of units K of capital input. The numbers at the corresponding intersection of the grid lines indicate the corresponding output levels. For each labour-capital combination (L, K), the production function gives the maximum output Y that the firm could produce using the best technology and the best method of organization available and feasible. For example, when the number of units of labour input is equal to 2 units and the number of units of capital input is equal to 3 units, the maximum number of units of output produced is equal to 6 units. 1Cartago Research and Development, 2024-08-20, 4:22 PM Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 2 Keep the number of units K of capital input constant. Output increases as the number of units L of labour input increases. For example, when the number of units of capital input is equal to 6 units, output increases from 6 to 12 units when we increase the number of units of labour input from 1 to 2 units. Similarly, for a fixed number of units of labour input of 2 units, output increases from 12 units to 14 units when we increase the number of units of capital input from 6 to 7 units. We call the increase in output the marginal productivity of capital. In general, we define the marginal productivity of capital as: The marginal productivity of capital (MPK) is the additional output resulting from the employment of an additional unit of capital. Change in the number of units of Output Thus: MPL = Marginal Productivi ty of Labour = Change in the number of units of Labour Change in the number of units of Output MPK = Marginal Productivi ty of capital = Change in the number of units of capital For example, suppose that the current number of units of labour input L is 2 units and the current number of units of capital input is 2 units. According to figure 1, output is equal to 4 units. When we increase the number of units of capital input to 4 units without changing the number of units of labour input, output increases to 8 units. The change in the number of units of capital input is 2 units and the corresponding change in output is 4 units. Therefore, the marginal productivity of capital is 4/2 = 2 units of output per additional unit of capital input. Figure 1 The Production Function and its Isoquants K 9 8 16 24 32 40 48 8 7 1 21 28 35 7 42 12 C 6 F 18 24 30 6 36 Capital 5 10 25 30 5 15 20 8 A 4 12 16 4 G 16 18 6 3 9 12 3 15 16 4 2 6 8 H 12 10 2 6 8 2 3 4 6 D 1 1 4 B 2 4 2 0 2 0 1 2 3 4 5 6 Labour L Figure 1 of the production function shows that the firm can produce the same level of output using many different combinations (L, K) of labour and capital inputs. For example, the firm can produce 6 units of output with 1 unit of labour input and 6 units of capital input or alternatively 2 units of labour Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 3 input and 3 units of capital input, and so on. Of particular interest are the curves that connect for each level of output all the labour capital combinations (L, K) capable of producing that level of output. For example, the curve labelled 2 in figure 1 connects all labour capital combinations capable of producing 2 units of output. The combination 1 unit of L and 2 units of K, denoted (1, 2), produces 2 units of output. So do combinations (2, 1), (4, 0.5) and (6, 0.33). Similarly, each one of combinations (1, 4), (2, 2) and (4, 1) produces the same number 4 of units of output. We call each one of those curves an isoquant. An isoquant is the collection of labour-capital combinations each one of which produces the same number of units of output There is an infinite number of isoquants: one for each level of output. Two isoquants never cross each other.2 Each isoquant is downward sloping. If we increase the number of units of labour input, we can produce the same number of units of output with less units of capital input. Starting from any point on a given isoquant and keeping the number of units of capital input unchanged, an increase in the number of units of labour input will result in an increase in output. To keep output constant, we need to reduce the number of units of capital input by an appropriate number of units in order to offset the effect of the increase in the number of units of labour input. That is, we are substituting labour for capital. We give the special name of marginal rate of technical substitution to the terms under which the substitution is possible. MRTS (marginal rate of technical substitution) is the maximum number of units of capital input that can be withdrawn from production per additional unit of labour input while keeping the number of units of output produced constant. MRTS is the minimum number of units of capital input that we must add when we withdraw one unit of labour input in order to keep the number of units of output produced constant For example, suppose we start from the labour capital combination (1, 4) on the green isoquant AB in figure 1, along which the level of output is equal to 4 units. Let us increase the number of units of labour input by one unit. To keep moving on the same green isoquant AB keeping output equal to 4 units, we must reduce the number of units of capital input by 2 units from 4 to 2 units. The marginal rate of technical substitution is MRTS = 2 units of capital for one unit of labour. In general, to compute the marginal rate of technical substitution along a given isoquant, we divide the change in the number of units of capital input by the change in the number of units of labour input, keeping the level of output constant. Furthermore, by definition of the slope of a curve, the marginal rate of technical substitution MRTS at a given labour capital combination is a good approximation of the absolute value of the slope of the tangent to the isoquant that goes through that labour capital combination. Long Run Costs and the Optimal Choice of the Labour Capital Combination In the long run, a firm’s managers can change both the number of units of labour input and capital input. Thus, there are no fixed costs in the long run. To maximize total economic profit, a firm’s managers must minimize the costs of production of any given level of output. 2 Otherwise, the same combination of labour and capital would produce two different levels of output and the production process that produces the lower level of output is not efficient. The firm should never use this combination. We should not use it in the definition of the production function because the production function gives the maximum level of output for each labour capital combination. Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 4 In the short run, the number of firms is fixed and the market absorbs unit cost increases. For instance, in response to an increase in the quantity demanded of a product, it is much easier to increase the number of units of labour input even if decreasing returns raise the marginal cost. In the long run, free entry and exit is a characteristic of markets that operate under perfect competition. Thus, in the long run new firms enter such markets with an appropriate technology and number of units of capital input and labour input enabling their managers to achieve a lower average cost. They attract demanders away from some existing firms with a higher average total cost and inappropriate technology, and capital and labour combinations. The managers of some or of all existing firms producing the same product are forced to adjust the number and the quality of units of their capital and labour inputs in order to minimize the long run average cost which enables them to compete with the new entrants. Otherwise, their firms must exit that product’s market. The concepts developed in the previous section help us understand how a firm’s managers or owners adjust their firm’s labour-capital combination to minimize the total cost of producing any given output. Figure 2 Isoquants and Marginal Productivities Q Capital = K MPK = 1, MPL = 25 KA= 50 A MPK = 2.5, MPL = 10 C KC=20 MPK = 10, MPL = 2.5 B Q = 100 KB = 5 0 LA= 2 LC=5 LB = 20 Labour Suppose that a firm’s managers wish to produce a given level of output equal to 100 units. In figure 2, curve ACB is the corresponding isoquant. Isoquant ACB shows that the firm can produce 100 units of output using any labour capital (L, K) combination (for example A, B or C) located on the isoquant. Which combination will they choose: one with a high capital labour ratio ( K / L ) such as Labour-capital combination A (= a large number of units of capital input and a small number of units of labour input), Labour capital combination B with a low capital labour ratio ( K / L ) (= a small number of units of capital input and a large number of units of labour input), or Any labour capital combination located on isoquant ACB such as C? We are now ready to answer this question. Characteristics of the Least Costly Labour Capital Combination Obviously, to maximize total economic profit, the firm’s managers would choose the labour capital combination that minimizes total cost TC. With each combination (L, K) is associated a capital labour ratio K/L and a certain level of total cost TC. To hire the services of an additional unit of labour, the firm’s managers must pay the corresponding market wage rate. To use the services of an additional Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 5 unit of capital they must pay the corresponding price or opportunity cost, which we call the rental price of capital. Rental price of capital = (interest rate) x (price of a unit of capital) + Allowance for capital depreciation. The total cost TC is the sum of the labour cost and the capital cost. That is: TC = (wage x L) + (rental price of capital x K) As the (L, K) combination changes, TC changes. In their pursuit of self-interest, i.e. a higher total economic profit, a firm’s owners and/or managers, who are operating under perfect competition in their product and factors input markets, must choose for any given output the (L, K) combination that minimizes the total cost TC of producing it. To find out the characteristics of this combination, we use the concepts of marginal cost of producing an additional unit of output using additional units of either one of the two factors of production capital or labour. Since a firm’s managers can vary in the long run the number of units of capital and/or labour inputs, we can compute the long run marginal cost in two ways: We know from our analysis of the operation of perfect competition markets in the short run that when the firm’s manager increases the number of units of labour input to produce an additional unit of output without changing the capital input then wage Marginal cost of producing one more unit of output using additional labour units only = MPL By analogy, Marginal cost of producing one more unit of output using additional units of capital only = rental price of captial. MPK These two different ways of calculating the marginal cost must yield the same result when we start from a labour capital combination that minimizes the total cost of producing a given level of output. That is: At the labour-capital combination that minimizes the total cost TC of producing an additional unit of output, the following equation must hold: rental price of capital wage (4) = MPK MPL The reason is simple. Let us consider an arbitrary level of output such as 100 units. We know there are many ways to produce it with different labour capital combinations located on the corresponding isoquant for 100 units output as curve ACB in figure 2 shows. Let us suppose that the wage rate is equal to $80 and the rental price of capital is equal to $20. Each one of combinations A, B, and C on isoquant ACB can produce an output of 100 units. K At combination A, with 2 units of labour input and 50 units of capital input, = 25, MPL = 25, MPK = L 1, Total cost = ($80 x 3 units of labour) + ($20 x 50 units of capital) = $160 + $1000 = $1160. wage $80 Marginal cost of producing using labour = = = $ 3.2. MPL 25 Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 6 rental price of capital $20 Marginal cost of producing using capital = = = $20. MPK 1 Thus, At A, it is cheaper to produce one additional unit of output using more labour units than using more capital units since rental price of captial wage At A, = $20 > $3.2 = MPK MPL Let the firm’s manager increase output by one unit using more units of labour, total cost will increase by the marginal cost using labour of $3.2. At the same time let her reduce output by one unit using less units of capital, then total cost TC will decrease by the marginal cost $20 of using less capital input. As a result, total output does not change but total cost falls by $16.8 = $20 – $3.2. It follows that: rental price of captial wage The firm’s manager would substitute labour for capital if: >. MPK MPL The firm’s labour capital combination would move along isoquant ABC towards a labour capital with les capital and more labour such as at combination C with a lower K/L ratio. In contrast, at combination B with labour input = 20 units and capital input = 5 units, we have: K = 0.25, MPL = 2.5 units of output, MPK = 10 units of output, and L Total cost = ($80 x 20 units of labour) + ($20 x 5 units of capital) = $1700. However, wage $80 Marginal cost of producing an additional unit of output using labour = = = $32 MPL 2.5 Marginal cost of producing an additional unit of output using capital = rental price of capital $20 = = $2 MPK 10 Thus, at labour combination B, it is cheaper to produce one additional unit of output using more capital units than using more labour units and rental price of captial wage At labour combination B, = $2 < $32 = MPK MPL Let the firm’s managers increase output by one unit using more units of capital input, the total cost would increase by the marginal cost of $2 of using additional units of capital input. At the same time let them reduce output by one unit using less units of labour input. Then total output does not change but total cost would decrease by the marginal cost $32 of using less units of labour input. Total output does not change but total cost would decrease by $32- $2 = $30. It follows that: rental price of captial wage The firm’s managers would substitute capital for labour if <. MPK MPL By doing so the labour capital combination would move along isoquant ABC towards labour capital combination C. Accordingly, the total cost of producing the 100 units output is at its minimum only when Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 7 rental price of capital wage (4) = MPK MPL We have proved equation (4). We verify that this condition is satisfied at the labour capital combination C. rental price of capital 20 80 wage At the labour capital combination C = = = = = $8 MPK 2.5 10 MPL The minimum total cost of producing 100 units of output is achieved at C (5, 20). It is equal to = $800 = $20 x 5 + $20$ x 20. The average total cost = $800/ 100 = $8. The firm’s managers would produce the 100 units of output using combination C. At the labour capital combination that minimizes total cost in the long run, equation (4) says that the prices of the services of units of factors of production are proportional to the corresponding marginal productivities. The left-hand side of equation (4) is the marginal cost of producing an additional unit of output using additional units of capital. The right hand side of equation (4) is the marginal cost of producing an additional unit of output using additional units of labour. Equation (4) says that both ways of calculating the marginal cost yield the same value when we start from a labour capital combination that minimizes total cost. We call this common value of marginal costs the long run marginal cost. At the labour capital combination that minimizes total cost TC, we have: rental price of capital wage (5) Long Run Marginal Cost = = MPK MPL We call the total cost at C ($800) the long run total cost of producing 100 units of output. The 800 corresponding long run average total cost at a 100 units of output is thus equal to =$8 =. The 100 long run marginal cost at a 100 units of output is also equal to $8. Returns to Scale and Long Run Average Costs In the long run, an increase in output corresponds to an increase in the scale of production. To minimize total cost, a firm’s managers increase output by increasing both the number of units of capital input and labour input in the appropriate proportions while maintaining MRTS equal to the (wage/rental price of capital) ratio or making sure that the new labour capital combination satisfies equation (4) Constant Returns to Scale In many cases, when the number of units of capital and labour inputs are doubled the number of units of output doubles. In this case, we say there are constant returns to scale. Let us start from combination C in figure 2 and assume that the production function exhibits constant returns to scale. The corresponding numbers of units of labour and capital inputs minimize the total cost of production of an output equal to 100 units. The corresponding minimum total cost is $800 and equation (4) holds. Under constant returns to scale, when the firm’s managers double the number of units of capital and labour inputs, the total cost will also double and the total output will double. Now, recall that average productivity of labour is equal to the ratio of the number of units of output to the number of units of labour input. Similarly the average productivity of capital is equal to the ratio of the number of units of output to the number of units of capital input. Thus, Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 8 When the number of units of capital input and those of labour units inputs are doubled, the average productivity of labour and the average productivity of capital will not change The only way that the average productivity of a factor or production does not change is if the corresponding marginal productivity does not change and must therefore be equal to the average productivity. If the wage and the rental price do not change, it follows that the marginal cost using capital and the marginal cost using labour remain constant and equal to each other Hence, equation (4) holds before and after the doubling of inputs and output. Furthermore, doubling the inputs of both labour and capital with no change in the prices of the services of the factors of production will double the total cost. Thus, Under constant returns to scale, if the firm starts from a combination such as C where the total cost of producing the corresponding output is minimized, doubling labour and capital inputs doubles output and doubles total cost and this double total cost is the minimum total cost of producing the double output. It follows that Under constant returns to scale, the long run average total cost will not change when the firm doubles the number of units of labour input, capital input, and output, and hence total cost. Since under constant returns to scale, the long run average total cost does not change and the long run marginal cost does not change, they must be equal to each other. Indeed, in our example of figure 2, our calculations at combination C shows that they are equal to $8. It follows, that for our example and for any level of output, Long run total cost = $8 x the number of units of output. In general, if the production function exhibits constant returns to scale and if both the wage and the rental price of capital are constant, then the long run marginal cost is constant independent of the number of units of output produced. That is: Long run total cost = (a constant long run marginal cost) x number of units of output. In general and as illustrated in figure 4.a, under constant returns to scale, the long run average total cost is constant and the long run total cost is proportional to output. Figure 4.a Constant Returns to Scale Long Run Total Cost Long Run Average Total Cost = Long Run Marginal Cost Constant returns to Scale Constant returns to Scale Output Long Run Marginal Cost Output Note that the concept of constant returns to scale is a long run concept. It is different from the concept of constant returns to a single factor of production since the latter applies to changes in only one factor of production such as labour, keeping all the other factors of production constant. The concept of constant returns to scale is compatible with both increasing and decreasing returns to changes in a single factor of production in the short run. Furthermore, a firm may experience constant returns to scale over a certain range of outputs only, Over other ranges of output, the returns to scale can be increasing or falling. Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 9 In the long run, production functions can be quite complicated. However, data and econometric analysis show that there is a definite order that production functions follow if they exhibit different kinds of returns to scale. Increasing and Decreasing Returns to Scale Let us consider the case of doubling both the number of units of capital input and the number of units of labour input. If the number of units of output more than doubles, we have increasing returns to scale. If the number of units of output less than doubles, we have decreasing returns to scale. In the first case, both the average productivity of capital and that of labour rise with the number of units of output. For a given wage rate and rental price of capital, output rises faster than the long run total cost. The long run average total cost is falling as output increases The Long run marginal cost may fall and rise but it must be lower than the long run average total cost. In the second case, both the average productivity of capital and that of labour fall as the number of units of output increases. For a given wage rate and rental price of capital, output rises slower than the long run total cost. The long run average total cost is rising with output The Long run marginal cost rises with output and it is higher than the long run average total cost. Firms frequently encounter increasing returns to scale at low levels of output. Increasing returns are the result of a firm’s managers taking advantage of ample opportunities of specialization of units of capital and of labour inputs. Sooner or later, however the advantages from specialization are more than offset by increased administrative and management costs. Thus, usually decreasing returns to scale follow increasing returns to scale. The average productivity of capital and that of labour start and continue falling after reaching a maximum. The long run total cost rises faster than the increase in output. Thus, the long run average total cost rises. Figure 4.b Increasing and Decreasing Returns to Scale Long Run Average Total Cost Long Run Total Cost Increasing returns to Scale Decreasing returns to Scale Decreasing returns to Scale Increasing returns to Scale Output Output Figure 4.b illustrates the behaviour of the long run average total cost for a firm that experiences first increasing returns to scale followed by decreasing returns to scale. Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 10 Relationship between Short Run and Long Run Average Total Costs Suppose that the firm starts from labour capital labour combination A in figure 5.a. Combination A minimizes the long run total cost of producing a given output say 100 for a given wage rate and a given rental price of capital. When we fix the number of units of capital input to be equal to K A , there is only one level of labour LA that can produce 100 units of output at the lowest total cost. In this case, the short run total cost is equal to the total long run total cost of producing 100 units of output equal to $1400 for example so that the long run average total cost is equal to the short run average total cost equal to $14. Point A on the long run average cost ABD in figure 5.b represents this situation with output equal to 100 units and long run average total cost equal t o $14. Now suppose that the market demand curve for the firm's industry shifts unexpectedly to the right causing the equilibrium price to rise. In response, the firm’s managers want to raise its output level to 110 units. We distinguish two different cases depending on whether they can change the number of units of capital input or not in their attempt to increase their firm’s output. Case 1 The Long run case: Suppose that the firm’s managers can change the number of units of capital input and those of labour input immediately in order to increase the output. They would move the firm along expansion path OAB in figure 5.a and use optimal combination B = (LB, KB) at the intersection of expansion path OAB and isoquant curve 110. They would increase the number of units of capital input and those of the labour input to maintain the equality of the marginal cost of labour and the marginal cost of capital. The firm would move along its long run average cost curve ABD from A to B in figure 5.b. Its long run average cost would drop from $14 to $10. Figure 5 Long and Short Run Average Total Costs 5.a 5.b Unit costs Capital = K Long Run Average Cost Curve Expansion Path = Long Run direction Short Run Average Total Cost Curve K = KA KB B F 14 A C 13 A Short Run Direction C KA B 10 D Output = 110 E Short Run Average Total Cost Curve Output = 100 K = Minimum Efficiency Size O LA LB LC Labour = L 100 Q = 110 QD QE Output Case 2, The Short Run Case: In the short run, the firm’s managers cannot change the number of units of its capital input immediately. They can increase the number of units of output only by increasing the number of units of labour input. Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 11 In figure 5.a, we use the isoquant corresponding to a level of output equal to 110 units to find the number of units of labour input needed to produce the 110 units of output. To keep the number of units of capital unchanged, the firm’s managers must move along horizontal line AC through combination A because they cannot change the number of units of capital input in the short run which remains equal to K A. This line intersects at point C the isoquant corresponding to 110 units of output. The intersection point LC of the vertical line through point C and the horizontal axis of labour units input gives the required number of units of labour input. The movement from A to C violates the condition of equality of the marginal cost using labour and the marginal cost using capital at the labour capital combination C, a condition that is necessary for ensuring that the labour capital combination C minimizes the total long run cost of producing an output equal to 110 units. Combination C on isoquant 110 in figure 5.a does not minimize the total cost of producing a number of units of output equal to 110 units. Combination B on isoquant 110 units of output does. Thus, the average total cost of producing an output equal to 110 units, by increasing the number of units of labour input while not changing the number of units of capital input, is a short run average total cost and it will be higher than the long run average cost of $10 at B in figure 5.b given by the long run average total cost curve ABDE in figure 5.b. The movement from A to C in figure 5.a corresponds to a movement from A to C in figure 5.b along the short run average total cost curve passing through A. The labour capital combination C = (LC, KA) produces 110 units of output. However, the associated short run average total cost is greater than the long run average total cost of producing 110 units associated with point B in figure 5.a. Point C in Figure 5.b shows that the short run average total cost of producing 110 units of output with an unchanging number of units of capital input equal to KA (as for combination A in figure 5.a) is equal to $13. This short run average total cost of producing 110 units of output is greater than the long run average total cost of $10 of producing 110 units of output represented by the long run average cost at combination B in figure 5.b using the higher number of units of capital input KB as at combination B in figure 5.a. That is, in figure 5.b, the short run average total cost curve AC corresponding to a fixed number of units of capital input equal to KA must lie above the long run average total cost curve ABDE. The two curves have only one point in common, point A, corresponding to an output equal to 100 units. The two curves are tangent at point A. In the long run, the firm’s managers are able to increase the number of units of capital input to KB of combination B in figure 5.a and reduce the number of units of labour input from LC to LB. After the adjustment process is completed, the firm’s managers could move the firm up along the isoquant of output 110 units to combination B in figure 5.a and down the vertical line through point B in figure 5.b to point B on its long run average cost curve ABDE. At B, the firm is capable of producing an output equal to 110 units efficiently at the minimum average cost of $10. In general, for any given output of Q units, for example Q =110 units as in figure 5.a, there is a combination of number of units KB of capital input and a number of units LB of labour input represented by point combination B in figure 5.a that minimizes the total cost of producing output Q and a long run average cost given by QB = $10 in figure 5.b. As illustrated in figure 5.b, with a number of units of capital input equal to KB, there is associated a short run average total cost curve which is tangent to the long run average cost curve at combination B, where output is equal to 110 units. The short run average total cost curve associated with a fixed capital input equal to KB lies entirely above the long run average cost curve except at combination B. Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 12 This property reflects the fact that for any output other than Q = 110 units the capital input K B is inadequate to produce that output in the short run at minimum long run total cost, being either too much or too little. As illustrated in figure 5.b, there are many such short run average total cost curves. The long run average cost curve ABDE is their envelope from below. That is, the long run average cost curve touches each short run average total cost curve only at one point where they are tangent to each other. Minimum Efficiency size Consider the short run average total cost curve in figure 5.b that is tangent to the long run average cost curve ABDE at the minimum point D of the latter. Associated with this curve, there is a number KD of units of capital input that when combined with the appropriate number of units of labour input would produce output QD at the lowest long run average cost possible. We call this number KD of units of capital input the minimum efficiency size. At output levels smaller than the minimum efficiency size such as QD in figure 5.b, there are increasing returns to scale and the corresponding long run average cost is greater than the minimum efficiency size QD. At output levels immediately greater than the minimum efficiency size, there may be constant returns to scale such as along section DE of the long run average cost curve of figure 5.b. Between output levels QD and QE in figure 5.b, the long run average cost is constant and equal to its minimum level. With each one of these output levels, there is associated a number of units of capital input which would achieve the minimum long run average cost when combined with an appropriate number of units of labour input. To each on these levels of output corresponds an associated capital input that is efficient. The smallest level of efficiency size KD of capital input is that corresponding to output QD. The largest level of efficiency size KE of capital input is that corresponding to output QE. When output is greater than the output QE, the corresponding capital input is larger than the largest efficiency size KE, decreasing returns to scale set in and the long run average cost is increasing with the number of units of output produced as section EF of long run average cost curve ABDEF in figure 5.b shows. Long Run Equilibrium under Perfect Competition In the long run under perfect competition, The managers or owners of every firm are able to change the number of units of their firm’s labour and capital inputs at no cost beyond paying respectively their corresponding wage or rental price of capital, Full information including technological know-how is available to every owner and manager of any firm, existing and potential producer, and There is Free Entry and Exit: New or prospective producers can enter or exit the market freely. These characteristics of perfect competition help markets operating under perfect competition achieve an overall efficient allocation of resources. Suppose that market of a product is operating under perfect competition and the short run market equilibrium price of the product is $8 given by the intersection of the market demand curve JP and the market supply curve JK, as shown in figure 6.b below. Figure 6.a describes the unit costs curves of a representative firm of the industry producing this product. It shows that the equilibrium price is greater than the minimum long run average cost of $4. Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 13 At this equilibrium price, every existing firm in the industry can make an economic profit given by the green rectangle ABCD in figure 6.a. This industry is attractive to new comers who can make an economic profit by entering the market with a number of units of capital input corresponding to the minimum efficiency size of 10 units of output and using the appropriate number of units of labour input to achieve the minimum long run average cost of $4. The entry of new firms in the market shifts the market supply curve to the right from JK say to LM in figure 6.b. As figure 6.b shows, this shift causes a fall in the equilibrium price from $8 to say $6. Thus If the market equilibrium price is greater than the minimum long run average cost, there is a pressure on the market equilibrium price to fall. In contrast, suppose now that the market supply curve is TQ as shown in figure 6.b. The market equilibrium price is now $2, lower than the minimum long run average cost of $4. No firm can make an economic profit. In this case every firm would make an economic loss equal to the red rectangle FGHN in figure 6.a. Figure 6 Long Rung Equilibrium in Perfectly Competitive Markets Price Figure 6.a Figure 6.b Price Market Supply Curves K Average Total Cost Curve market Demand Curve Marginal Cost Curve M B J Z A 8 L 6 S D C Minimum Long Run Average Cost E Q 4 N =Long Run Equilibrium Price F 3 R 2 T H G V 0 10 Quantity 0 3000 Quantity Market representative Firm To avoid the losses some of the existing firms either go bankrupt or change their main line of activity. In either case, the market supply curve shifts to the left from TQ to RS as shown in figure 6.b. The market equilibrium price would rise and the economic loss incurred by the remaining firms is lower. Thus If the market equilibrium price is less than the minimum long run average cost, there is a pressure on the market equilibrium price to increase. Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 14 Hence, a market equilibrium price above the minimum long run average cost or below it cannot last for long. When the market equilibrium price is exactly equal to the minimum long run average cost of $4, no firm is making an economic profit and no firm is making an economic loss. Every firm is making a normal profit. This occurs when the market demand curve assumes position VZ as in figure 6 as a result of it shifting right or left through changes in the number of firms. The industry achieves its long run equilibrium as at point E in figure 6.b. No new firms would enter the market and no existing firms would exit. Also in this situation, the long run marginal cost is equal to the short run marginal cost of the minimum efficiency size, It is also equal to the minimum long run average cost. In addition the long run marginal cost at the minimum efficiency size is equal to the marginal social cost. In the long run, markets operating under perfect competition equate marginal social cost, which is equal to the long run marginal cost of producing an additional unit of the product, to its marginal social benefit given by the demand curve as shown at point E in figure 6.b. Furthermore, markets operating under perfect competition produce at the minimum long run average cost by causing an appropriate adjustment of the number of firms in the industry. Each firm is forced to use a level of capital equal to the minimum efficiency size. Each firm has access to this technology because there is free flow of information and no firm has a patent on the technology. Thus, perfectly competitive markets are overall efficient; Adam Smith's invisible hand has done its job. Finally, we can compute the appropriate number of firms at the long run equilibrium of a market operating under perfect competition by dividing the total quantity demanded and produced of 3000 units of the product at the long run equilibrium of figure 6.b and the output of 10 units at the minimum long run average cost as given in figure 6.a. The number of firms at the long run equilibrium is equal to 300 firms = (3000/10). Externalities There are two kinds of Externalities: Positive Externalities or External Economies and Negative Externalities or External Diseconomies. Positive Externalities Positive externalities occur when the minimum of the long run average cost of a representative firm in an industry decreases as the output of another industry or another firm increases. The best example of a positive externality is that of an apple orchard farm and a honey producer. When the farmer plants more apple trees, there will be more flowers. The bees of the honey producer will be able to collect more nectar and produce more honey. For the same total cost, the honey producer can produce more honey. Her long run average cost decreases. An increase in average income causes a rightward shift of the demand curve for apples as from HJ to KL in figure 7.b. The equilibrium in the apple market shifts from E 0 to E1. The equilibrium output of apples increases from 2000 units to 3000 units. Farmers plant more apple trees. Consequently, there will be more flowers and nectar food for bees. Honey producers are able to produce more honey at the same total cost. Average total cost of honey falls and the long run average cost curve shifts down as in figure 7.a from DFG to ABC. Figure 7 Positive Externalities Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 15 Figure 7.a Figure 7.b Price Price Long Run Average Cost Curve Before Demand Curve After Increase in Apple Production Demand Curve Before Increase Increase G N D K E1 C Supply H Curve A 8 F L E0 B 4 M Long Run Average Cost Curve After J 3 Increase in Apple Production 0 10 Quantity 0 2000 3000 Quantity Apple Market Honey Producer Under perfect competition, the long run equilibrium price of honey falls from $8 to $4 and equilibrium output and consumption of honey rise. As we shall see later, the resulting overall equilibrium in both markets does not represent an efficient allocation of resources. Negative Externalities Negative externalities occur when the minimum of the long run average cost of a representative firm in an industry increases as the output of an industry or another firm increases. The best example of a negative externality is that of a steel plant and a fisherman. When its output increases, a steel mill dumps more effluent or sludge in a river. This raises the temperature of the water and kills a lot of fish. The output of the fisherman decreases for the same total cost. Thus his average total cost rises. Figure 8 Negative Externalities Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 16 Figure 7.a Figure 7.b Price Price Long Run Average Cost Curve After Demand Curve After Demand Curve Before Increase in Steel Production Increase Increase G N D K E1 C Supply H Curve A F L 8 E0 B 4 M 3 Long Run Average Cost Curve Before J Increase in Steel Production 0 10 Quantity of fish 0 2000 3000 Quantity Fish Production Steel Market Let an increase in the average income cause a rightward shift of the demand curve of steel as from HJ to KL in figure 8.b. The equilibrium in the steel market shifts from E 0 to E1. The equilibrium output of steel increases from 2000 units to 3000 units. As a result, the water temperature down the river rises and kills a lot of fish. Fishermen produce less fish at the same total cost. Average total cost of fish rises and the long run average cost curve shifts upward as in figure 8.a from ABC to DFG. Under perfect competition, the long run equilibrium price of fish rises from $4 to $8 and equilibrium output and consumption of fish falls. As we shall find out in a later chapter, the resulting overall equilibrium in both markets does not result in an efficient allocation of resources. The equality of the long run marginal cost and the marginal social is not valid anymore. Conclusions Since the middle of the twentieth century, privatization has become a common currency among most politicians and many economists. They extol the virtues of private markets but fail to explain to the public that there are many kinds of private markets. Only markets operating nearly under perfect competition in the absence of externalities are efficient in the long run. Markets operating under perfect competition produce an efficient allocation of resources because free entry and exit and complete information are available to every existing or potential producer and consumer. In the long run, all costs are variable costs. When perfect competition prevails; there is free entry and exit, and full information including technological know-how and there are no patents that protect their owner’s economic profit for a long time in excess of the costs incurred to produce better technology. Under perfect competition, every producer or supplier must operate in the long run at the minimum of a common long run average cost curve, To minimize the total cost of producing any given output, a producer chooses the capital and labour inputs so that the marginal productivity of capital and the marginal productivity of labour are proportional to the rental price of capital and the wage rate. Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 17 The rental price of capital is equal to (the interest rate plus the deprecation rate of physical capital) times the price of a unit of physical capital. At a given output, the optimal labour capital combination is that which minimizes the total cost of producing that output. The long run total cost is equal to the sum of the rental price of capital times the optimal number of units of capital plus the wage rate times the optimal number of units of labour (we abstract from including the cost of raw material or other processed products, which we ignore for simplicity). The long run average cost is the long run total cost divided by the corresponding number of units of output. At any given level of output, the long run average total cost is always less than the short run average total cost except when the number of units of capital input is equal to the optimal number of units of capital input corresponding to that output. In the latter case, the two average costs are equal and we use the term long run average cost to refer to both. Starting from a zero output level, an increase in output lowers the long run average total cost due to increasing returns and greater specialization. This is the region of increasing returns to scale as both the capital and labour inputs are increased in the appropriate way. At a large enough output, the long run average total cost reaches a minimum and levels off. For a certain range of output thereafter, the long run average cost may remain constant. This is the region of constant returns to scale. At the end of the region of constant returns of scale, the long run average cost starts to increase due to increasingly higher management and communications costs and lower workers motivation. This is the region of decreasing returns to scale and increasing long run average cost. The minimum efficiency size is equal to the optimal number of units of capital input corresponding to the output level at which the long run average cost stops falling and reaches its minimum. In the short run, given the number of units of capital input or capital stock, a producer maximizes total economic profit by producing and supplying an output at which marginal cost is equal to the market equilibrium price. Because he/she cannot change the capital stock without paying a great cost, a producer may make a negative (loss) or a positive economic profit in the short run depending on the relative position of the market demand and supply curves and the size of her/his capital stock. In the long run, there is free entry and exit and producers can change their capital stock. In the long run, free entry and exit insures that a producer cannot earn a positive or a negative economic profit. When there is a positive economic profit, new producers enter in the market with a capital stock equal to the minimum efficiency size, attracted by the positive economic profit. Their entry shifts the market supply curve to the right and causes a fall in the market equilibrium price. The entry of new producers continues until the price is driven down to a level equal to the minimum long run average cost. When this happens the market equilibrium price stops falling. The market has reached its long run equilibrium. If there is a negative economic profit, given enough time every producer will change or he/she will be forced to change his/her capital stock to make it equal to the minimum efficiency size in order to avoid the negative economic profit. If the total economic profit is still negative, some producers will exit. The market supply curve will shift to the left causing the market equilibrium price to increase and the total economic profit of every producer increases (the total economic loss decreases). The exit of some producers continues until the equilibrium price has reached the minimum long run average cost. When this happens the market equilibrium price stops rising. The market has reached its long run equilibrium. In the process, total economic profit maximization requires that every remaining producer must equate his/her corresponding marginal cost to the market equilibrium price. Furthermore, he/she will choose the minimum efficiency size where the market equilibrium price is equal to the minimum long Chapter 8: Long run Supply and Equilibrium under perfect Competition, 8/20/2024 4:22 PM, 8- 18 run average cost. Thus, at this stage the marginal cost is the same for all producers and it is equal to the minimum long run total cost equal to the marginal social cost. In the long run equilibrium, Total economic profit is zero. Market equilibrium price is equal to the minimum long run average cost, Marginal social cost is equal to marginal social benefit since both of them are equal to the long run market equilibrium price. The number of producers is that number that makes the market supply curve intersect the market demand curve at a price equal to the minimum long run average cost. The producers produce the equilibrium quantity of the product at the minimum long run average cost. Perfect competition produces an efficient allocation of resources and maximizes total net social benefit. When the demand curve shifts in either direction, the number of producers adjusts in the long run to bring the market supply curve to intersect the new market demand curve at a price equal to the minimum long run average cost. Other things equal, the only way to lower the equilibrium price is through technological improvement including better organization. External positive economies can also lower the minimum long run average cost. External positive economies occurs when an expansion in the economic activity in the industry as a whole or in other industries causes a reduction in the number of units of services used by the industry of some factors of production per unit of output or an increase in the industry's output for the same number of units of services of every factor of production used in the industry. In contrast, external negative economies raise the minimum long run average cost of every producer in the industry. External negative economies occurs when an expansion in the economic activity in the industry as a whole or in other industries causes an increase in the number of units of services used by the industry of some factor of production per unit of output or a reduction in the industry's output for the same number of units of services of every factor of production used in the industry. With the help of the concepts developed in this chapter and the previous chapters, we are now ready to confront the murky real world of posturing and monopolization of productive activity.. Otherwise, he/she can increase economic profit by increasing or decreasing the capital input and changing the labour input correspondingly.