9-1 Learning Objectives  Graph a typical production isoquant and discuss the properties of isoquants  Construct isocost curves  Use optimization theory to find optimal input combination  Construct the firm’s expansion path and show how it relates to the firm’s long-run cost structure  Calculate long-run total, average, and marginal costs  Explain how a variety of forces affect long-run costs: scale, scope, learning, and purchasing economies.  Show the relation between long-run and short-run cost curves using long-run and short-run expansion paths

9-2 Production Isoquants  In the long run, all inputs are variable & isoquants are used to study production decisions ~An isoquant is a curve showing all possible input combinations physically capable of producing a given level of output ~Isoquants are downward sloping; if greater amounts of labor are used, less capital is required to produce a given output

9-3 A Typical Isoquant Map (Figure 9.1)

9-4 Marginal Rate of Technical Substitution  The MRTS is the slope of an isoquant & measures the rate at which the two inputs can be substituted for one another along an isoquant while maintaining a constant level of output The minus sign is added to make MRTS a positive number since ∆K/∆L, the slope of the isoquant, is negative

9-5 Leontif Production Y=min(AL, BK), allows no substitution between K & L, they are perfect complements

9-6  Does the marginal rate of technical substitution vary along the isoquant for the firm that produced potato salad using Idaho and Maine potatoes? What is the MRTS at each point along the isoquant?

9-7 Isoquant Answer  The potato salad isoquants are straight lines because the two types of potatoes are perfect substitutes.  The slope is the same at every point, so the MRTS is constant.  MRTS is -1 at each point along the isoquant. Because the two inputs are perfect substitutes, 1 lb of Idaho potatoes can be replaced by 1lb of Maine potatoes.

9-8  The MRTS can also be expressed as the ratio of two marginal products: Marginal Rate of Technical Substitution As labor is substituted for capital, MP L declines & MP K rises causing MRTS to diminish

9-9 Isocost Curves  Show various combinations of inputs that may be purchased for given level of expenditure (C) at given input prices (w, r)  Slope of an isocost curve is the negative of the input price ratio (-w/r)  K - intercept is C/r ~ Represents amount of capital that may be purchased if zero labor is purchased

Copyright ©2015 Pearson Education, Inc. All rights reserved.7-10 Table 7.2 Bundles of Labor and Capital That Cost the Firm $200

Copyright ©2015 Pearson Education, Inc. All rights reserved.7-11 Figure 7.4 A Family of Isocost Lines K, Units of capital per y ear a d e $200 isocost L, Units of labor peryear $200 $20 10 = $200 $10 = 20 Isocost Equation K = r - L w r C Initial Values C = $200 w = $10 r = $ c b  L = 5  K = 2.5 For each extra unit of capital it uses, the firm must use two fewer units of labor to hold its cost constant. Slope = -1/2 = w/r

Copyright ©2015 Pearson Education, Inc. All rights reserved.7-12 Figure 7.4 A Family of Isocost Lines (cont.) K, Units of capital per y ear a e $300 isocost$200 isocost L, Units of labor peryear $200 $20 15 = $200 $20 10 = $200 $10 = 20 $300 $10 = 30 Isocost Equation K = r - L w r C C = $300 w = $10 r = $20 An increase in C….

Copyright ©2015 Pearson Education, Inc. All rights reserved.7-13 Combining Cost and Production Information The firm can choose any of three equivalent approaches to minimize its cost: –Lowest-isocost rule - pick the bundle of inputs where the lowest isocost line touches the isoquant. –Tangency rule - pick the bundle of inputs where the isoquant is tangent to the isocost line. –Last-dollar rule - pick the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input.

Copyright ©2015 Pearson Education, Inc. All rights reserved.7-14 Figure 7.5 Cost Minimization K, Units of capital per hour 500 L, Units of labor per hour $3,000 isocost $2,000 isocost $1,000 isocost Which of these three Isocost would allow the firm to produce the 100 units of output at the lowest possible cost? Isocost Equation K = r - L w r C Initial Values q = 100 w = $24 r = $8 Isoquant Slope MP L MP K =MRTS -

Copyright ©2015 Pearson Education, Inc. All rights reserved.7-15 Figure 7.5 Cost Minimization K, Units of capital per hour L, Units of labor per hour q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost x Isocost Equation K = r - L w r C Initial Values q = 100 C = $2,000 w = $24 r = $8 Isoquant Slope MP L MP K =MRTS - y z

Copyright ©2015 Pearson Education, Inc. All rights reserved.7-16 Cost Minimization At the point of tangency, the slope of the isoquant equals the slope of the isocost. Therefore, last-dollar rule: cost is minimized if inputs are chosen so that the last dollar spent on labor adds as much extra output as the last dollar spent on capital.

Copyright ©2015 Pearson Education, Inc. All rights reserved.7-17 Figure 7.5 Cost Minimization K, Units of capital per hour y x z L, Units of labor per hour q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost Spending one more dollar on labor at x gets the firm as much extra output as spending the same amount on capital. Initial Values q = 100 C = $2,000 w = $24 r = $8 w r MP L MP K = MP L = 0.6q/L MP K = 0.4q/K = = = 0.05

Copyright ©2015 Pearson Education, Inc. All rights reserved.7-18 Figure 7.5 Cost Minimization K, Units of capital per hour y x z L, Units of labor per hour q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost if the firm shifts one dollar from capital to labor, output falls by because there is less capital but also increases by 0.1 because there is more labor for a net gain of more output at the same cost…. So …the firm should shift even more resources from capital to labor— which increases the marginal product of capital and decreases the marginal product of labor. Initial Values q = 100 C = $2,000 w = $24 r = $8 w r MP L MP K MP L = 0.6q/L MP K = 0.4q/K = = = 0.1 = 0.017

9-19 Optimal Combination of Inputs ~Two slopes are equal in equilibrium ~Implies marginal product per dollar spent on last unit of each input is the same  Minimize total cost of producing a given Q by choosing the input combination on the isoquant for which Q is just tangent to an isocost curve

9-20 Optimal Input Combination to Minimize Cost for Given Output (Figure 9.4)

9-21 Output Maximization for Given Cost (Figure 9.5)

9-22 Optimization & Cost  Expansion path gives the efficient (least- cost) input combinations for every level of output ~Derived for a specific set of input prices ~Along expansion path, input-price ratio is constant & equal to the marginal rate of technical substitution

9-23 Expansion Path (Figure 9.6)

9-24 Change in capital cost Cost of K falls, leads to steeper curve & substitution between K and L. Firm has choice between same cost (B) or same output (C) with lower costs (similar to lower budget in consumer theory – has higher profit than A.

9-25 What does the US & India Look like?

9-26 Long-Run Costs  Long-run total cost (LTC) for a given level of output is given by: LTC = wL * + rK * Where w & r are prices of labor & capital, respectively, & (L *, K * ) is the input combination on the expansion path that minimizes the total cost of producing that output

9-27 Long-Run Costs  Long-run average cost (LAC) measures the cost per unit of output when production can be adjusted so that the optimal amount of each input is employed ~ LAC is U-shaped ~Falling LAC indicates economies of scale ~Rising LAC indicates diseconomies of scale

9-28 Long-Run Costs  Long-run marginal cost (LMC) measures the rate of change in long-run total cost as output changes along expansion path ~ LMC is U-shaped ~ LMC lies below LAC when LAC is falling ~ LMC lies above LAC when LAC is rising ~ LMC = LAC at the minimum value of LAC

9-29 Derivation of a Long-Run Cost Schedule (Table 9.1) Least-cost combination of OutputLabor (units) Capital (units) Total cost (w = $5, r = $10) LAC LMC LMC $ $ $

9-30 Long-Run Total, Average, & Marginal Cost (Figure 9.8)

9-31 Long-Run Average & Marginal Cost Curves (Figure 9.9)

9-32 Economies of Scale  Larger-scale firms are able to take greater advantage of opportunities for specialization & division of labor  Scale economies also arise when quasi- fixed costs are spread over more units of output causing LAC to fall  Variety of technological factors can also contribute to falling LAC

9-33 Economies & Diseconomies of Scale (Figure 9.10)

9-34 The Learning Curve  Learning by doing - the productive skills and knowledge that workers and managers gain from experience.

9-35 Learning by Doing

9-36 Why Costs Fall over Time  Technological or organizational progress may increase productivity.  Operating at a larger scale in the long run may lower average costs due to increasing returns to scale.  The firm’s workers and managers may become more proficient over time due to learning by doing.

9-37 Constant Long-Run Costs  Absence of economies and diseconomies of scale ~Firm experiences constant costs in the long run ~ LAC curve is flat & equal to LMC at all output levels

9-38 Constant Long-Run Costs (Figure 9.11)

9-39 Minimum Efficient Scale (MES)  The minimum efficient scale of operation (MES) is the lowest level of output needed to reach the minimum value of long-run average cost

9-40 Minimum Efficient Scale (MES) (Figure 9.12)

9-41 MES with Various Shapes of LAC (Figure 9.13)

9-42 Economies of Scope  Exist for a multi-product firm when the joint cost of producing two or more goods is less than the sum of the separate costs for specialized, single-product firms to produce the two goods: LTC(X, Y) < LTC(X,0) + LTC(0,Y)  Firms already producing good X can add production of good Y at a lower cost than a single-product firm can produce Y: LTC(X, Y) – LTC(X,0) < LTC(0,Y)  Arise when firms produce joint products or employ common inputs in production

9-43 Purchasing Economies of Scale  Purchasing economies of scale arise when large-scale purchasing of raw materials enables large buyers to obtain lower input prices through quantity discounts

9-44 Purchasing Economies of Scale (Figure 9.14)

9-45 Learning or Experience Economies  “Learning by doing” or “Learning through experience”  As total cumulative output increases, learning or experience economies cause long-run average cost to fall at every output level

9-46 Learning or Experience Economies (Figure 9.15)

9-47 Relations Between Short-Run & Long-Run Costs  LMC intersects LAC when the latter is at its minimum point  At each output where a particular ATC is tangent to LAC, the relevant SMC = LMC  For all ATC curves, point of tangency with LAC is at an output less (greater) than the output of minimum ATC if the tangency is at an output less (greater) than that associated with minimum LAC

9-48 Long-Run Average Cost as the Planning Horizon (Figure 9.16)

9-49 Application: Long-Run Cost Curves in Beer Manufacturing

9-50 Restructuring Short-Run Costs  Because managers have greatest flexibility to choose inputs in the long run, costs are lower in the long run than in the short run for all output levels except that for which the fixed input is at its optimal level ~Short-run costs can be reduced by adjusting fixed inputs to their optimal long-run levels when the opportunity arises

9-51 Restructuring Short-Run Costs (Figure 9.14)

9-52 Summary  In the long run, all fixed inputs become variable inputs ~An isoquant is a curve showing all possible input combinations capable of producing a given level of output ~The marginal rate of technical substitution, MRTS, is the slope of an isoquant and measures the rate at which the two inputs can be substituted for one another while maintaining a constant level of output  Isocost curves show the various combinations of inputs that may be purchased for a given level of expenditure at given input prices ~The isocost curve’s slope is the negative of the input price ratio

9-53 Summary  Minimize total cost of producing a given quantity of output by choosing the input combination on the isoquant that is just tangent to an isocost curve ~The two slopes are equal in equilibrium ~Maximizing output for a given level of expenditure requires choosing an input combination satisfying the exact same conditions as for minimizing costs  The expansion path shows the optimal (or efficient) input combination for every level of output; long-run cost curves are derived from the expansion path  LMC lies below (above) LAC when LAC is falling (rising); LMC equals LAC at LAC ’s minimum value

9-54 Summary  When LAC is decreasing, economies of scale are present, and when LAC is increasing, diseconomies of scale are present; Economies of scope arise when firms produce joint products or when firms employ common inputs in production  Because managers possess the greatest flexibility in choosing inputs in the long run, long-run costs are lower than short-run costs for all output levels except the output level for which the short-run fixed input is at its optimal level