Chapter 9: Production and Cost in the Long Run McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

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 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 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 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

9-6 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

9-7 Isocost Curves (Figures 9.2 & 9.3)

9-8 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 Q by choosing the input combination on the isoquant for which Q is just tangent to an isocost curve

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

9-10 Output Maximization for Given Cost (Figure 9.5)

9-11 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

9-12 Expansion Path (Figure 9.6)

9-13 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

9-14 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

9-15 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

9-16 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 $ $ $

9-17 Long-Run Total, Average, & Marginal Cost (Figure 9.8)

9-18 Long-Run Average & Marginal Cost Curves (Figure 9.9)

9-19 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

9-20 Economies & Diseconomies of Scale (Figure 9.10)

9-21 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

9-22 Constant Long-Run Costs (Figure 9.11)

9-23 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

9-24 Minimum Efficient Scale (MES) (Figure 9.12)

9-25 MES with Various Shapes of LAC (Figure 9.13)

9-26 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

9-27 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

9-28 Purchasing Economies of Scale (Figure 9.14)

9-29 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

9-30 Learning or Experience Economies (Figure 9.15)

9-31 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

9-32 Long-Run Average Cost as the Planning Horizon (Figure 9.16)

9-33 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

9-34 Restructuring Short-Run Costs (Figure 9.14)