Bài giảng Managerial Economics - Chapter 09: Production and Cost in the Long Run

Chapter 9: Production and Cost in the Long RunMcGraw-Hill/IrwinCopyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.Production IsoquantsIn the long run, all inputs are variable & isoquants are used to study production decisionsAn isoquant is a curve showing all possible input combinations capable of producing a given level of outputIsoquants are downward sloping; if greater amounts of labor are used, less capital is required to produce a given outputA Typical Isoquant Map (Figure 9.1)Production Function8-4Typical Isoquants9-5Marginal Rate of Technical SubstitutionThe 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 outputThe minus sign is added to make MRTS a positive number since ∆K / ∆L, the slope of the isoquant, is negativeThe MRTS can also be expressed as the ratio of two marginal products:Marginal Rate of Technical SubstitutionAs labor is substituted for capital, MPL declines & MPK rises causing MRTS to diminish6–8Marginal Rate of Technical SubstitutionSlope of production isoquantSlope of production isoquant reflects relative marginal product of labor and capitalIsocost 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 purchasedIsocost curve. Isocost Curves (Figures 9.2 & 9.3)Optimal Combination of InputsTwo slopes are equal in equilibriumImplies 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 Optimal Input Combination to Minimize Cost for Given Output (Figure 9.4)Optimal Allocation of InputsIs the firm using the right combination of inputs?If not, how should the firm reallocate its expenditure?Use the last dollar ruleOptimal Allocation of InputsOutput Maximization for Given Cost (Figure 9.5)Optimization & CostExpansion path gives the efficient (least-cost) input combinations for every level of outputDerived for a specific set of input pricesAlong expansion path, input-price ratio is constant & equal to the marginal rate of technical substitutionExpansion Path (Figure 9.6)Long-Run CostsLong-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 outputLong-Run CostsLong-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 employedLAC is U-shaped Falling LAC indicates economies of scaleRising LAC indicates diseconomies of scaleLong-Run CostsLong-run marginal cost (LMC) measures the rate of change in long-run total cost as output changes along expansion pathLMC is U-shaped LMC lies below LAC when LAC is fallingLMC lies above LAC when LAC is risingLMC = LAC at the minimum value of LACDerivation of a Long-Run Cost Schedule (Table 9.1) Least-cost combination ofOutputLabor (units)Capital (units)Total cost(w = $5, r = $10)LACLMC100500600200300400700LMC10405212203060 72230 8101542 $120420560 140200300720 $1.200.840.93 0.700.670.751.03 $1.201.201.40 0.200.601.001.60Long-Run Total, Average, & Marginal Cost (Figure 9.8)Long-Run Average & Marginal Cost Curves (Figure 9.9)Economies of ScaleLarger-scale firms are able to take greater advantage of opportunities for specialization & division of laborScale economies also arise when quasi-fixed costs are spread over more units of output causing LAC to fallVariety of technological factors can also contribute to falling LAC9-26Returns to ScaleIf all inputs are increased by a factor of c & output goes up by a factor of z then, in general, a producer experiences:Increasing returns to scale if z > c; output goes up proportionately more than the increase in input usageDecreasing returns to scale if z < c; output goes up proportionately less than the increase in input usageConstant returns to scale if z = c; output goes up by the same proportion as the increase in input usagef(cL, cK) = zQReturns to Scale9-27Economies & Diseconomies of Scale (Figure 9.10)Constant Long-Run CostsAbsence of economies and diseconomies of scaleFirm experiences constant costs in the long runLAC curve is flat & equal to LMC at all output levelsConstant Long-Run Costs (Figure 9.11)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 costMinimum Efficient Scale (MES) (Figure 9.12)MES with Various Shapes of LAC (Figure 9.13)Economies of ScopeExist 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 Purchasing Economies of ScalePurchasing economies of scale arise when large-scale purchasing of raw materials enables large buyers to obtain lower input prices through quantity discountsPurchasing Economies of Scale (Figure 9.14)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 levelLearning or Experience Economies (Figure 9.15)Relations Between Short-Run & Long-Run CostsLMC intersects LAC when the latter is at its minimum pointAt each output where a particular ATC is tangent to LAC, the relevant SMC = LMCFor 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 LACLong-Run Average Cost as the Planning Horizon (Figure 9.16)Restructuring Short-Run CostsBecause 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 levelShort-run costs can be reduced by adjusting fixed inputs to their optimal long-run levels when the opportunity arisesRestructuring Short-Run Costs (Figure 9.14)