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## Chapter 5: Production and Cost

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**Chapter 5: Production and Cost**Brickley, Smith, and Zimmerman, Managerial Economics and Organizational Architecture, 4th ed.**Production and costobjectives**Students should be able to • Write a production function and distinguish between returns to scale and returns to a factor • Use isocosts and isoquants to illustrate production trade-offs • Employ short- and long-run cost curves to describe firm characteristics**Production functions**A production function specifies maximum output from given inputs:**Empirical production functions**• Cubic Q=a0+a1XY+a2X2Y+a3XY2+a4X3Y+a5XY3 • Cobb-Douglas Q = aXbYc log Q = log a + b log X + c log Y**Returns to scale**Defined: The relation between output and a proportional variation of all inputs together Increasing returns to scale:Q=KL Decreasing returns to scale:Q=K1/3L1/3 Constant returns to scale:Q=K1/2L1/2**Returns to a factor**Returns to a factor refer to the relation between output and variation in only one input • Total product • Average productQ/L • Marginal productQ/L**Returns to a factor**Production function: Q=S1/2A1/2**Illustrating production choices with isoquants**• Isoquants portray technical combination of inputs to produce a given level of output • Shape of isoquants indicates substitutability between inputs**Isocost lines**• Isocosts portray combinations of inputs that entail the same cost • Isocosts change as input prices change**Optimal input mix**Where MPi is the marginal product of input i and Piis the price of input i.**Cost concepts**• Total cost • relation between total cost and output • Marginal cost • change in total cost when output rises one unit • Average cost • total cost divided by total output • Opportunity cost • value of best alternative resource use**Short run versus long run**• Short run • at least one input is fixed • cost curves are operating curves • Long run • all inputs are variable • cost curves are planning curves • Fixed costs--incurred even if firm produces nothing • Variable costs--change with the level of output**Long-run average costenvelope of short-run average cost**curves**Additional cost concepts**• Minimum efficient scale • plant size at which long-run average cost first reaches its minimum point (Q*) • Economies of scope • cost of producing a joint set of products is less than cost of producing separately in separate firms • Learning curves • costs decline with production experience**Profit maximization**• A firm should increase output as long as marginal revenue exceeds marginal cost • A firm should not increase output if marginal cost exceeds marginal revenue • At the profit-maximizing level of output, MR=MC**Factor demand**Efficient production requires that MPi/Pi= MPj/Pj The reciprocals represent marginal cost Pi/MPi=Pj/MPj=MC At the optimum output level Pi/MPi=MR From which we derive the demand curve for input i Pi=MRMPi**Cost estimation**• Effective management decisions should incorporate estimates of short- and long-run costs • Use regression analysis • Short-run costs may be approximately linear VC = a + bQ