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**Chapter 5: Production and Cost**

Brickley, Smith, and Zimmerman, Managerial Economics and Organizational Architecture, 4th ed. Chapter 5: Production and Cost

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**Production and cost objectives**

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

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Production functions A production function specifies maximum output from given inputs:

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**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

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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

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Returns to a factor Returns to a factor refer to the relation between output and variation in only one input Total product Average product Q/L Marginal product Q/L

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**Production function: Q=S1/2A1/2**

Returns to a factor Production function: Q=S1/2A1/2 S A Q MPS APS 1 9 3.00 2 4.24 1.24 2.12 3 5.20 0.96 1.73 4 6.00 0.80 1.50 5 6.70 0.70 1.34

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**Returns to a factor a common case**

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**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

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**Optimal input combination isoquants**

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**Differing input substitutability isoquants**

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Isocost lines Isocosts portray combinations of inputs that entail the same cost Isocosts change as input prices change

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Isocost lines

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**Isocost lines changes in input prices**

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Optimal input mix Where MPi is the marginal product of input i and Pi is the price of input i.

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Cost minimization

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**Optimal input mix input price changes**

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**Cost concepts Total cost Marginal cost Average cost Opportunity 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

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Cost curves

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**Short run versus long 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

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Short-run cost curves

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**Long-run average cost envelope of short-run average cost curves**

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**Long-run average and marginal cost curves**

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**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

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Learning curve

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**Economies of scale versus learning effects**

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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

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**Optimal output and changes in marginal cost**

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**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

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Factor demand curve

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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

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