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PRODUCTION As always, the firm will organize its means of production to maximize profit. Chapter 5 slide 1 To do this it must balance input productivity and input costs. The firm ’ s production function: Q = F(L, K), lists the amount of output it can produce with specified amounts of labor and capital.

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PRODUCTION in the SHORT RUN In the short run, only 1 input is variable and the other inputs are fixed. 5.2 For instance, with the firm ’ s plant and capital fixed, it increases output by using more and more labor hours. The “ Law ” of Diminishing Returns: With other inputs fixed, the marginal product of labor declines as more and more hours are added.

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PRODUCTION in the SHORT RUN Optimal use of the Variable Input 5.3 occurs at L* where Marginal Revenue Product = MC INPUT, P MP L = Wage. Example. Q = 60L – L 2, P = $2 per unit, and wage = $16 per hour. Then, MP L = 60 – 2L, so we have (2)(60 – 2L) = 16, implying, L* = 26 hours. In turn, Q* = (60)(26) – (26) 2 = 884 units, and Profit = ($2)(884) – ($16)(26) = = $1,352.

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PRODUCTION in the LONG RUN In the long run, the firm can vary all its inputs and change the “ scale ” of its operations. 5.4 Returns to Scale measures the percentage change in output for a given percentage change in all inputs. Constant Returns to Scale Increasing Returns to Scale Decreasing Returns to Scale

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LONG RUN DECISIONS In the long run, how can the firm produce a given quantity of output at least cost? 5.5 By equating the ratios of MPs to input costs for all inputs: MP L /P L = MP K /P K Capital Labor Isoquant, Q = 636 Graphic Demonstration Cost Line (C = $220) L*=10 K* = 8 Isoquant Slope: MRTS = MP L /MP K Cost Line Slope: P L /P K At the optimal tangency: MP L /MP K = P L /P K, which (after rearrangement) is equivalent to condition above.

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MEASURING PRODUCTION FUNCTIONS Linear Production: Q = aL + bK. Isoquants are straight lines. Input allocation is “ all or nothing. ” 5.6 Fixed Proportions: No substitution between inputs Cobb-Douglas: Q = cL K (1) Each input has diminishing returns. (2) Returns to scale depends on whether + or = 1.

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MAXIMIZING PROFIT W/ LIMITED IMPUTS How should the firm allocate crude oil Across two of its production facilities? 5.7 Answer: The allocation should ensure that the plants ’ marginal products are equal. MP A = MP B Example Refinery A: Q = 24M A -.5M A 2 Refinery B: Q = 20M B – M B 2 M A + M B = 10 thousand barrels of oil Equating MP A = MP B implies 24 – M A = 20 – 2M B. The solution to these simultaneous equations is: M A = 8 and M B = 2.

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