# 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.

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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.

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.

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.

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

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.

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.

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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