1. The New Age firm produces clean coal. New Age's production function is given by q = L3S3, where L denotes labor and S denotes its cutting-edge machinery. The price of labor is given by the wage, w, and price of machinery is denoted ps. Suppose that in the short run number of machines is fixed at 5 = 1 while L is variable. a. Write down the expression for the short-run production function. In no more than two sentences, describe the fundamental difference between the short-run and long-run time horizons in production. b. Invert the short-run production and derive variable costs, VC(q) = wL(q), where labor is a function of the level of output L(q). Next derive fixed costs and the short run cost function, C(q). Compute the marginal productivity of labor (MPL) and show that MPL is diminishing, i.e. C. OMPL SL < 0.

1. The New Age firm produces clean coal. New Age's production function is given by q = L3S3, where L denotes labor and S denotes its cutting-edge machinery. The price of labor is given by the wage, w, and price of machinery is denoted ps. Suppose that in the short run number of machines is fixed at 5 = 1 while L is variable. a. Write down the expression for the short-run production function. In no more than two sentences, describe the fundamental difference between the short-run and long-run time horizons in production. b. Invert the short-run production and derive variable costs, VC(q) = wL(q), where labor is a function of the level of output L(q). Next derive fixed costs and the short run cost function, C(q). Compute the marginal productivity of labor (MPL) and show that MPL is diminishing, i.e. C. OMPL SL < 0.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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