The New Age firm produces clean coal. New Age's production function is given by q = L3S3, where L denotes la and S denotes its cutting-edge machinery. The price of labor is given by the wage, w, and price of machiner denoted pc. 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 sentenc 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 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. d. Compute marginal cost (MC(q) = C) and show that it is increasing, i.e., . > 0. C. амс Sa aMPL SL <0.

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Short-Run Costs and Long-Run Costs

Cost of short-run and the long-run is an economic term that describes the cost involved in the production of goods in a firm in the short as well as long period.