The production function of a firm is as follows: y(K,L) = 500 1 -KLOS, where Kis capital measured in machine-hours, L is labor in person-hours, and y is the yearly output. The hourly wage rate, w, is Ł10, and the hourly rental rate of capital, r, is £20. a. Show what type of returns to scale the technology of this firm displays (constant, increasing, or decreasing). b. Calculate the marginal products of labor and capital. c. Derive the firm's short-run cost function (as a function of output given the factor prices) if the capital is fixed at 10,000 machine hours. Start with setting the short-run cost minimization problem of the firm subject to the technology constraint. d. Derive the firm's short-run marginal cost function and the short-run average cost function. At what level of output do these curves intersect? Show that at this point, the average cost function is at its minimum.

The production function of a firm is as follows: y(K,L) = 500 1 -KLOS, where Kis capital measured in machine-hours, L is labor in person-hours, and y is the yearly output. The hourly wage rate, w, is Ł10, and the hourly rental rate of capital, r, is £20. a. Show what type of returns to scale the technology of this firm displays (constant, increasing, or decreasing). b. Calculate the marginal products of labor and capital. c. Derive the firm's short-run cost function (as a function of output given the factor prices) if the capital is fixed at 10,000 machine hours. Start with setting the short-run cost minimization problem of the firm subject to the technology constraint. d. Derive the firm's short-run marginal cost function and the short-run average cost function. At what level of output do these curves intersect? Show that at this point, the average cost function is at its minimum.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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