Part 1) Consider the Cobb-Douglas production function: Y = AK'-ªLª. where K and L are the capital stock and labor uses respectively. Consider that the economy is composed of a representative firm that maximizes profits by hiring L workers and paying them some real wage w, for a total wage bill of wL The firm also rents capital K at a rate r, paying rK. Labor and capital are its only costs. a) Define the labor share and the capital share of income. What do they represent? b) Write the firm's profit function. c) Calculate the firm's choice of labor and capital inputs, taking prices as given.

Part 1) Consider the Cobb-Douglas production function: Y = AK'-ªLª. where K and L are the capital stock and labor uses respectively. Consider that the economy is composed of a representative firm that maximizes profits by hiring L workers and paying them some real wage w, for a total wage bill of wL The firm also rents capital K at a rate r, paying rK. Labor and capital are its only costs. a) Define the labor share and the capital share of income. What do they represent? b) Write the firm's profit function. c) Calculate the firm's choice of labor and capital inputs, taking prices as given.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Please continue to solve from Part d to Part f. Thank you.
3. Suppose a firm has the following production function q = LK4. Let the unit price of capital be 1 and the unit price of labour be w. a) Use the Lagrangian method to find the optimal number of each input used to produce an order of q'units b) Find the long-run cost function. c) How does the cost function change if the wage rate changes?