ECON 4531, Labor Economics

Text: Labor Economics, Borjas, 8th edition

Problem 3

In this problem, you can assume all solutions are interior.

Suppose the hourly wage is $w and the price of each unit of capital is $r. The price of output is constant at $p per unit. The production function is

f(E,K) = E^1/5K^1/2

(a) How much labor and capital should the firm use in the long run as functions of w, r and p?

(b) Now, assume p = 50, w = 20 and r = 20. What is the value of the firm's labor and capital demand based on what you derived in (a)?

(c) Now, assume p = 50, w = 15 and r = 20. What is the value of the firm's labor and capital demand based on what you derived in (a)?

(d) Find substitution and scale effects from (b) to (c). Include a table like the one at the end of this document. Not just with the signs but the actual values of substitution and scale effects!

(e) On a graph below, draw isoquant and isocost curves for (b) and (c) and show the allocations that you find in (b), (c) and (d).

(f) Are the substitution and scale effects that you find in (d) consistent with the theory? Why?