1. A firm has a production function Q = K¹² + L. The firm faces a price of labor, w, and a price of capital services, r. a. Derive the long-run input demand functions for L and K. (Assume an interior solution.) b. Suppose the firm must produce 100 units of output. What must be true of the relative price of labor in terms of capital for the firm to use a positive amount of labor? c. Assuming the relative price of labor meets the condition you specified in part (b), graph the firm's expansion path. d. Suppose the economy takes a downturn, and the price of labor falls by 50% and is expected to stay at that level for a long time. Show graphically how this change affects the firm's expansion path.

1. A firm has a production function Q = K¹² + L. The firm faces a price of labor, w, and a price of capital services, r. a. Derive the long-run input demand functions for L and K. (Assume an interior solution.) b. Suppose the firm must produce 100 units of output. What must be true of the relative price of labor in terms of capital for the firm to use a positive amount of labor? c. Assuming the relative price of labor meets the condition you specified in part (b), graph the firm's expansion path. d. Suppose the economy takes a downturn, and the price of labor falls by 50% and is expected to stay at that level for a long time. Show graphically how this change affects the firm's expansion path.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.4P

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