Fixed Input Relations

Essay

Fixed Input Relations. Extreme Biking, Inc., assembles high-end extreme mountain bicycles at a plant in Lexington, Massachusetts. The plant uses labor (L) and capital (K) in an assembly line process to produce output (Q) where:

A. Calculate how many units of output can be produced with 25 units of labor and 400 units of capital, and with 225 units of labor and 3,600 units of capital. Are returns to scale increasing, constant, or diminishing?
B. Calculate the change in the marginal product of labor as labor grows from 25 to 36 units, holding capital constant at 400 units. Similarly, calculate the change in the marginal product of capital as capital grows from 400 to 625 units, holding labor constant at 25 units. Are returns to each factor increasing, constant, or diminishing?
C. Assume now and throughout the remainder of the problem that labor and capital must be combined in the ratio 25L:400K. How much output could be produced if the company faces a constraint of L = 25,000 and K = 500,000 during the coming production period?
D. What are the marginal products of each factor under the conditions described in part C?