Question

1. A firm’s production function is ? = ?L^α ?^β where A, α, and β are positive constants. The firm currently uses 500 units of labor and 40 units of capital. If the firm adds 1 more unit of labor, what happens to productivity of capital? Explain.

1. b. Given a production function Q = f(L, K), if marginal product of labor and marginal product of capital are both positive, then this function displays diminishing MRTS. Explain if this statement is true or false.
2. c. You are trying to maximize your output subject to a budget. At one possible input bundle, where the constraint is binding, you find MPL > MPK. As long as MPL > MPK, you should keep spending more of your budget on labor and less on capital. Briefly explain if this statement is true or false

Answer 1

A. The function is ALaKb where A, a, b are constant. If we increase 1 unit of labour, the production will increase AabK times.

B. It is true if marginal product of labour and marginal product of capital are positive then MRTS is diminishing. We can think of intuitively with the help of an example, if we we have land as capital and labours. And we want to dig a hole in the land then one worker is enough to dig a hole but as we increase the no of labours and capital that is land is fixed, productivity of labours will decrease.