1. Read the following cases and answer the questions that follows.

a. A firm's production function is = L where A, , and 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.

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.

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

d. A factory has production function Q = f(L, K).

In year 1: 212 = f(78, 144)

In year 5: 309 = f(117, 216)

What kind of returns to scale does the production function display over the five years period? Explain.

e. If a firm's fixed cost decreases. The firm's should take advantage of this drop by producing more. Briefly explain if this statement is true or false

( I you can try explaining in words this would be helpful)