Chapter 7, Problem 9RE

In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q = f(L,K), - ²³. q=6LK +4L² where q is output, L is workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MPL = (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.)

Consider the table below that describes the production function for a good (Q) in terms of inputs labor (L) and capital (K) in the short run.

The production function is the relationship between the maximum amount of output that can be produced and the inputs required to make that output. Comment.

In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q = f(L,K), q = 6LK + 7L2 – where g is output, Lis workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MP, =. (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.) For example, if L = 5 and K= 23, then the marginal product of labor equals MP, =. (Enter a numeric response using an integer.) If L=9 and K= 23, then the marginal product of labor equals MP, =. (Enter a numeric response using an integer.) 20 tv MacBook Air S0 F2 F3 F4 % & 4 6 { E R Y P F G J K > C V M command option レ .. .- V * C B *3

A firm minimizes its costs by using inputs such that the marginal product of labor is 10 and the marginal product of capital is 20. The price of capital is $10 per unit. What must the price of labor be? (hint: the marginal product per dollar should be equal for both inputs)

A firm has a short run production function: Q = 16L^(1/2) where q = units of output, L = units of labor. Write down an expression for the marginal product of labor (MPL) and evaluate q and MPL for L = 9, L = 16, L = 36 and L = 100. On separate graphs, sketch q in terms of L and sketch MPL in terms of L. Confirm that the short run production function satisfies the law of diminishing returns.

A firm produces output according to a production function: Q = F(K,L) = min {4K,4L). a. How much output is produced when K= 2 and L = 1? unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $40 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $40 per hour but the rental rate on capital remains at $40 per hour? O Capital decreases and labor increases. O It does not change. O Capital increases and labor decreases. O Capital and labor increase.