Consider a firm with production function given by q = f(E, K) = E^(1/4)K^(1/4), where E...

Consider a firm with production function given by q = f(E, K) = E^(1/4)K^(1/4), where E is number of workers and K is capital. The price of labor is w = 4 and price of capital is r = 8. The price of the output that firm produces is 20. The firm can adjust both its inputs.

1) Derive an expression for MRT S for this firm.

2) The firm wants to produce q0 units of output. What would be cost-minimizing combination of inputs (E, K) to produce q0 units of output. Note that this combination would be a function of q0.

3) Firm wants to maximize its profits. What is the profit maximizing level of inputs? How many units of output are produced? What is the firm’s profit if it produces at this optimal?

4) Consider a change in price of labor, such that w = 2. What would be the new optimal levels of both inputs? How does quantity of output produced change?

5) Decompose this change in inputs from part (3) to part (4), into scale and substitution effects

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Consider the firm with production function given by q = f ( L , K )...

Consider the firm with production function given by q = f ( L , K ) = L ^(1/4) K^(1/4). If w = r = 4, what is the change in the producer surplus when the price increases from $16 to $32? (round your answer to one decimal place if necessary)

1. Consider production function of the form Q= f(H, K), where Q is the output measure...

1. Consider production function of the form Q= f(H, K), where Q is the output measure and H and K are hours worked and gross capital stock, respectively. Based on 33 observations we obtain the following results: ?og(?) = 0.129 + 0.448 ?og (?) + 0.559 ?og (?) (Standard Error) (0.546) (0.704) (0.816) R2= 0.886 a. Interpret the regression results. b. What is the output elasticity of hours worked? c. Verify that the coefficients of log(H) and log(K) are statistically...

Consider a firm using a technology defined by the linear production function = q = f(K,...

Consider a firm using a technology defined by the linear production function = q = f(K, L) = K + L Which of the following statements are correct? There might be multiple a) The elasticity of output with respect to capital is equal to the inverse of the average product of capital b) The elasticity of output with respect to labor is constant c) The elasticity of long-run cost with respect to output is equal to 1 d) The elasticity...

Consider a firm whose production is given by Q(K, L) = K^1/3L^1/3, where K and L...

Consider a firm whose production is given by Q(K, L) = K^1/3L^1/3, where K and L are, respectively, the quantities of capital and labour production inputs. Prices of capital and labour are both $1 per unit. (a) Derive and interpret the firm’s demand functions for capital and labour. (b) Derive and interpret the firm’s Long-Run Cost Function. (c) In the long-run, if the firm wished to produce 16 units of output, what quantities of capital and labour would it optimally...

Suppose the production function of a firm is given by q=L^1/4 K^1/4. The prices of labor...

Suppose the production function of a firm is given by q=L^1/4 K^1/4. The prices of labor and capital are given by and w=10 and r=20, respectively. Write down the firm’s cost minimization problem. What returns to scale does the production function exhibit? Explain. What is the Marginal Rate of Technical Substitution (MRTS) between capital and labor? What is the optimal capital to labor ratio? Show your work.

Suppose that output Q is produced with the production function Q = f(K,L), where K is...

Suppose that output Q is produced with the production function Q = f(K,L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the proﬁt maximizing rules be for the hiring of L and K? (b) What is the MRTSK,L for the following production function: Q = 10K4L2? Is this technology CRS, IRS...

Suppose that output Q is produced with the production function Q = f(K;L), where K is...

Suppose that output Q is produced with the production function Q = f(K;L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the prot maximizing rules be for the hiring of L and K? (b) What is theMRTSK;L for the following production function: Q = 10K4L2? Is this technology CRS, IRS or...

A given firm has the following production function; Q=f (L, K) the cost constraint is C=...

A given firm has the following production function; Q=f (L, K) the cost constraint is C= wL+rK, show that the optimal inputs is obtained at the point where the marginal rate of technical substitution is equal to the price ratio.

a.The production function of Firm X is given as follow: q=10(K0.5)(L0.5) where q, K and L...

a.The production function of Firm X is given as follow: q=10(K0.5)(L0.5) where q, K and L denote firm's output, capital and labor respectively. The marginal product of labor (MPL ) and capital (MPK ) are expressed as follow: MPL =5(K0.5)(L-0.5) MPK =5(K-0.5)(L0.5) i. What are the capital elasticity of output and labor elasticity of output respectively? ii. If the wage of labor (w) and rental of capital (r) are $100 and $400 respectively, what is the minimum cost required to produce...

The production function of a certain country is given by Q = f(K,L) = 90K1/3,L2/3 where...

The production function of a certain country is given by Q = f(K,L) = 90K1/3,L2/3 where Q is the number of output produced in units of millions , K is the capital expenditures in units of $1 million and L is the size of labor force in thousands of worker – hours . Find the level of output if the capital expenditure is Tsh 27 million dollars and the labor level is 8,000 workers – hours. At the same level...

Subjects