Suppose in Jack’s production function, capital and labor are perfectly substitutable such that q = K...

Suppose in Jack’s production function, capital and labor are perfectly substitutable such that q = K + L. Assuming, as we have all term, that the wage rate is w and r is the rental rate of capital, find Jack’s long-run total cost function representing Jacks’ total costs in terms of output, TC(q) = C(q)

Expert Solution

Rahul Sunny answered 6 months ago

Consider the production function Q = K2L , where L is labor and K is capital....

Consider the production function Q = K2L , where L is labor and K is capital. a.[4] What is the Marginal Product of Capital for this production function? Is it increasing, decreasing, or constant? Briefly explain or show how you arrived at your answer. b.[4] Does this production function exhibit increasing, constant or decreasing returns to scale? Briefly explain or show how you arrived at your answer. c.[5] If the firm has capital fixed at 15 units in the short...

Suppose output, Q, is produced by labor, L, and capital, K, according to the following function:...

Suppose output, Q, is produced by labor, L, and capital, K, according to the following function: Q = K ½ L½.. Suppose the firm sells each unit of output in a competitive market for a price P = $100. Suppose the firm hires each unit of labor in a competitive market for a wage W = $25. Suppose the firm has to make do for now with a stock of capital K = 49; moreover, suppose each unit of capital...

1a. The production function for computers is q(K,L) = 7K1/3L2 where K=capital and L=labor. A firm...

1a. The production function for computers is q(K,L) = 7K1/3L2 where K=capital and L=labor. A firm has two units of capital (K=2) which it cannot change. A manager wants to know the marginal productivity of labor if the firm goes from 2 to 3 workers. Calculate the marginal productivity of labor for the manager. Explain your answer carefully to the manager who is not familiar with what the marginal productivity of labor means. 1b. Last year the price of bread...

Firm A’s production function is the following: Q=Q(L,K)=20LK Calculate the demand functions for labor and capital.

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...

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...

3. Consider the production function Q = K2L , where L is labor and K is...

3. Consider the production function Q = K2L , where L is labor and K is capital. a.[4] What is the Marginal Product of Capital for this production function? Is it increasing, decreasing, or constant? Briefly explain or show how you arrived at your answer. b.[4] Does this production function exhibit increasing, constant or decreasing returns to scale? Briefly explain or show how you arrived at your answer. c.[5] If the firm has capital fixed at 15 units in the...

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 production of widgets requires capital and labor. The production function is constant returns to...

Suppose that production of widgets requires capital and labor. The production function is constant returns to scale and capital investment is sunk. There are no other barrier to entry. Is the investment in sunk capital a barrier to entry? Explain. What will the market equilibrium be if there are many possible entrants?

Consider a production function of two inputs, labor and capital, given by Q = (√L +...

Consider a production function of two inputs, labor and capital, given by Q = (√L + √K)2. Let w = 2 and r = 1. The marginal products associated with this production function are as follows:MPL=(√L + √K)L-1/2MPK=(√L + √K)K-1/2 a) Suppose the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q. Show how the cost-minimizing quantity of capital depends on the quantity Q. b) Find the equation...

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