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 DRS? How do you know? (c) If the production function was Q = 4KL1=2, what are the conditional demand functions for K and L? Find the cost function C(w; r;Q) for the production function in part (a). Show 3 general properties of cost functions hold for this cost function. (d) Suppose you know the cost function is C(w; r;Q) = 2wQ + rQ 2 : Can you determine the returns-to-scale of the technology? If so, what is it?

Expert Solution

Rahul Sunny answered 7 months ago

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. Frisbees are produced according to the production function q = 2K+L where q =output of...

3. Frisbees are produced according to the production function q = 2K+L where q =output of frisbees per hour, K =capital input per hour, L =labor input per hour. a) If K = 10, how much L is needed to produce 100 frisbees per hour? b) If K = 25, how much L is needed to produce 100 frisbees per hour? c) Graph the q = 100 isoquant. Indicate the points on that isoquant deÖned in part a and part...

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...

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...

A firm produces output according to the production function: Q= F(K, L) = 4K + 8L.

A firm produces output according to the production function: Q= F(K, L) = 4K + 8L. a. How much output is produced when K= 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? c. If the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour, what is the...

Consider the following production function: x = f(l,k) = lb kb where x is the output,...

Consider the following production function: x = f(l,k) = lb kb where x is the output, l is the labour input, k is the capital input, and b is a positive constant. Suppose b < 1/2. (a) Set up the cost minimization problem and solve for the conditional labour and conditional capital demand functions. Let w and r be the wage rate and rental cost of capital respectively. (b) Using your answer in (a), derive the cost function and simplify...

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)

The production function of an economy is F(K,L) = 20(K0.5L0.5), where L is labour and K...

The production function of an economy is F(K,L) = 20(K0.5L0.5), where L is labour and K is capital with L = 400 and K = 400. What type of returns to scale does this production function exhibit?

Output is produced according to Q=4LK, where L is the quantity of labor input and K...

Output is produced according to Q=4LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5,then the cost minimizing combination of K and L capable of producing 32 units of output is:

Suppose a production function is given by F ( K , L ) = K 1 2...

Suppose a production function is given by F ( K , L ) = K 1 2 L 1 2, the price of capital “r” is $16, and the price of labor “w” is $16. a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run? b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the long...

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