A firm can manufacture a product according to the production function: Q = F(K, L) =...

A firm can manufacture a product according to the production function: Q = F(K, L) = K3/4L1/4. a. Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. Instruction: Enter your responses rounded to three decimal places. 3.375 What is the average product of labor when the firm uses 256 units of labor? 0.422 b. Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 81 units. Instruction: The second response is the exponent on L in the expression. Enter your responses rounded to two decimal places. MPL = 6.75 × L ^ 0.75 Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor. Instruction: Enter your responses rounded to three decimal places. MPL when L = 16: 0.844 MPL when L = 81: 0.25 c. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit of output and can hire labor at $50 per unit of labor, how many units of labor should the firm hire in order to maximize profits? Instruction: Enter your response as a whole number 81

Expert Solution

Rahul Sunny answered 3 years ago

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 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)

A firm produces output according to the following function: q = f (L, K) = L^1/2...

A firm produces output according to the following function: q = f (L, K) = L^1/2 K^1/4 . The cost of labor is $8 per hour and the rental cost of capital is $2 per hour. a. Determine the returns to scale for this function. b. Suppose the firm wishes to produce at cost $96. How much capital and how much labor does the firm employ? c. Derive the short-run cost function with optimal amount of K from part b....

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...

A firm that produces shirts has a production function q=f(K,L)=K*L/10, that has a cost price of...

A firm that produces shirts has a production function q=f(K,L)=K*L/10, that has a cost price of labor= $10 and cost price of capital=$100. a) Find the isoquant if q=1 when q=2 and when q=3. Draw the graph. b) Does this firm’s production exhibit increasing, decreasing or constant returns to scale? c) Find the labor demand and the capital demand, as a function of q. d) Find the firm’s long-run cost function TC(q). e) If the firm wanted to produce 1...

Consider a firm with a production function Q(L,K) = √L + 2√K, that faces an inverse...

Consider a firm with a production function Q(L,K) = √L + 2√K, that faces an inverse demand function P (Q) = 250 - 2Q, and the labor and capital markets are also in perfect competition. A) Derive the expression for the profit function of the firm in terms of labor and capital and express the profit maximization problem the firm faces. B) Derive the first-order conditions, and use them to get the expressions for the optimal amounts of labor and...

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