Question
In: Economics
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
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
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...
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.
The production function of a firm is given by F(K, L)=KL. Assume that capital (K) is...
The production function of a firm is given by F(K, L)=KL. Assume
that capital (K) is fixed at K=1 in the short run. Then the amount
of labor (L) needed to produce 4 unit of output is equal to
___.
The production function of a firm is given by F(K, L)=KL. Assume that capital (K) is...
The production function of a firm is given by F(K, L)=KL. Assume
that capital (K) is fixed at K=1 in the short run. Then the amount
of labor (L) needed to produce 4 unit of output is equal to ___.
Group of answer choices 16 1 4 8 2
A firm has a production function of Q = KL + L, where MPL = K...
A firm has a production function of Q = KL +
L, where MPL = K + 1 and
MPK = L. The wage rate (W) is
$100 per worker and the rental (R) is $100 per unit of
capital.
a. In the short run, capital (K) is fixed at 4 and the
firm produces 100 units of output. What is the firm's total
cost?
b. In the long run, what is the total cost of producing 100
units of...
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