A factory produces output (Q) using capital (K) and labor (L) according to the production function...
A factory produces output (Q) using capital (K) and labor (L) according to the production function Y(K,L)=K1/5*L4/5 Let r denote the price per unit capital, and w denote the price per unit labor, so that the total expenditure on these factors is rK + wL.
a) As the factory manager, you have been told to produce 625 units of output. Give the equation for the relevant isoquant, written with L as a function of K.
b) If r = 80 and w = 20, what is the less expensive method to produce 625 units of output? Give the optimal factor choices (K*, L*) as well as the total expenditure. [HINT: You can solve this problem by constructing a table; you can assume that K is purchased in increments of 10.]
c) If r = 120 and w = 20, what is the less expensive method of production? Again give the optimal factor choices (K*, L*) as well as the total expenditure.
d) Find the factor demands and the cost function for this firm (express K and L in terms of the output and factor prices). Find if your results for parts b and c are correct using the factor demands you just found.
Homework Answers
Add Answer to:
A factory produces output (Q) using capital (K) and labor (L)
according to the production function...
A firm produces output Q by using capital K and labor L in fixed proportions, i.e....
A firm produces output Q by using capital K and labor L in fixed proportions, i.e. Q = F (K ,L ) = min {K, L/3}. The price of a unit of labor is w = 6, the price of a unit of capital is r = 2 and the price of output is p = 20. a) Draw the isoquant for Q = 8. b) Find the marginal product of labor. Suppose that (in part c and d) the...
- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital...
- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital (K). The firm's production function is Q f(L, K) = min{L, K}}. The per-unit price of labor is w = 1 and the per-unit price of capital is r = 1. Recently, the government imposed a tax on Julia's firm: For each unit of labor that Julia employs, she must pay a tax of £t to the government. (a) Graph the Q unit of...
All firms produce according to a Cobb-Douglas production function. This production function should look familiar to...
All firms produce according to a Cobb-Douglas production function. This production function should look familiar to you. It says that output Q is related to inputs K and L as: This production function implies that the cost-minimizing demand for capital will be Ou where w is the wage rate, r is the cost of capital, Q is output level, and α and β are parameters We will assume that α + β 1; this is the constant-returns-to-scale assumption we saw...
9. A firm uses capital and labor to produce a single output good. The production function...
9. A firm uses capital and labor to produce a single output good. The production function is given by F(K,L)=K^0.5L, where K is the amount of capital and L is the amount of labor employed by the firm. The unit prices of capital and labor are given by, respectively r=$5 and w=$6. Based on this information, characterize the optimal (output maximizing) allocation of inputs given that the firm decided to limit its total cost to $12,000. Illustrate your solution graphically:...
consider an industry that uses capital, K and labor, L to produce output, X, according to...
consider an industry that uses capital, K and labor, L to produce output, X, according to a Cobb-Douglas production function: x=K L where 0 <X<1 is the share parameter for capital and 0<B,1 is the share parameter for labor. Denote the rental price of capital by r and the wage by w. Determine the capital to labor ratio (K/L) wh9ich minimizes the cost of producing a fixed amount of output, X. Under what conditions does optimal ratio of capital to...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm e...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
Acme produces anvils using labor (L) and capital (K) according to the production function Q= f(L,K)=LK...
Acme produces anvils using labor (L) and capital (K) according to the production function Q= f(L,K)=LK with associated marginal products MPL=K, MPK =L. The price of labor is w=2 and the price of capital is r=1. Does Acme's production function for anvils exhibit increasing, constant or decreasing returns to scale? Justify your answer
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor. a. Find marginal product of labor and marginal product of capital.b. Define what is marginal rate of technical substitution, MRTS. Calculate the MRTS for the above case.c. When K = 10, L = 16, what is the total output? Sketch this isoquant function on a diagram where K is the vertical axis and L is the horizontal axis.
Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital,...
Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function.
- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital (K). The firm's production function is Q f(L, K) = min{L, K}}. The per-unit price of labor is w = 1 and the per-unit price of capital is r = 1. Recently, the government imposed a tax on Julia's firm: For each unit of labor that Julia employs, she must pay a tax of £t to the government. (a) Graph the Q unit of...
All firms produce according to a Cobb-Douglas production function. This production function should look familiar to you. It says that output Q is related to inputs K and L as: This production function implies that the cost-minimizing demand for capital will be Ou where w is the wage rate, r is the cost of capital, Q is output level, and α and β are parameters We will assume that α + β 1; this is the constant-returns-to-scale assumption we saw...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function.
Most questions answered within 3 hours.
-
def sorted(numbers):
num = numbers[0]
for i in numbers:
if i < num:
return False
num...
asked 33 minutes ago -
Discuss the Dred Scott case and how effective it was in settling
the conflict over slavery
asked 32 minutes ago -
Consider the following reaction:
CO(g)+H2O(g)⇌CO2(g)+H2(g)
Kp=0.0611 at 2000 K
A reaction mixture initially contains a CO...
asked 1 hour ago -
Question 6
The future value of a dollar _________ as the
interest rate increases and __________...
asked 2 hours ago -
If the government gave you a subsidy of $100 per month that you
had to spend...
asked 2 hours ago -
2. Company B uses Process Costing System(FIFO
Method). Data about Company B is given below.
Data...
asked 2 hours ago -
City Machine Inc. currently makes a part for an equipment at a
cost of $20 /...
asked 3 hours ago -
T or F: If factors are easily evaluated independently, they are
said to be confounded.
T...
asked 3 hours ago -
You are conducting a test of the claim that the row variable and
the column variable...
asked 4 hours ago -
Do an independent research to acquire a basic understanding of
Radio Frequency Identification (RFID). Discuss the...
asked 4 hours ago -
3. You frequent a popular fast food restaurant that serves
tacos...and they frequently
get your order...
asked 4 hours ago -
ECONOMICS QUESTION ANSWER IN 15 MIN
FOR THUMBS UP
In order to calculate CSF, among other...
asked 4 hours ago