Question

5. A competitive firm has a production function described as follows. “Weekly output is the square...

5. A competitive firm has a production function described as follows. “Weekly output is the square root of the minimum of the number of units of capital and the number of units of labor employed per week.” Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labor freely.

a) Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (Be careful at the boundaries.)

b) If the wage is w=$1 and the price of output is p=$4, how much labor will the firm demand in the short run?

c) What if w=$1 and p=$10?

(SOLVED, DO NOT ANSWER)

Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Part A

The long run formula for this firm is,

So, in the short run, labor greater than 16 unit have no effect on total output of the firm. Hence, the short run production function is,

  

  

The marginal product of labor would be,

  

Part B

Here wage is $1 and price of output is $10.

The optimal demand for labor is,

. Here,

or,

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A competitive firm has a production function described as follows. “Weekly output is the square root...
A competitive firm has a production function described as follows. “Weekly output is the square root of the minimum of the number of units of capital and the number of units of labor employed per week.” Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labor freely. a. Write down a formula that describes the marginal product of labor in the short run as a function of the amount...
a firm produces a product with labor and capital as inputs. The production function is described...
a firm produces a product with labor and capital as inputs. The production function is described by Q=LK. the marginal products associated with this production function are MPL=K and MPK=L. let w=1 and r=1 be the prices of labor and capital, respectively a) find the equation for the firms long-run total cost curve curve as a function of quantity Q b) solve the firms short-run cost-minimization problem when capital is fixed at a quantity of 5 units (ie.,K=5). derive the...
A firm produces a product with labor and capital. Its production function is described by Q...
A firm produces a product with labor and capital. Its production function is described by Q = min(L, K). Let w and r be the prices of labor and capital, respectively. a) Find the equation for the firm’s long-run total cost curve as a function of quantity Q and input prices, w and r. b) Find the solution to the firm’s short-run cost minimization problem when capital is fixed at a quantity of 5 units (i.e., K = 5). Derive...
Suppose that production of a firm's output is described by the following production function Q =...
Suppose that production of a firm's output is described by the following production function Q = K0.25 L0.5 In the short run, the firm's capital is fixed at 10,000. Suppose further that the market price of the output is $37, and that the market wage is $25. What is the Marginal Revenue Product of Labor (MRPL) for the 147th worker? Enter your answer rounded to the nearest two decimals.
Suppose that production of a firm's output is described by the following production function Q =...
Suppose that production of a firm's output is described by the following production function Q = K0.25 L0.5 In the short run, the firm's capital is fixed at 10,000. Suppose further that the market price of the output is $70, and that the market wage is $25. What is the Marginal Revenue Product of Labor (MRPL) for the 129th worker? Enter your answer rounded to the nearest two decimals.
A firm has a daily production function q = 2.5L^1/3K^1/3. Currently, the firm rents 8 pieces...
A firm has a daily production function q = 2.5L^1/3K^1/3. Currently, the firm rents 8 pieces of equipment. The amount of equipment is fixed in the short run. The unit wage rate is $25 while the rental cost of capital is $100. Find the short run production function. Find the number of workers the firm wishes to employ to produce q units (the short run conditional demand for labor). Find the firm’s short run total cost Find the firm’s short...
2. Consider a firm that sells output and buys labor in a competitive market. The firm’s...
2. Consider a firm that sells output and buys labor in a competitive market. The firm’s production function is given by q=K1/2L1/2 where q is the quantity of output, K is the amount of capital, and L is the number of labor hours.  The marginal product of labor is MPL=1/2K1/2L-1/2 .Suppose the amount of capital is fixed at 100 units (i.e., short-run). a.) If the output can be sold for $10 per unit and labor can be purchased for $5 per...
Assume that a competitive economy can be described by a constant-returns-to-scale Cobb-Douglas production function and all...
Assume that a competitive economy can be described by a constant-returns-to-scale Cobb-Douglas production function and all factors of production are fully employed. Holding other factors constant, including the quantity of capital and technology, carefully explain how a one-time, 10 percent increase in the quantity of labor as a result of a special immigration policy, will change the following: (12 points) The level of output produced The real wage of labor The real rental price of capital Labor share of total...
The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L...
The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L where Q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. (a)Use Excel to calculate the total short run output Q(L) for L = 0, 1, 2...20, given that capital is fixed in the short run at K = 1. (b) Use Excel to calculate the total long run output Q(L) for...
1. A firm production function is given by q(l,k) = l0.5·k0.5, where q is number of...
1. A firm production function is given by q(l,k) = l0.5·k0.5, where q is number of units of output produced, l the number of units of labor input used and k the number of units of capital input used. This firm profit function is π = p·q(l,k) – w·l – v·k, where p is the price of output, w the wage rate of labor and v the rental rate of capital. In the short-run, k = 100. This firm hires...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT