# 1. Imagine a firm has the following short-run production function: q=f(L,K) = K L – L?...

1. Imagine a firm has the following short-run production function: q=f(L,K) = K L – L? Assume K = 25. a. Fill in the following table. (First, find the total output from the production function, then find the marginal product by dividing the change in total output by change in labor.) Capital MPL Labor 7 Total Output 126 APL 18 25 12 25 25 25 25 25 10 11 12 13 14 15 25 25 25 b. How many units of labor should the firm hire to maximize output? C. Draw the short-run TP, MP and AP, curves (You will probably want to use two diagrams)

(a) Given, $q=f(L, \bar{K})=\bar{K}L-L^2$    or     $q=25L-L^2$

where K is constant and K=25 (Short run situation)

Thus, $MP_L=\frac{\partial q}{\partial L}(\bar{K}L-L^2)=\bar{K}-2L=25-2L$

and $AP_L=\frac{q}{L}=\frac{\bar{K}L-L^2}{L}=\bar{K}-L=25-L$

Now using the above formulas we get the following results,

(b) To maximize output the firm should hire 12 units of labor as seen in the above table that when L=12 the total output q=156.

(c) Graphs

#### Earn Coin

Coins can be redeemed for fabulous gifts.

Similar Homework Help Questions
• ### 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. Instruction: Enter your responses rounded to three decimal places. 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. ____ What is the average product of labor when the firm uses 256 units of labor? ____ Instruction: The second response is the exponent on L in the...

• ### The production function of the Auto parts firm is given by Q-5L-L, where Q is the...

The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...

• ### Q6: CH 10 (15%) You are planning to estimate a short-run production function for your firm,...

Q6: CH 10 (15%) You are planning to estimate a short-run production function for your firm, and you have collected the following data on labor usage (L) and output (Q): Labor usage (L) Output (0) a. Please key in the data into MS Excel for regression analysis. Estimate your firm's short-run production function. Do the parameter estimates have the appropriate algebraic signs? Are they statistically significant at the 5 percent level? (Hint: Run the production function as Q = AL...

• ### Suppose that a firm has a production function given by: ? = ?^?.???^?.? . The wage...

Suppose that a firm has a production function given by: ? = ?^?.???^?.? . The wage rate is \$18 and the rental rate is \$9. 12. Suppose that the firm has 4 units of capital in the short run. Find the short run total cost function. ________________________________ 13. Find the marginal product of labor (MPL) function. ________________________________ 14. Solve the optimization condition for K and write that equation. ________________________________ 15. Suppose the firm wants to minimize the cost of producing...

• ### Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the...

Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the firm has 256 units of capital. Find the Marginal Product of Labor (MPL). Fill in the appropriate numbers in the function below. MPL = ( ) L-0.5

• ### Consider the production function Q = 20K 1/2 L 1/2

Consider the production function Q = 20K 1/2 L 1/2. The firm operates in the short run with 100 units of capital.a. The firm’s short-run production function is Q = __________.c. The average product of labor function is AP = __________.d. The marginal product of labor function is MP = _________. Show that the marginal diminishes for all levels of labor usage.e. Assuming that the firm in question 2 is in the long run where its fixed endowment is \$1000,...

• ### Please answer the two sub-parts Question 4 (20 points) A firm has the following short-run production...

Please answer the two sub-parts Question 4 (20 points) A firm has the following short-run production function as follows: Q = 15L +18L2-0.5L, where Q = total products per period and L = number of workers employed per period. 4.1) (3 points) Derive the marginal product of labor (MPL). At what number of workers (L) does the law of diminishing returns begin? MPL = f(L) = Law of diminishing return begins when L = workers. . 4.2) (3 points) Derive...

• ### Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the...

Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the firm has 16 units of capital. Find the Marginal Product of Labor (MPL). Fill in the appropriate numbers in the function below. MPL = Answer ___ L-0.5 (Round to the nearest 2 decimal places if necessary.)

• ### 5) Liming's building company has the production function q = 20L – L?, where is the...

5) Liming's building company has the production function q = 20L – L?, where is the number of houses built and L is the quantity of labor employed. Derive the MPZ and APL. b. For what values of L is the MPL > 0? For what values of L is the MP, diminishing? Draw the MP_ and AP, on a graph. a. c.

• ### 5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK...

5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK . In the short-run, the firm's amount of capital equipment is fixed at K = 100. The rental rate of capital is r=\$1, and the wage rate of labor is w=\$4. a. Derive the firm's short-run total cost curve. What is the short-run average total cost? What is the short-run average variable cost? b. Find the short-run marginal cost function. What are the total...

Free Homework App