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1. Suppose that a firm is producing in the short run with output given by:

Q = 50L - .75L2 ,

The firm hires labor at a wage of $16 per hour and sells the good in a competitive market at P = $8 per unit. Find the firm's optimal use of labor and associated level of output.

2. Determine whether the following production functions are characterized by increasing decreasing or constant returns to scale:

a. Q = 20 +3K + 2L

b. Q = 50 K.75 L .5

c. Q = 75 K.5 L .5

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Sonal Bahl
Sonal BahlLv10
29 Sep 2019

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Related questions

A firms product function is Q=5L^0.5K^0.5. Labor costs $40 per unit (Pl=$40) and capital costs $10 per unit (Pk=$10). K=16 in the short run.

5. Determine the firms short run cost function
A. C=160+2Q^2
B. C= 640+Q^2/20
C. C= 160+Q^2/10
D. C= 640+q^2/10

6. Determine the level of output that minimizes SAC for the firm.
A. 40
B. 80
C. 113
D. 135

7. If K is not fixed, determine the lease cost combination of L and K to produce 1000units of Q
A. L=100, K=400
B. L=100, K=25
C. L=200, K=200
D. L=400, K=100

8. Derive the long-run cost function for the firm.
A. C=4q
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C. C=8q
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9. Suppose the production of a firm is Q=5+2K+L. Which of the following statements is correct?
A. The firms productions exhibits constant returns to scale.
B. The firms production exhibits increasing returns to scale.
C. The firms production exhibits decreasing returns to scale.
D. The firms production exhibits first increasing returns to scale and then decreasing to returns to scale.

10. Suppose the production function of a firm is Q=5+2K+L. Which of the following statements is correct.
A. the firms LAC is increasing as the firm expands Q in the long run.
B. The firms LAC is decreasing as the firm expands Q in the long run.
C. The firms LAC is constant as the firm expands Q in the long run.
D. The firms LAC is first decreasing and then increasing as the firm expands Q in the long run.

A firm has the following short-run production function: Q 5 50L 1 6L2 2 0.5L3 where Q 5 Quantity of output per week L 5 Labor (number of workers) a. When does the law of diminishing returns take effect? b. Calculate the range of values for labor over which Stages I, II, and III occur. c. Assume each worker is paid $10 per hour and works a 40-hour week. How many workers should the firm hire if the price of the output is $10? Suppose the price of the output falls to $7.50. What do you think would be the short-run impact on the firm’s production? The long-run impact?

1. Calculate the returns to scale for the following production functions.

a. Q = AL + BK (A and B are constants)

b. Q = AL(1/2)K(1/2)

c. Q= AL(1/2)K(3/2)

d. Q= AL(1/2)K(1/4)

e. Q= ALK

2. Calculate the elasticity of substitution (ε) between L and K for the following production functions. [ Formula: ε = dlog(K/l)/dlog(MRTS L,K) ]

a. Q = AL(1/2)K(1/2)

B. Q= [AL(η) + (1-A)K(η)] (1/η)

c. Q= AL(1/2)K(3/2)

d. Q= AL(1/2)K(1/4)

3. The Production function of a firm is given by Q = AL(1/2)K(1/2). The Wage rate is $2 per hour and the rental rate is $3 per hour. The firm cannot exceed it's cost above $600. Find out the optimal amounts of L and K the firm should hire. What is maximum amount of output the firm ends up producing.

4. The Production function of a firm is given by Q = LK. The Wage rate is $2 per hour and the rental rate is $3 per hour. The firm has to produce at least 15,000 units of output.

a. Find out the optimal amounts of L and K the firm should hire.

b. What is the minimum cost the firm ends up incurring?

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