MGEA01H3 Lecture Notes - Lecture 7: Profit Maximization, Fixed Capital, Fixed Cost

A price taking firm chooses its inputs to maximize short-run profits. Its Cobb-Douglass production function has the following form: q(L, K) = L^(1/2) K ^(1/3) . The output price is 1,000 per unit and the cost of each unit of input is 10. In the short-run, capital is fixed at 27 units.

(a) Set up the profit function in terms of labor only.

(b) Find the optimal choice of labor, L ∗ .

(c) Given your answer to part (b), do you think that there is excess capital compared to the optimal level of quantity?

Another price taking firm chooses its inputs to maximize long-run profits. Labor and capital are substitutes in production and both exhibit decreasing returns to scale, q(L, K) = L^(1/2) + K^(1/2) . The output price is 100 and the price of each of the inputs is 10.

(a) Set up the firm’s profit function and provide the two conditions for profit maximization.

(b) Find the profit maximizing levels of capital and labor.

(c) How does a change in labor change the optimal choice of capital?

A price taking firm chooses its inputs to maximize short-run profits. Its Cobb-Douglass production function has the following form: q(L, K) = L ^(1/2)K^(1/3) . The output price is 1,000 per unit and the cost of each unit of input is 10. In the short-run, capital is fixed at 27 units.

(a) Set up the profit function in terms of labor only.

(b) Find the optimal choice of labor, L* .

(c) Given your answer to part (b), do you think that there is excess capital compared to the optimal level of quantity?

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
B. C=17q
C. C=8q
D. C=10q

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.