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A firm has production function f(L, K)=min [L1/2 , K1/3/2]. Let w be the price of labor and r be the price of capital.

(a) Determine whether this production function exhibits decreasing, constant, or increasing returns to scale.

(b) Find the firm’s (long-run) cost function.

(c) Let p=2 be the price of the output good, and let w=4 and r=1. Find the firm’s long-run profit-maximizing output level.

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Related questions

 Consider a firm whose technology is given by the production function: y = f (K,L) = (N+1)L + 2√K. Assume that input prices for labour, L, and capital, K, are w = 1 and r = 2 respectively. a)Find the firm’s short run total cost function assuming the firm cannot hire more workers nor fire its only worker, i.e. L = 1 is fixed. 

b)Find the firm’s short run marginal cost, average variable cost and average fixed cost. Draw the three of them in the same graph. What is the short-run supply of the firm?

c)Find the firm’s long run total cost function, i.e. when all factors are variable. 

d)Find the firm’s long run marginal cost and average cost. Draw them in the same graph. What is the long-run supply of the firm?

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?

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.

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