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Consider the following production and cost functions
q=〖(10K^(2/5)+5L^(2/5))〗^(5/2)
1250=20K+8L
Which implies
〖MP〗_K=10〖(10K^(2/5)+5L^(2/5))〗^(3/2) K^(-3/5)
〖MP〗_L=5〖(10K^(2/5)+5L^(2/5))〗^(3/2) L^(-3/5)
What is the profit maximizing combination of K and L?

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Irving Heathcote
Irving HeathcoteLv2
3 Apr 2019

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Related questions

A cost-minimizing firm has the following short run production function
Q=f(L,K)=72L + 5L^2 - 0.2L^3

(a) Briefly explain why this is a short-run production function.
(b) At what level of employment would diminish returns set in for the variable input?
(c) If the market-determined real wage rate is $20 determine the amount of labor a cost-minimizing firm would hire in order to minimize the total of production

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.

This is due today!! Thank you!!

Consider a firm with production function f(L, K)=2L+6K. Assume that capital is fixed at K=6. Then, the amount of labor necessary to produce q units is?

A  

L(q,6)= q-12
B  

L(q,6)= q/18-5
C  

L(q,6)= q/2-18
D  

L(q,6)= 3q/5-2
E  

L(q,6)= q2/2-12

Consider a firm with production function f(L, K)= 4L2/3K1/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=4 and the price of labor w=2. Then, the average cost of producing q units is?

A  

AC(q)= 4/q+q1/2/4.
B  

AC(q)= 2/q+1/4q1/3.
C  

AC(q)= 2/3q+1/q1/3.
D  

AC(q)= 1/3q+q1/2.
E  

AC(q)=8/q+2q1/2.

Consider a firm with production function f(L, K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the cost of producing q units is?

A  

C(q)=3+q2/9.
B  

C(q)=10+q3.
C  

C(q)=5+q3/9.
D  

C(q)=2/3+q2/3.
E  

C(q)=1/3+q3/3.

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