Production Functions?

Question

Q = KL^1/2

Suppose K = 10

A. What is the total product schedule for L?

B. Waht is the average product schedule for L?

C. Is there diminishing marginal product for L?

Suppose k = L

D. Waht is the total product schedule for L?

E. What is the average product schedule for L?

At point A alongan isoquant, the firm uses K = 4 units of capital and L = 9 units of labor. At point B along the same isoquant, teh firm uses 16 units of labor.

F. How much capital is used at point B?

G. What is the MRTS (L,M) between these two points?

H. Does the production fuction exhibit increasing returns to scale?

Answer 1

(I) For Q=K(L^1/2)

A: Q=10L^1/2

B: AQ=10/L^1/2

C: Yes

D: Q=L^3/2

E: AQ=L^1/2

(II) For Q=(KL)^1/2

A: Q=(10L)^1/2

B: AQ=(10/L)^1/2

C: Yes

D: Q=L

E: AQ=1

F:

(I) Q=4*3=12,... 12=K*4 .. K=4/12=3

(II) Q=2*3=6,... 6=4*(K^1/2), ... K=(√6)/2

G:

(I) MRTS= -1/7≈ -0.143

(II) MRTS≈ -1.75/7≈ -0.25

H:

(I) Yes

(II) No - it's constant.