Question

1. at what quantity will the marginal cost curve cross the average cost curve C=10q-12q^2+2q^3 ,

3.

Does the following production function have diminishing marginal returns to labor in the SR? Q = 2L 1/2K1/2 yes no Cannot be determined from the information B Next Previous MacBook Air 8 # 3 $ 4. IR E W TH

Answer 1

1.

C=10q-12q² +2q³

Average cost(AC)= C/q= 10-12q+2q²

Marginal cost(MC)= dC/dq= 10-24q+6q²

To find quantity where MC and AC intersect:

AC=MC

10-12q+2q² = 10-24q+6q²

10-24q+6q² -2q² +12q-10= 0

4q² -12q = 0

4q(q-3) =0

q= 0 and q= 3

So MC and AC curve will intersect each other at q=0 and q=3

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3.

Diminishing marginal return to labor means when increase in quantity of labor cause less proportional rise in quantity produced.

Q= 2L^1/2 K^1/2

Suppose quantity of labor doubles:

Q'= 2(2L)^1/2 K^1/2

Q'= 2(2)^1/2 L^1/2K^1/2

Q'= (2)^1/2 (2L^1/2 K^1/2 )

Q'= (2)^1/2 Q

Q'= 1.41Q

Here we can observe that as the value of labor increases by 2 times, the rise in output is by 1.41 times which less than the rise in output. It implies that yes production function have diminishing marginal return to labor.

Option 1st is the correct answer.