Answer to Question #180957 in Economics for Million Kifle

Question

Part I: Discussion questions

1. Can accounting cost be greater economic cost? Explain.

2. The short run AVC, AC and MC are all U-shaped. Why?

Part II: Workout Questions

1. Suppose the production function is given by Q(L,K) = L4/3 K1/4 . Assuming capital is fixed,

find APL and MPL

2. Consider the following short run production function:

Q = 6L^2-0.4L^3

a) Find the value of L that maximizes output

b) Find the value of L that maximizes marginal

product

c) Find the value of L that maximizes average

product

3. Given a short run cost function as TC=1/3Q^3-2Q^2+ 60Q+100, find the minimum value of AVC and MC.

Answer 1

Part I: Discussion questions

1. Accounting cost can't be greater than economic cost, because it doesn't take into account implicit cost.

2. The short run cost curves AVC, AC and MC are U shaped because of the law of variable proportions.

Part II: Workout Questions

1. Q(L,K) = L4/3 K1/4, if capital is fixed, then $APL = Q/L = L^{1/3} ×K^{1/4}$ and $MPL = Q'(L) = 4/3×L^{1/3} ×K^{1/4}.$

2. Q = 6L^2 - 0.4L^3

a) The value of L that maximizes output is:

Q'(L) = 0,

$12L - 1.2L^2 = 0,$

L(10 - L) = 0,

L = 0 isn't acceptable, L = 10 units.

b) The value of L that maximizes marginal product is:

MPL'(L) = 12 - 2.4L = 0,

L = 5 units.

c) The value of L that maximizes average product is:

APL = 6L - 0.4L^2,

APL'(Q) = 6 - 0.8L = 0,

L = 7.5 units.

3. TC = 1/3Q^3 - 2Q^2 + 60Q + 100.

AVC is minimized, when AVC = MC.

$AVC = VC/Q = 1/3Q^2 - 2Q + 60,$

$MC = TC'(Q) = Q^2 - 4Q + 60,$

$1/3Q^2 - 2Q + 60 = Q^2 - 4Q + 60,$

$2/3Q^2 - 2Q = 0,$

Q(1/3Q - 1) = 0,

Q = 0 or Q = 3 units.

MC is minimized, when MC'(Q) = 0,

2Q - 4 = 0,

Q = 2 units.