Question

Suppose, the production function for X company is given by ? = 5(??) 0.5 where, Q is the amount of output produced, K is the amount of capital employed in production and L is the amount of labor employed in production. The prices of capital and labor are given by ?? = $48 and ?? = $75.

a)Express the total cost in terms of K and Q.

b)Derive the expression of marginal cost of capital.

c)Derive the long-run cost function in terms of Q.

Answer #1

a)

We are given

Squaring both sides

Total Cost, TC is given as

TC=P_{k}*K+P_{L}*L

b)

In this case, price of capital is constant. So,

**Marginal Cost of capital=PK=$48**

Marginal cost of output keeping K constant is given as

**MC of product=dTC/dQ=6Q**

c)

In long run

K/L=25/16

**K=(25/16)*L**

Set K=(25/16)*L in production function

**or L=0.8Q**

**K=(25/16)*L=(25/16)*0.8*Q=1.25Q**

Long run cost is given as

LRTC=KP_{K}+LP_{L}

LRTC=(1.25Q)*48+(0.8Q)*75

**LRTC=120Q**

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