Question

There are two inputs labor, L, and capital, K. Their cost minimizing levels are given by K(y) = 2y and L(y) =y^2.L and K are respectively priced w=1/2 and r= 3

.a) Find the firm’s cost curve.

b) What is the firm’s exit price

c) Graphically show how the long run supply curve is derived from cost curves (make sure to label the axes, the curves, the intercepts, and the slope).

d) A tp= $12, what is the profit-maximizing level of output in the short-run?

Answer 1

Solution :-

(a) :-

There are two inputs labor,( L) capital ( K).

Their cost minimizing levels are given by

K(y)= 2y

L(y) =y^2.

L and K are respectively priced w=1/2 and r= 3

C = wL + rK

= 1/2 x y^2 + 3 x 2y

[ C = ( 1/2)y^2 + 6y]......cost function

(b) :-

Now, firm's exit price:-

In the absence of the fixed costs, the firm's exit price is equal to the Marginal cost of producing the first unit of output, because this is where the MC curve crosses the AC curve.

Now, MC = y + 6

= 1 + 6.....(y = 1)

[ P = 7 ]

So, firm's exit price is = 7

(c) :-

The long run supply curve is derived from cost curves.

The firm's supply curve is the portion of the MC curve above the price.

Intercept = 6

Slope = 1

(d) :-

At P = $12

P = MC

12 = y +6.......( P = 12)

y = 12 - 6

[y* = 6 ]

So, the profit-maximizing level of output in the short-run is 6.