A competitive firm has a long-run total cost function c ( y ) = 5 y 2 + 1,125 fo

Question

A competitive firm has a long-run total cost function c(y) = 5y2 + 1,125 for y > 0 and c(0) = 0. Its long-run supply function is described as

a.

y = p/5 if p > 148, y = 0 if p < 148.

b.

y = p/10 if p > 150, y = 0 if p < 150.

c.

y = p/10 if p > 153, y = 0 if p < 153.

d.

y = p/5 if p > 153, y = 0 if p < 165.

e.

y = p/5 if p > 155, y = 0 if p < 145.

a.

y = p/5 if p > 148, y = 0 if p < 148.

b.

y = p/10 if p > 150, y = 0 if p < 150.

c.

y = p/10 if p > 153, y = 0 if p < 153.

d.

y = p/5 if p > 153, y = 0 if p < 165.

e.

y = p/5 if p > 155, y = 0 if p < 145.

Explanation / Answer

Long run total cost, LRTC = 5y2 + 1,125

LRAC = LRTC / y = 5y + (1,125 / y)

In competitive long run, price equals the minimum point of LRAC.

LRAC is minimum when dLRAC / dy = 0

5 - (1,125 / y2) = 0

(1,125 / y2) = 5

y2 = 1,125 / 5 = 225

y = 15

LRAC = 5y + (1,125 / y) = 15 x 5 + (1,125 / 15) = 150 = Price (p)

Therefore,

If p < 150, y = 0

If p > 150, y = 15 = (p / 10)

Correct option (b)

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