Question

4. Suppose the wine industry is made up of many small identical firms. A represe tative firm's long-run cost function is C(yi) = y + y if yı > 0, C(v) = 0 otherwise. (a) Derive the representative firm's market supply curve for wine. (b) If the market demand for wine is yo = 1,140 - 10p, calculate the long-run competitive equilibrium of this industry (that is, indicate the equilibrium price. the amount of good y exchanged in the market, the number of firms in the market, and each firm's output and profit).
question 4 please.

Answer 1

(a)

Firm supply function is its MC curve.

MC = dC(y)/dy = - y + 3y²

So, firm supply curve: p = - y + 3y²

(b)

In long run equilibrium, p = MC = AC.

AC = C(y)/y = (99/2y) - (y/2) + y²

Equating with MC,

(99/2y) - (y/2) + y² = - y + 3y²

99 - y² + 2y³ = - 2y² + 6y³

4y³ - y² - 99 = 0

Solving this polynomial (using online solver),

y = 3 (other two roots are imaginary)

p = MC = - 3 + 3 x 3 x 3 = - 3 + 27 = 24

yD = 1,140 - 10 x 24 = 1,140 - 240 = 900

Number of firms = yD / y = 900 / 3 = 300

In long run equilibrium since p = AC, each firm earns zero profit.