Suppose the wine industry is formed by many small identical firms. A representat

Question

Suppose the wine industry is formed by many small identical firms. A representative firm's long run cost function is C(y_i) = 49.5 - 0.5 y^2_i+ y^3_i if y_i > 0, C(y_i) = 0 otherwise. Deficits the individual long run supply of wine. If the market demand for wine is yD = 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 the output and profits of each of them).

Explanation / Answer

(a)

MC(y) =3y2 - y

for profit maximisation p=mc,

therefore p= 3y2 -y

12p=36p2-12y

12p+1=36y2-12y+1

12p+1=(6y+1)2

(12p+1)1/2=6y+1

y=1/6[1+(12p+1)1/2]

The individual long run supply curve for wine is y = 0 if p is less than 24 and y=1/6[1+(12p+1)1/2] for any p more than or equal to 24.

(b)

In the long run equilibrium profit =0, supply curve is parallel to x axis at p=24=minimize ATC.

individual firm will produce 3 units, total output is 900, so one firm produces 300units.

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