Question

Consider a competitive industry with two firms and the production level of y. One has cost function ?1 (?) = ? 2 , and other has cost function ?2 (?) = 2? 2 . Assume the output price is p. Find the industry supply function.

Answer 1

Answer

In order to maximize profit a perfect competitive firm produces that quantity at which P = MC where P = Output Price and MC = Marginal Cost.

FIRM 1 :

C₁ = y²

MC₁ = dC₁/dy₁ = 2y₁ Thus P = MC₁ => P = 2y₁ => y₁ = P/2 ----------------------Supply of firm 1

Here y₁ = quantity of output of firm 1

FIRM 2 :

C₂ = 2y²

MC₂ = dC₁/dy₂ = 4y₂ Thus P = MC₂ => P = 4y₂ => y₂ = P/4 ----------------------Supply of firm 2

Here y₂ = quantity of output of firm 2

Market or industry supply curve is the horizontal summation of individual supply curve.

Thus industry supply curve is given by :

y = y₁ + y₂ => P/2 + P/4

=> y = 0.75P ----------------------------Industry supply curve