Question

You are the manager of a perfectly competitive firm that produces a product according to the cost function C(Q) = 160 + 58Q − 6Q2 + Q3. Determine the short-run supply function for the firm.

Answer 1

-Explanation-

A- A perfectly competitive firm's supply curve is its marginal cost curve about the minimum of its AVC curve .

-Here MCi= 58- 12qi + 3qi(power2 ) and AVCi= ( 58qi- 6qi(power2 )+ qi(power3) / qi =58-6qi +qi(power2. ).

-Since MC and AVC are equal at the minimum point of AVC ,set MCi= AVCi to get 58- 12qi + 3qi(power2) = 58 -6qi + qi(power2,), or qi =3 .

-Thus ,AVC is minimized at an output of 3 units, and the corresponding AVC is AVC =58- 6(3) + (3)2 = 49. Thus the firm's supply curve is described by the equation MCi = 58 - 12qi + 3qi(power2 )

-if P is greater than $49; otherwise, the firm produces zero units.

B- Monopoly produces where MR=MC and thus does not have a supply curve.

C-A monopolistically competitive firm produces where MR=MCand thus does not have a supply curve.