Question

You are the manager of a perfectly competitive firm that produces a product according to the cost function C(Q) = 160 + 58Q − 6Q 2 + Q 3 . Determine the short-run supply function for the firm.

Answer 1

Solution :

Given That :

The cost function C(Q) = 160 + 58Q − 6Q ₂ + Q₃

A.)

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

Here

Since

MC and AVC are equal at the minimum point of AVC ,

set to get

  or

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

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.