The Percam Company produces copper wire, which sells for $16 per unit when the market is in equilibrium. This is a Competitive industry, so Percam assumes that a change in its own supply will not affect the market price.
Let y denote the amount of output produced by the firm, which has the total cost function y2 + 14
It follows that marginal cost equals 2y when the firm produces y units of output.
1. What is the firm's fixed cost?
2. What is the firm's average variable cost as a function of its output level, y?
3. What is the firm's average total cost as a function of its output level, y?
4. What is the firm's profit maximizing level of output, and what is the resulting profit?
5. Derive the firm's supply function.
6. The market demand function is Q = 160 ! 5P, where Q is the total amount demanded at the price P. There are ten firms in the industry, each identical to Percam. Derive the market supply function and confirm that P* = 16 is the equilibrium price.