Profit maximization
The firm will choose the level of output to maximize the difference between Revenues and Costs
Revenues are p·y, where p is the market price of firm’s output, y denotes quantity produced
Costs are C(y), The optimal output maximizes p·y – C(y). The first order condition for profit
maximization gives p – MC(y) = 0. Therefore, the optimal level of output y* is such that p = c(y*)
Why p = MC(y*) ?
If p > MC(yo) for some yo, then the firm can increase output by one unit, this will increase revenues by p
and costs by MC, since p > MC profits will increase by te difference p – MC > 0....
If P < MC(yo) then for some yo, then the firm can decrease output by one unit, this will …
The condition p = MC(y*) gives the supply of the firm
For each price p (given), the firm decides how much to produce so as to satisfy this condition
The condition p = MC(y*) has one exception
Maybe profits of the firm are higher if the firm produces y = 0
The supply of the firm is
Π(y*) denotes profit when firm produces and output level that satisfies p = MC(y).
Shutdown Condition
1. What are the profit of the firm when y = 0?
2. In the Long Run Π(0) = 0.
3. Therefore supply of the firm is
4. That can be written as
 0 if p  AC  y *
S  p  
y * if p  AC  y *