Question

3. Imagine a perfectly competitive firm producing good A with cost function TC=400+20Q-2Q ² +2/3Q ³ , where Q is quantity produced

a. determine the firm’s short run supply curve

b. What is the profit maximizing level of output when price of A is birr 180?

4. Suppose the perfectly competitive price is given as $46 and the total cost of the firm is given by TC=14X+2X ² , find

a. The profit maximizing level of output for the firm?

b. The profit of the firm?

Answer 1

3.

a). Firm’s short run supply curve

A perfectly competitive firm producing good A with cost function;

$TC=400+20Q-2Q^2+\frac{2}{3}Q^3$

Firm's short run supply curve is marginal cost (MC).

$MC=\frac{dTC}{dQ}=\frac{d}{dQ}(400+20Q-2Q^2+\frac{2}{3}Q^3)$

$MC=20-4Q+2Q^2$

b). Profit maximizing level of output

In case of perfectly competitive firm, profit maximizing occurs when;

$MC=P$

$20-4Q+2Q^2=180$

$2Q^2-4Q-160=0$

$Q^2-2Q-80=0$

$Q^2-10Q+8Q-80=0$

$Q(Q-10)+8(Q-10)=0$

$Q-10=0$

$Q=10$

$Profit=(180\times10)-[20-(4\times10)+2(10)^2]$

$Profit=\$1620$

4.

a). Profit maximizing level of output

Price = $46

$TC=14X+2X^2$

$MC=\frac{dTC}{dQ}=\frac{d}{dQ}(14X+2X^2)$

$MC=X+4X$

$MC=P$

$X+4X=46$

$5X=46$

$X=\frac{46}{5}=9.2\approx9$

b). Profit of the firm

$Profit=(46\times9)-[9+(4\times9)]$

$Profit=\$369$