Answer to Question #272092 in Microeconomics for Celine

Question

Assume a firm is facing the market demand curve: q = 100-2p, its total cost function is: c(q) = 2q²

1. What is the firm’s marginal revenue?

2. What is the firm’s marginal cost?

3. What is the output level “q” when the firm is maximizing its profit?

4. What is the firm’s maximum profit?

Answer 1

1. Marginal revenue (MR):

demand curve: q = 100-2p

$p = \frac{100-q}{2}$

$R=pq$

$R=(\frac{100-q}{2})q$

$R=(\frac{100q-q^2}{2})$

$R=50q-0.5q^2$

$\frac{dR}{dq}=50-q$

$MR = 50-q$

2. Marginal cost (MC):

total cost function is: c(q) = 2q²

$MC=\frac{dTC}{dq}=4q$

3. Output level at profit maximizing:

The profit-maximizing level of output for a firm occurs where MR = MC

$MR = MC$

$50-q=4q$

$4q+q=50$

$5q=50$

$q=\frac{50}{5}$

$q=10$

4. Firm’s maximum profit:

If q = 10 then price is:

$p = \frac{100-q}{2}= \frac{100-10}{2}$

$p=45$

$TC=2q^2=2\times(10)^2=200$

$Revenue =pq=45\times10=450$

$Profit =Revenue-TC$

$Profit=450-200$

$Profit=250$