Question

Suppose that an industry is characterized as follows:

C = q² each firm’s total cost function

P =12-q industry demand curve

a. If there is only one firm in the industry, find the monopoly price, quantity, and level of

profit.

b. Graphically illustrate the demand curve, marginal revenue curve, marginal cost curve, and average cost curve.

c. If the government decides to levy a tax of $2 per unit on this product, what will be the new level of production, price, and profit?

Answer 1

$C=q^2$

$MC=2q$

$P=12-q$

$TR=p \times q$

$=(12-q )\times q$

$=12q-q^2$

$MR=12-2q$

a) For profit Maximization,

MR=MC

$12-2q=$ 2q

$4q=12$

$q=3$

$P=12-3=9$

$\Pi$= TR-TC

$TR= 9\times 3= 27$

$TC= 3^2= 9$

$\therefore$ $\Pi$ =27-9=18

b) Diagram

c) If a tax of $2 is imposed.

Because the tax increases the price of each unit, total revenue for the monopolist decreases by TQ, and marginal revenue, the revenue on each additional unit, decreases by T;

$MR=12-2q-T$

$\therefore MR=10-2q$

New profit Maximization

MR=MC

$10-2q=2q$

$4q=10$

$q=2.5$

$P=12-q-T$

$=12-2.5-2=7.5$

$TC=q^2$

$=2.5^2= 6.25$

$TR=p\times q$

$=2.5\times 7.5=18.75$

$\therefore \Pi=18.75-6.25$

$= 12.5$