Monopoly

a) Marginal Revenue

A single seller of a video game console faces an aggregate demand of

P (Q) = 500 -Q/2000

i. What is the total revenue function?

ii. What is the marginal revenue?

b) Costs

Each unit requires 1 hour of labor, parts, and shipping. The costs of these inputs are

$15, $65 and $20, respectively.

i. What is the total cost of producing Q units?

ii. Marginal cost?

c) Profit

What is the profit function of this firm?

d) Market Equilibrium:

i. What is the condition that ensures profit maximization?

ii. Using the condition from part i., find the number of units produced that maximizes

profits, Q^*.

iii. What is the price charge at the optimal quantity, P(Q^*)?

e) Welfare

i. What is the profit of the monopolist?

ii. What is the consumer surplus?

f) Graph

On a single graph with price on the vertical axis and quantity on the horizontal axis

(label axes), plot and label demand, marginal cost, and marginal revenue. On the same

graph label the optimal price, quantity combination, profit, and consumer surplus.

g) Comparison with perfect competition

i. What are the price and quantity at the market equilibrium under perfect competition?

ii. What is the firm's profit in this case?

iii. What is the consumer surplus?

iv. What are the differences between profits, consumer surplus, and total welfare (profits

plus consumer surplus) between monopoly and perfect competition?