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3rd degree price discrimination. We have the same market conditions as the previous problem. p1(q1) = 1, 000 − q1 p2(q2) = 500 − q2 This producer also faces a constant marginal cost of 100.

i. If the monopolist is able to effectively conduct 3rd degree price discrimination, what are the optimal price-quantity pairs for each group of consumers?

ii. What is the total CS, PS, and W from both markets?

iii. If the monopolist can only charge a single price, what are the optimal output and price?

iv. How much is sold to each type of consumer?

v. Find the CS, PS, and W for this scenario.

vi. Compare the three welfare measures in the two scenarios.

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Related questions

Taxing a monopolist. A monopolist faces an inverse demand function and experiences a the following cost of production. P(Q) = 11, 000 − 5Q C(Q) = 1, 000Q + 5Q 2

i. What is the optimal quantity and price for the monopolist?

ii. Find CS, PS, and W. iii. Find DWL

iv. If a specific tax of τ = 20 is imposed, what is the monopolist’s new optimal price and quantity?

v. Find CS, PS, T, and W. vi. Find DWL.

1) Taxing a monopoly (20 Points) Suppose that a monopolist sells a product to consumers with an aggregate demand that is downward sloping in quantity, D(Q) = 200 − 2Q. The total cost of producing Q units is C(Q) = 20Q + 2Q2 .

a) Identify the unregulated equilibrium (P ∗ , Q∗ )

b) What are the consumer and producer surpluses (CS and PS) and total welfare (W) at this equilibrium?

c) Suppose that a specific tax of τ = 20 is imposed on each unit. i. What price-quantity pair (P 1 , Q1 ) would we expect? ii. What are CS, PS, tax revenue (T), and W? iii. What is deadweight loss?

d) Instead of a specific tax, an ad valorem tax, α = 16 is imposed i. What price-quantity pair (P 2 , Q2 ) would we expect? ii. What are CS, PS, T, and W? iii. What is deadweight loss?

e) Welfare distribution i. Which scenario results in the highest producer surplus? ii. Which scenario results in the greatest gains for consumers, assuming that all tax revenues are perfectly redistributed to consumers only.

3. A monopolist has two sets of customers. The inverse demand for Group 1 is described by P1 = 200 - Q1. For Group 2, the inverse demand is P2 = 100- Q2. The monopolist faces ca constant marginal cost of 40. Let Q be the aggregate quantity demanded.

a. (10 points) Show that the monopolist's total demand if the two markets are treated as one is: Q=0; P =200

Q=200-P;100<P =200
Q=300-2P;0<P = 100
b. (10 points) Show that the monopolist's profit-maximizing price is P = 95 if both groups are to be charged the same price. At this price, how much is sold to members of Group 1 and how much

to members of Group 2? What is the consumer surplus of each group? What are the total profits?

4. Now suppose that the monopolist in problem #3 can separate the two groups and charge separate, profit-maximizing prices to each group.

a. (10 points) What will these prices be? What is consumer surplus? What are the total profits?
b. (10 points) If the total surplus is consumer surplus plus profit, how has price discrimination affected total surplus?

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