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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.

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Retselisitsoe Pokothoane
Retselisitsoe PokothoaneLv10
28 Sep 2019

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Related questions

(1) Monopolist’s optimization problem. A monopolist faces an inverse demand function and experiences a the following cost of production.

P(Q) = 90 − Q

C(Q) = 10Q + 1/2 Q^2

i. Find the monopolist’s optimal production choice, Q∗ , and corresponding price, P ∗ = P(Q∗ ).

ii. Find CS, PS, and W.

iii. What is the deadweight loss in this market?

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.

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.

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