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 â 2Q. The total cost of producing Q units is C(Q) = 20Q + 2Q2 .
a) Identify the unregulated equilibrium (P â , Qâ )
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 Ï = 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.
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 â 2Q. The total cost of producing Q units is C(Q) = 20Q + 2Q2 .
a) Identify the unregulated equilibrium (P â , Qâ )
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 Ï = 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.
