ECON 1 Lecture Notes - Lecture 8: Deadweight Loss, Economic Surplus, Dwls

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.

QD 950 - P and QS = 2P - 160

Welfare Effects of a Tariff:
Given the demand and supply equations above, suppose the free trade (world) price is $200.

a. Solve for the amount imported, consumer surplus, and producer surplus.

b. Suppose a per unit tariff of $30 is imposed by the government. Solve for the consumer surplus, producer surplus, government revenue and total surplus with the tariff.

c. Solve for the change in consumer surplus, the change in producer surplus, the change in government revenue and change in total surplus (i.e. the deadweight loss) from the free trade case (without the tariff). [To do this, make the calculations using your answers in 3a, and calculate total surplus under free trade].

The market for packets of cigarettes has been described by the following supply and demand functions:

Supply: P = 10 + 4Q Demand: P = 100 - 5Q where P is the price in dollars and Q is the quantity of packets of cigarettes per month (in thousands).

Part A) Construct a graph of supply and demand for this market showing all intercepts. What are the equilibrium prices and quantities? Show these on your graph.

Part B) At the market equilibrium price, what would be the total monthly revenue?

Part C) Calculate consumer surplus at the market equilibrium and indicate this surplus as an area on your diagram.

Part D) Calculate producer surplus at the market equilibrium and indicate this surplus as an area on your diagram.

Part E) Assume that a per-unit tax of $9.00 per packet of cigarettes is imposed by the government on the suppliers of cigarettes. Depict this on your demand and supply diagram. (Hint: the new tax inclusive supply function will be: P = 19 + 4Q). What is the new market equilibrium quantity? What price will consumers now pay and what price will suppliers now receive?

Part F) How much is the government revenue from the tax on suppliers?

Part G) Calculate consumer surplus and producer surplus after the imposition of the tax and any deadweight loss associated with the tax. Indicate these surplus and tax revenue areas on your diagram. Explain what the deadweight loss represents.

Part H) Now assume that instead of imposing a per-unit tax of $9.00 per pack on the suppliers of cigarettes the government decides to apply the same per-unit tax of $9.00 on consumers. Depict this on your demand and supply diagram. (Hint: the new tax inclusive demand function will be: P = 91 - 5Q) What is the new market equilibrium quantity? What price will consumers now pay and what price will suppliers now receive? (5 marks)

Part I) How much is the government revenue from the tax on consumers? (1 mark)

Part J) Who bears the greatest burden of the tax in each case, producers or consumers? Does your answer depend on whether the tax is levied on producers or consumers?

I am really having difficulty understanding Part J - can that please be answered with some detail?