Question

Microeconomics

Party leader’s speech: “Our party proposes a new tax on lottery tickets of USD 5 per lottery ticket. Since 20 million tickets are sold per year in this country, this will give the state an extra income of USD 100 million per year.”

Discuss the party leader’s statement. Is it true, is it not true, is it a good idea microeconomically speaking? Reason your answer with 2 examples. Keep in mind that the lottery market is not characterized by competition.

Answer 1

The statement is not true because it assumes that even when the price increases by 5 dollars, the demand will remain same at 20 million tickets per year.

It is not a good idea microeconomically speaking since it will result in deadweight loss.

As an example, lets say a firm has a demand function of Q = 500 – P (P=500-Q) and a marginal cost of MC = 150. Its revenue will be PQ=500Q-Q². MR=500-2Q. Since the firm will produce where MR=MC, 150=500-2Q

Q=175. Hence P=500-175=325.

Profit= (325-150)*175=30625.

Now, lets say government imposed a tax of 50 on each quantity, new P=450-Q. Revenue= 450Q-Q². MR=450-2Q. Since MR=MC, so

450-2Q=150

Q=150. Now P for 150 is 350.

So the supplier produces output of 150 and sells at a price of 350, 50 goes to the government and 300 goes to the supplier.

firm’s profit=TR-TC=PQ-(MC)Q=300*150-150*150=22500

Governments profit=50*150=7500.

Total profit=22500+7500=30000, which is lesser than pre-tax profit of 30625-30000=625. This is the deadweight loss!