Exercises: Price Controls and Per-Unit Taxes

A city government passes a law that says landlords cannot charge more than $\$900$ per month for a one-bedroom apartment. The equilibrium rent in the city without the law is $\$1,400$ per month. Is this price control a price ceiling or a price floor? Is it binding? Explain in two or three sentences what you expect to happen to the quantity of apartments demanded and the quantity supplied.

A state sets a minimum price of $\$5.00$ per gallon for milk to help dairy farmers. Without the policy, the equilibrium price is $\$3.50$ per gallon. Define a price floor in your own words, and state whether this one creates a shortage or a surplus. Identify which side of the market (buyers or sellers) wants to trade more at the controlled price.

The federal government places a per-unit tax of $\$2$ on every pack of cigarettes sold, collected from sellers. On a standard supply and demand graph, state which curve shifts, in which direction, and whether the equilibrium quantity rises or falls. Also say whether the price buyers pay rises or falls.

The market for concert tickets in Chicago has the demand curve $Q_d = 800 - 10P$ and the supply curve $Q_s = 20P - 100$, where $P$ is the price in dollars and $Q$ is tickets per night.

(a) Find the equilibrium price and quantity.

(b) The city imposes a price ceiling of $\$20$ per ticket. Find the quantity demanded, the quantity supplied, and the size of the shortage.

(c) Does the ceiling help or hurt consumers who are able to buy a ticket? Explain briefly.

In a market for corn, the demand curve is $Q_d = 500 - 20P$ and the supply curve is $Q_s = 30P$, where $P$ is dollars per bushel and $Q$ is thousands of bushels. The government sets a price floor of $\$12$ per bushel.

(a) Find the free-market equilibrium price and quantity.

(b) Find the quantity demanded and the quantity supplied at the floor.

(c) State the size of the surplus and explain why the quantity actually traded is the smaller of the two quantities.

The market for pizza slices in a college town has an equilibrium price of $\$4.00$ and an equilibrium quantity of 1,000 slices per day. The town imposes a per-unit tax of $\$1.00$ per slice, collected from sellers. After the tax, buyers pay $\$4.60$ per slice and the quantity falls to 800 slices per day.

(a) How much of the tax does each slice's buyer bear? How much does the seller bear (the price the seller keeps is the buyer's price minus the tax)?

(b) Calculate the tax revenue the government collects per day.

(c) Calculate the deadweight loss, treating the lost-trade region as a triangle.

(d) Which side of the market bears the larger share of the tax, and what does that suggest about relative elasticities?

The market for rental apartments in a city has the linear demand curve $P = 2{,}000 - 2Q$ and the linear supply curve $P = 200 + Q$, where $P$ is monthly rent in dollars and $Q$ is thousands of apartments.

(a) Find the equilibrium rent and quantity, and compute consumer surplus and producer surplus.

(b) The city imposes a rent ceiling of $\$800$. Find the quantity supplied and the quantity demanded, and state the quantity actually rented.

(c) Compute consumer surplus, producer surplus, and the deadweight loss under the ceiling. Assume that the apartments that are rented go to the consumers with the highest willingness to pay.

(d) Explain why this assumption is probably unrealistic, and how relaxing it would change the size of the deadweight loss.

The market for gasoline in a state has the demand curve $P = 8 - 0.02Q$ and the supply curve $P = 2 + 0.01Q$, where $P$ is dollars per gallon and $Q$ is millions of gallons per week. The state imposes a per-unit tax of $\$0.60$ per gallon collected from sellers.

(a) Find the pre-tax equilibrium price and quantity.

(b) Write the new supply curve including the tax and find the new quantity, the price paid by buyers, and the price received by sellers.

(c) Compute the tax incidence on buyers and on sellers per gallon, and the government's weekly tax revenue.

(d) Compute the deadweight loss.

(e) The state is considering a second proposal: a tax of $\$1.20$ per gallon. Without recalculating everything, explain what happens to the deadweight loss relative to the $\$0.60$ tax, and why economists describe the relationship the way they do.