Chapter 8 — Exercises
Section A — Computing consumer surplus
A1. A demand curve is given by P = 100 − Q (where P is price and Q is quantity). The market price is $40. Find: - (a) The equilibrium quantity demanded at this price - (b) The maximum willingness to pay (the y-intercept) - (c) The consumer surplus (use the triangle formula)
A2. A demand curve is P = 80 − 2Q. The market price is $20. Find consumer surplus.
A3. Suppose the demand for a good at the equilibrium price is 50 units, and the maximum willingness to pay (where the demand curve crosses the y-axis) is $30 above the market price. What is the consumer surplus?
A4. Now suppose the market price for the same good in A3 falls by $10 (and the maximum willingness to pay stays the same). What happens to consumer surplus? (Hint: don't use a fixed demand curve — think about the geometry.)
Section B — Computing producer surplus
B1. A supply curve is P = 10 + Q. The market price is $40. Find: - (a) The quantity supplied at this price - (b) The minimum willingness to sell (the y-intercept) - (c) The producer surplus
B2. A supply curve is P = 20 + 2Q. The market price is $60. Find producer surplus.
B3. Why is producer surplus measured above the supply curve and below the market price (rather than the other way around)?
Section C — Computing total surplus
C1. Demand: P = 100 − Q. Supply: P = 10 + Q. Find: - (a) Equilibrium price and quantity - (b) Consumer surplus - (c) Producer surplus - (d) Total surplus
C2. Demand: P = 60 − Q. Supply: P = Q. Find equilibrium and surpluses.
C3. In which of C1 and C2 is consumer surplus larger than producer surplus? Why?
Section D — Surplus effects of taxes
D1. Use the demand and supply from C1. A tax of $20/unit is imposed. Show that: - (a) The quantity falls - (b) Consumer surplus shrinks - (c) Producer surplus shrinks - (d) The government collects revenue - (e) There is a deadweight loss (compute it)
D2. Compute the change in consumer surplus, producer surplus, and total surplus from D1. Verify that consumer + producer + government revenue + deadweight loss = the original total surplus.
D3. Now imagine the tax in D1 is doubled to $40/unit. What happens to the deadweight loss? (Hint: it more than doubles. Why?)
Section E — Surplus effects of price controls
E1. Use the demand and supply from C1. A price ceiling at $40 is imposed. Show that: - (a) Quantity supplied falls below the equilibrium quantity - (b) Some consumers benefit (those who get units at the controlled price) - (c) Other consumers are hurt (those who can't get units at all) - (d) Producers lose surplus - (e) There is deadweight loss (and no government revenue)
E2. Use the same supply and demand. A price floor at $70 is imposed. What happens to total surplus?
Section F — Conceptual
F1. Why does the deadweight loss of a tax exist? Explain in your own words why some trades that "would have happened" no longer happen with a tax in place.
F2. Why is the deadweight loss of a tax bigger when supply or demand is more elastic?
F3. Why are economists generally suspicious of government policies that don't include some accounting for deadweight loss? What does it tell you about the policy?
F4. "Maximizing total surplus" is one way to evaluate a policy. Are there policies you can think of where maximizing total surplus would lead to a clearly bad outcome for moral or distributional reasons?
Section G — The efficiency-equity tradeoff
G1. Suppose a tax raises $1 million in revenue and creates $300,000 of deadweight loss. Compare this to a different tax that raises $1 million but creates $100,000 of deadweight loss. Which is more efficient? Could the more efficient one still be a worse policy on other grounds?
G2. A monopolist who captures all consumer surplus is "efficient" in the sense of producing the equilibrium quantity, but the resulting distribution is one most people consider unjust. Use the surplus framework to articulate this tension.
G3. "If we just maximize total welfare, we can ignore distributional concerns because there will be more total wealth to share around." Use the framework from this chapter to evaluate this argument. Where does it work, and where does it fail?
G4. Find a real-world policy debate (in the news or in your community) and frame it as an efficiency-equity tradeoff. Which side is prioritizing efficiency? Which is prioritizing equity? Are they aware of the trade-off they're making?
Section H — Reflection
- The surplus framework lets you put a number on "how much value a market creates." Are there things of value the framework doesn't capture?
- After reading this chapter, do you think competitive markets are "efficient"? In what sense? Are there other senses in which they are not?
- The chapter argues that Pareto efficiency is "not the same as fair." Can you imagine a Pareto-efficient outcome that everyone would agree is fair? Can you imagine an unfair outcome that is also Pareto efficient?
Selected answers in appendices/answers-to-selected.md.