Source: Sample Midterm 1, Q6a and Q6b
Difficulty: Intermediate (part a), Advanced (part b) | Prerequisites: Supply and demand, consumer and producer surplus, price controls.
This topic applies welfare analysis to two different housing-market policies: a price ceiling (rent control) and a per-unit subsidy to landlords. It tests whether you understand how each policy affects surplus and, critically, the concept of misallocation. Part (a) on the price ceiling is expected to be straightforward; part (b) on the subsidy comparison is challenging. The misallocation concept is the key differentiator for a strong answer.
A price ceiling below equilibrium creates a shortage, reduces the quantity traded to the quantity supplied, and lowers producer surplus. A per-unit subsidy that achieves the same consumer price avoids the shortage and eliminates misallocation among consumers, giving consumers strictly higher surplus than the price ceiling. The crucial difference is that the subsidy allocates apartments by price (efficiently), while the price ceiling forces non-price allocation (search, connections), which wastes surplus.
Price ceiling
A legally imposed maximum price. When set below the equilibrium price, it creates a shortage. Think of it as the government saying "you cannot charge more than this."
Shortage (excess demand)
The gap between quantity demanded and quantity supplied when price is held below equilibrium. Quantity actually transacted equals the smaller of the two, which is quantity supplied.
Producer surplus
The area above the supply curve and below the price, up to the quantity sold. It measures how much better off producers are from selling at the market price versus their minimum acceptable price.
Consumer surplus
The area below the demand curve and above the price, up to the quantity bought. With a price ceiling, actual consumer surplus may be less than this area because of misallocation.
Misallocation (among consumers)
When goods are not allocated to the consumers with the highest willingness to pay. Under a price ceiling with a shortage, apartments are rationed by non-price mechanisms (queuing, connections), so the Q_S people who get apartments are unlikely to be the Q_S with the highest marginal benefit.
Per-unit subsidy
A payment from the government to producers for each unit sold, which shifts the supply curve downward by the subsidy amount. It increases the quantity traded and lowers the price consumers pay.
Setting up the diagram
Initial equilibrium: price P₁, quantity Q₁.
The price ceiling P_C is set below P₁.
At P_C: quantity supplied = Q_S (less than Q₁), quantity demanded = Q_D (more than Q₁). There is a shortage (excess demand).
Quantity traded under a shortage
When there is a shortage, the quantity bought and sold equals the quantity supplied (Q_S), not the quantity demanded. Landlords will only supply Q_S units at the ceiling price, and that is all that can be rented.
Producer surplus
Before the ceiling: producer surplus = area a + b (the area under the price P₁ and above the supply curve, up to Q₁).
After the ceiling: producer surplus = area b only (under P_C and above the supply curve, up to Q_S).
The price ceiling reduces producer surplus by area a.
How the subsidy works
A per-unit subsidy paid to landlords shifts the supply curve downward by the subsidy amount.
The subsidy is sized so the new equilibrium price consumers pay equals P_C. This means S₁ shifts down to S₂, where S₂ intersects D₁ at P_C.
At this price, the quantity traded is Q₂, which is much larger than Q_S.
Consumer surplus under the price ceiling
With the ceiling, consumer surplus is less than area c (the triangle under D and above P_C up to Q_S). It is less because there is misallocation: apartments are not going to the consumers who value them most. Non-price rationing (search, connections, luck) means the Q_S renters are unlikely to be the Q_S highest-value consumers.
Consumer surplus under the subsidy
With the subsidy, consumer surplus = c + d + e (under D and above P_C = P₂ up to Q₂).
This is larger for two reasons: the quantity is bigger (Q₂ > Q_S), and apartments are allocated by price, so there is no misallocation. The Q₂ people who rent are exactly the Q₂ with the highest willingness to pay.
The key distinction: misallocation
Under the price ceiling: non-price allocation leads to misallocation among consumers. Consumer surplus is eroded.
Under the subsidy: price allocation means no misallocation. Every renter has a marginal benefit at least as high as P₂.
Producer surplus = area under price, above S, up to quantity sold.
Consumer surplus = area under D, above price paid, up to quantity bought (reduced by misallocation when non-price rationing occurs).
Diagram for part (a): standard S-D diagram. P_C below P₁. Q_S < Q₁ < Q_D. Areas a (lost PS) and b (remaining PS) between P₁, P_C, and S₁.
Diagram for part (b): S₁ shifts down to S₂ so S₂ meets D at P_C. The subsidy wedge between S₁ and S₂ is visible. Areas c, d, e form the consumer surplus triangle under D and above P_C up to Q₂.
Rent control in cities like New York and San Francisco creates the classic price-ceiling shortage: long waiting lists, apartments allocated by connections or luck, and landlords reducing maintenance. A housing subsidy (like Section 8 vouchers in the US) increases the quantity of housing available to lower-income renters and allocates units by willingness to pay, avoiding the worst misallocation problems of pure rent control.
Students sometimes say that when there is a shortage, the quantity traded is the quantity demanded. It is the quantity supplied. Landlords set the binding constraint.
Claiming that a price ceiling causes misallocation among producers and therefore producer surplus is less than area b. This is wrong; misallocation among producers is not the relevant issue here.
Forgetting misallocation entirely. Without discussing misallocation, you cannot explain why consumer surplus differs between the price ceiling and the subsidy.
Mentioning government spending on the subsidy. While true that the subsidy costs the government money, this is not relevant to the question about consumer surplus comparison.
⚠️ Part (a) was expected to be easy (mean of 11+ out of 15). A strong answer explicitly states that quantity traded equals quantity supplied when there is a shortage.
⚠️ For part (b), you must know how a subsidy paid to landlords appears on the diagram (supply shifts down by the subsidy amount) and size it correctly so the new equilibrium price = P_C. Failing to shift supply far enough costs at least 4 marks.
⚠️ Discussing misallocation is essential for part (b). An answer that omits it is capped at 10 out of 15.
⚠️ Government spending on the subsidy, while true, is irrelevant to the consumer surplus comparison and should not be a focus.
True or false: Under a binding price ceiling, quantity traded equals quantity demanded. (False, it equals quantity supplied.)
Fill in the blank: A per-unit subsidy to producers shifts the ______ curve downward. (supply)
True or false: Misallocation among consumers reduces consumer surplus below what the area under D and above P_C would suggest. (True.)
Fill in the blank: Under the subsidy, apartments are allocated by ______, so there is no misallocation. (price)
True or false: A price ceiling always increases consumer surplus relative to the free-market equilibrium. (False, misallocation can erode it.)
Q: Using a diagram, explain what happens to producer surplus in the housing market when a price ceiling is imposed below the equilibrium rent.
A: Before the ceiling, equilibrium is at P₁ and Q₁. Producer surplus is the area under P₁ and above S₁ up to Q₁ (areas a + b). When the ceiling P_C is imposed, landlords supply only Q_S at P_C. Producer surplus shrinks to area b (under P_C, above S₁, up to Q_S). Producer surplus falls by area a.
Q: Suppose the government replaces the price ceiling with a per-unit subsidy to landlords that brings the equilibrium rent down to P_C. Explain why consumer surplus is higher under the subsidy than under the price ceiling.
A: The subsidy shifts S₁ down to S₂ so D meets S₂ at P_C. The quantity traded rises to Q₂, much more than Q_S. Consumer surplus under the subsidy is the full triangle under D and above P_C up to Q₂ (areas c + d + e). Under the price ceiling, consumer surplus is less than area c alone, because the shortage means apartments are allocated by non-price mechanisms, and the Q_S renters are unlikely to be the highest-value consumers (misallocation). The subsidy eliminates misallocation because apartments are allocated by willingness to pay, and it increases the quantity available. Both effects make consumer surplus larger.
This connects to the externalities topic through welfare analysis: both ask you to compare surplus under different policies. It also links to tax incidence (a subsidy is a negative tax), and to the broader theme that non-price allocation mechanisms tend to reduce efficiency relative to price allocation.
Price ceiling, rent control, binding price ceiling, shortage, excess demand, quantity supplied, quantity demanded, producer surplus, consumer surplus, misallocation, non-price rationing, per-unit subsidy, supply shift, welfare analysis, housing market, Section 8, rent subsidy, deadweight loss, ECON 2, intro microeconomics, NYU Economics 2