Source: Chapters 9 & 11 Practice Questions, Microeconomic Theory (Texas A&M University)
Tags: consumer surplus, producer surplus, deadweight loss, DWL, welfare economics, total surplus, social welfare, price ceiling, rent control, per-unit tax, tax incidence, willingness to pay, WTP, reservation price, market efficiency, Pareto efficiency, competitive equilibrium
Consumer surplus measures the gap between what a buyer is willing to pay and what they actually pay. Producer surplus measures the gap between the price a seller receives and the minimum they would accept. When markets move away from the competitive equilibrium (through price controls, taxes, or restricted output), deadweight loss appears as the surplus that simply vanishes.
Consumer surplus (CS)
The difference between a consumer's maximum willingness to pay for a good and the price they actually pay. Graphically, it is the area below the demand curve and above the market price.
Producer surplus (PS)
The difference between the price a seller receives and the minimum price at which they would be willing to sell. Graphically, it is the area above the supply curve and below the market price.
Total surplus (social welfare)
The sum of consumer surplus and producer surplus in a market. At the competitive equilibrium, total surplus is maximised.
Deadweight loss (DWL)
The reduction in total surplus that results when output deviates from the competitive level. It represents gains from trade that are lost entirely, not transferred to anyone.
Willingness to pay (WTP)
The maximum amount a buyer would pay for a unit of a good. Revealed through behaviour: if someone refuses to sell at a given offer, their WTP must be at least that amount.
Reservation price (seller)
The minimum price at which a seller is willing to part with a good. For producer surplus calculations, it is the seller's cost or walk-away price.
Price ceiling
A legal maximum price set below the equilibrium price. Creates a shortage (quantity demanded exceeds quantity supplied) and generates deadweight loss.
Tax incidence
The division of a tax burden between buyers and sellers. A per-unit tax on sellers shifts the supply curve upward by the tax amount; the resulting price and quantity changes determine who bears more of the burden.
Consumer surplus can sometimes be inferred from observed choices rather than calculated from a demand curve.
If a buyer purchased a good at price P and later refuses an offer of $X to give it up, their valuation must exceed $X.
Their CS is therefore at least (valuation - purchase price), which is at least ($X - P).
Example: Mary buys a toy for $5 and refuses a $100 offer. Her valuation exceeds $100, so her CS is at least $100 - $5 = $95. But since her valuation could be much higher than $100, the correct bound is that CS is at least $95.
Correct answer to Q1: C) at least $95.
Common mistake: confusing the offer price with the valuation. The $100 is a lower bound on valuation, not the valuation itself.
With a linear supply curve p = a + bQ, producer surplus at a given price is the triangle between the price line and the supply curve, from Q = 0 to the quantity supplied.
Formula for a linear supply curve: PS = 0.5 × (P - a) × Q, where Q is the quantity supplied at price P.
Example: Supply is p = 5 + Q. At P = 10, quantity supplied Q = 5. PS = 0.5 × (10 - 5) × 5 = 12.50.
Correct answer to Q2: D) 12.50.
With a linear demand curve p = a - bQ, consumer surplus at a given price is the triangle between the demand curve and the price line.
Formula for a linear demand curve: CS = 0.5 × (a - P) × Q, where Q is the quantity demanded at price P.
When the good is free (P = 0), the consumer purchases up to their maximum quantity (where demand hits zero).
Example: Demand is p = 10 - Q. At P = 0, Q = 10. CS = 0.5 × (10 - 0) × 10 = 50.
Correct answer to Q3: B) $50.
For a single seller with a known minimum acceptable price (reservation price), PS = sale price - reservation price.
The asking price is irrelevant to producer surplus; what matters is the minimum the seller would accept.
Example: Jones would accept no less than $200,000 and sells for $205,000. PS = $205,000 - $200,000 = $5,000.
Correct answer to Q4: A) $5,000.
Common mistake: using the asking price ($220,000) or calculating the buyer's surplus instead.
DWL from a reduction in output below the competitive level equals the loss in total surplus (CS + PS) when moving from the competitive quantity to the lower quantity.
It is the area of the triangle between the demand curve and the supply curve, from the restricted quantity to the competitive quantity.
This is found by summing the change in CS and the change in PS (both will be negative; DWL is the absolute value of that combined change).
Correct answer to Q5: A) summing the change in the total consumer and producer surplus from moving from the competitive level of output to less output.
A price ceiling below equilibrium reduces the quantity transacted to the quantity supplied at the ceiling price.
The market moves from equilibrium (Q2 at the intersection) to the restricted quantity (Q1 at the ceiling price on the supply curve).
Consumer surplus may increase or decrease depending on which consumers end up with the units, but total surplus always falls.
The deadweight loss is the triangle of lost trades between Q1 and Q2.
Referring to the diagram with prices 350 and 450:
At the $350 rent ceiling, quantity falls to Q1 (on the supply curve).
The DWL triangle between Q1 and Q2, bounded by demand above and supply below, corresponds to areas f + g.
Correct answer to Q8: C) f + g.
Producer surplus decreases under the rent ceiling. Sellers receive a lower price and sell fewer units.
Correct answer to Q9: A) decreases.
A $2 per gallon tax on sellers shifts the supply curve upward by $2.
From the diagram: the initial equilibrium is at P = $3, Q = 1000.
After the tax, the new equilibrium price paid by buyers rises (toward $4), and the price received by sellers falls (toward $2). The exact split depends on the relative elasticities of supply and demand.
Quantity falls from 1000 to approximately 500.
Social welfare decreases by the deadweight loss triangle: DWL = 0.5 × tax × change in quantity = 0.5 × $2 × 500 = $500.
The tax also transfers surplus to the government as tax revenue (tax × new quantity), but DWL is the portion that disappears entirely.
For Q10: The price buyers pay rises, the price sellers receive falls, quantity drops, and social welfare decreases by the DWL triangle.
Consumer surplus (linear demand, p = a - bQ):
CS = 0.5 × (a - P) × Q
Producer surplus (linear supply, p = c + dQ):
PS = 0.5 × (P - c) × Q
Deadweight loss from a per-unit tax:
DWL = 0.5 × t × ΔQ
where t is the tax per unit and ΔQ is the reduction in quantity from the pre-tax equilibrium.
⚠️ Consumer surplus from behaviour: if someone refuses an offer, their valuation is at least that offer. The surplus is at least (offer - price paid), but could be more. Do not treat the offer as the exact valuation.
⚠️ Producer surplus uses the reservation price (minimum acceptable), not the asking price or the buyer's valuation.
⚠️ Deadweight loss is the change in total surplus, not the total surplus remaining. It is the surplus that is lost to nobody.
⚠️ A price ceiling reduces quantity to the amount supplied at the ceiling (supply curve, not demand curve). The shortage is the gap between quantity demanded and quantity supplied, but the quantity actually transacted is the lower of the two.
⚠️ Tax incidence: the legal assignment of the tax (on sellers vs. buyers) does not determine who bears the economic burden. That depends on relative elasticities.
Q: Mary buys a toy for $5 and refuses a $100 offer. What can you say about her consumer surplus?
A: Her valuation exceeds $100 (she refused the offer), so CS > $100 - $5 = $95. We can say CS is at least $95.
Q: If the supply curve is p = 5 + Q, what is producer surplus at P = 10?
A: Q = 5 at P = 10. PS = 0.5 × (10 - 5) × 5 = 12.50.
Q: Joe's demand is p = 10 - Q and the price is $0. What is his consumer surplus?
A: At P = 0, Q = 10. CS = 0.5 × 10 × 10 = $50.
Q: A seller's reservation price is $200,000 and they sell for $205,000. What is their producer surplus?
A: PS = $205,000 - $200,000 = $5,000. The asking price is irrelevant.
Q: How do you measure deadweight loss when output falls below the competitive level?
A: Sum the changes in consumer surplus and producer surplus from the competitive output to the restricted output. The net loss is the DWL.
Q: A rent ceiling of $350 is imposed in a market where equilibrium rent is $400. What happens to producer surplus?
A: Producer surplus decreases. Sellers receive a lower price and supply fewer units.
Q: A $2 per-unit tax is imposed on milk sellers. How does this affect social welfare?
A: Social welfare falls by the deadweight loss triangle. DWL = 0.5 × tax × reduction in quantity. Tax revenue is transferred to the government but the DWL is a net loss.
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