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Microeconomics practice questions with answers

Ten exam-style microeconomics problems with complete worked solutions — elasticity, market equilibrium, consumer surplus, price controls, tax incidence, perfect competition, and monopoly. Work each problem on paper before opening the solution; retrieval is the part that makes practice work. Free to use, no signup.

Problem 1

The price of a good rises from 4 euros to 5 euros, and quantity demanded falls from 100 units to 80 units. Calculate the price elasticity of demand using the midpoint method, and state whether demand is elastic, inelastic, or unit elastic over this range.
Show worked solution
Midpoint percentage change in quantity: 80−100(80+100)/2=−2090≈−22.2%\frac{80 - 100}{(80+100)/2} = \frac{-20}{90} \approx -22.2\%. Midpoint percentage change in price: 5−4(5+4)/2=14.5≈22.2%\frac{5-4}{(5+4)/2} = \frac{1}{4.5} \approx 22.2\%. So ϵD=−22.2%22.2%=−1.0\epsilon_D = \frac{-22.2\%}{22.2\%} = -1.0. Demand is unit elastic over this range: total revenue is unchanged by the price increase.

Problem 2

A market has demand QD=120−2PQ_D = 120 - 2P and supply QS=30+PQ_S = 30 + P. Find the equilibrium price and quantity.
Show worked solution
Set QD=QSQ_D = Q_S: 120−2P=30+P120 - 2P = 30 + P, so 90=3P90 = 3P and P∗=30P^* = 30. Substituting back: Q∗=30+30=60Q^* = 30 + 30 = 60. Check with demand: 120−2(30)=60120 - 2(30) = 60. Equilibrium is P∗=30P^* = 30, Q∗=60Q^* = 60.

Problem 3

Using the market from Question 2 (QD=120−2PQ_D = 120 - 2P, equilibrium P∗=30P^* = 30, Q∗=60Q^* = 60), calculate consumer surplus at equilibrium.
Show worked solution
The choke price (where QD=0Q_D = 0) solves 120−2P=0120 - 2P = 0, so P=60P = 60. Consumer surplus is the triangle between the demand curve and the price: CS=12×(60−30)×60=900CS = \frac{1}{2} \times (60 - 30) \times 60 = 900. Consumer surplus equals 900.

Problem 4

In the same market, the government imposes a price ceiling at P=20P = 20. Calculate the resulting shortage.
Show worked solution
At P=20P = 20: quantity demanded is 120−2(20)=80120 - 2(20) = 80; quantity supplied is 30+20=5030 + 20 = 50. The shortage is 80−50=3080 - 50 = 30 units. Because the ceiling is below the equilibrium price of 30, it binds, and quantity traded falls to the supplied quantity, 50.

Problem 5

The cross-price elasticity of demand between good X and good Y is ϵXY=+0.8\epsilon_{XY} = +0.8. What does this tell you about the relationship between the two goods, and what would a negative value have implied?
Show worked solution
A positive cross-price elasticity means a rise in the price of Y increases demand for X — the goods are substitutes (consumers switch toward X when Y becomes more expensive). A negative value would imply complements: goods consumed together, so a price rise in one reduces demand for both. The magnitude 0.8 indicates a moderately strong substitute relationship.

Problem 6

A perfectly competitive firm faces a market price of 15 and has marginal cost MC=3+0.2QMC = 3 + 0.2Q. Find the profit-maximizing output.
Show worked solution
A price-taking firm maximizes profit where P=MCP = MC: 15=3+0.2Q15 = 3 + 0.2Q, so 0.2Q=120.2Q = 12 and Q=60Q = 60. The firm produces 60 units. (Producing less leaves profitable units unsold; producing more means the last units cost more than they earn.)

Problem 7

A firm in a perfectly competitive market faces a price of 8, while the minimum of its average variable cost curve is 10. Should the firm produce in the short run? Explain the rule you are using.
Show worked solution
No. The short-run shutdown rule is: produce only if P≥min⁡AVCP \geq \min AVC. Here price (8) is below minimum average variable cost (10), so every unit produced fails to cover even its variable cost, and operating adds losses beyond the unavoidable fixed costs. The firm minimizes losses by shutting down and losing only its fixed costs.

Problem 8

Return to the market QD=120−2PQ_D = 120 - 2P, QS=30+PQ_S = 30 + P. The government levies a per-unit tax of 9 on sellers. Find the new price paid by consumers, the price received by sellers, and the share of the tax borne by each side.
Show worked solution
With the tax, sellers supply according to the price they keep: QS=30+(P−9)=21+PQ_S = 30 + (P - 9) = 21 + P. New equilibrium: 120−2P=21+P120 - 2P = 21 + P, so 99=3P99 = 3P and consumers pay PC=33P_C = 33. Sellers receive 33−9=2433 - 9 = 24. Relative to the original equilibrium price of 30, consumers pay 3 more (one third of the tax) and sellers receive 6 less (two thirds). Sellers bear more because supply (dQS/dP=1dQ_S/dP = 1) responds less to price than demand (∣dQD/dP∣=2|dQ_D/dP| = 2) — the less responsive side of the market bears the larger share.

Problem 9

A monopolist faces demand P=100−QP = 100 - Q and constant marginal cost MC=20MC = 20. Find the profit-maximizing price and quantity, and calculate the deadweight loss relative to perfect competition.
Show worked solution
Marginal revenue for linear demand has twice the slope: MR=100−2QMR = 100 - 2Q. Setting MR=MCMR = MC: 100−2Q=20100 - 2Q = 20, so QM=40Q_M = 40 and PM=100−40=60P_M = 100 - 40 = 60. Under perfect competition, P=MCP = MC gives QC=80Q_C = 80. Deadweight loss is the triangle between demand and marginal cost over the lost output: DWL=12×(80−40)×(60−20)=800DWL = \frac{1}{2} \times (80 - 40) \times (60 - 20) = 800.

Problem 10

The income elasticity of demand for a good is estimated at ϵI=−0.5\epsilon_I = -0.5. Classify the good and explain what happens to demand when consumer incomes rise by 10 percent.
Show worked solution
A negative income elasticity defines an inferior good: as income rises, consumers buy less of it, typically substituting toward higher-quality alternatives. A 10 percent rise in income reduces quantity demanded by about 10%×0.5=5%10\% \times 0.5 = 5\%, shifting the demand curve left. (A normal good has ϵI>0\epsilon_I > 0; a luxury has ϵI>1\epsilon_I > 1.)

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