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Supply and demand practice problems with answers

This page has 15 supply and demand practice problems with full worked solutions, ordered from easy to hard. They cover finding equilibrium from a table and from equations, shifts versus movements along a curve, consumer and producer surplus, price ceilings and floors with deadweight loss, per-unit taxes and subsidies and who bears them, quotas, and tariffs. Each solution shows every step with the numbers, so you can check your working as well as your final answer.

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Problem 1: Equilibrium from a demand and supply schedule

Difficulty: Easy

The table shows the weekly market for sandwiches on a university campus (price in euros, quantities in sandwiches per week). Find the equilibrium price and quantity. Is there a shortage or a surplus at a price of 4 euros, and at 10 euros? How large is it in each case?Price246810Quantity demanded10080604020Quantity supplied20406080100\begin{array}{c|ccccc} \text{Price} & 2 & 4 & 6 & 8 & 10 \\ \hline \text{Quantity demanded} & 100 & 80 & 60 & 40 & 20 \\ \text{Quantity supplied} & 20 & 40 & 60 & 80 & 100 \end{array}
Show worked solution
Equilibrium is the price at which quantity demanded equals quantity supplied. At 6 euros both are 60, so P∗=6P^* = 6 and Q∗=60Q^* = 60. At 4 euros (below equilibrium): QD=80Q_D = 80 and QS=40Q_S = 40, a shortage (excess demand) of 80−40=4080 - 40 = 40 sandwiches. Buyers who miss out bid the price up, which reduces quantity demanded and raises quantity supplied until the shortage disappears at 6 euros. At 10 euros (above equilibrium): QD=20Q_D = 20 and QS=100Q_S = 100, a surplus (excess supply) of 100−20=80100 - 20 = 80 sandwiches. Unsold stock pushes sellers to cut the price back toward 6 euros.

Problem 2: Equilibrium from linear equations

Difficulty: Easy

A market has demand QD=200−4PQ_D = 200 - 4P and supply QS=50+2PQ_S = 50 + 2P. Find the equilibrium price and quantity. What happens in this market if the price is currently 20?
Show worked solution
Set quantity demanded equal to quantity supplied: 200−4P=50+2P200 - 4P = 50 + 2P, so 150=6P150 = 6P and P∗=25P^* = 25. Substitute back: Q∗=50+2(25)=100Q^* = 50 + 2(25) = 100. Check with demand: 200−4(25)=100200 - 4(25) = 100. Equilibrium is P∗=25P^* = 25, Q∗=100Q^* = 100. At P=20P = 20: QD=200−4(20)=120Q_D = 200 - 4(20) = 120 and QS=50+2(20)=90Q_S = 50 + 2(20) = 90, a shortage of 30 units. Because the price is below equilibrium, competition among buyers pushes it up toward 25. (Problems 5, 6, 9 and 13 use this market again.)

Problem 3: Shift of a curve or movement along it?

Difficulty: Easy

For each event in the market for coffee, say whether it shifts the demand curve, shifts the supply curve, or is a movement along a curve, and predict the direction of change in the equilibrium price and quantity of coffee. (a) The price of coffee itself falls. (b) The price of tea, a substitute, rises. (c) Frost destroys part of the harvest in a major coffee-growing country. (d) The price of milk, which many people add to coffee, rises sharply. (e) A new roasting technology lowers production costs.
Show worked solution
(a) A movement along the demand curve: a change in the good's own price changes quantity demanded, not demand. The price change must itself come from a shift somewhere else (for example, an increase in supply), so this event on its own shifts nothing. (b) Demand for coffee shifts right: at every coffee price, some tea drinkers switch to coffee. Price rises and quantity rises. (c) Supply shifts left: less coffee is offered at every price. Price rises and quantity falls, and buyers respond with a movement up along the demand curve. (d) Demand for coffee shifts left, because milk is a complement and the combined cost of a coffee with milk has risen. Price falls and quantity falls. (e) Supply shifts right: each unit costs less to produce, so more is offered at every price. Price falls and quantity rises. Rule of thumb: a change in the good's own price moves you along a curve. A change in anything else that affects buyers (income, prices of related goods, tastes, expectations, number of buyers) or sellers (input prices, technology, number of sellers, expectations) shifts a curve.

Problem 4: Income changes: normal and inferior goods

Difficulty: Easy

Average incomes in a city rise. Explain what happens in (a) the market for restaurant meals, a normal good, and (b) the market for instant noodles, an inferior good. For each, name the curve that shifts and give the direction of change in the equilibrium price and quantity.
Show worked solution
(a) Restaurant meals are a normal good, so higher income raises demand: the demand curve shifts right. With supply unchanged, the new equilibrium has a higher price and a higher quantity. Sellers respond with a movement up along the supply curve; supply itself does not shift. (b) Instant noodles are an inferior good, so higher income reduces demand as people switch to foods they prefer: the demand curve shifts left. Equilibrium price and quantity both fall. In both cases only demand shifts, so price and quantity move in the same direction. That is a quick check that you have identified a demand shift rather than a supply shift.

Problem 5: A supply shift with numbers

Difficulty: Medium

Return to the market in Problem 2 (QD=200−4PQ_D = 200 - 4P, QS=50+2PQ_S = 50 + 2P). A rise in the price of a key input reduces supply to QS=20+2PQ_S = 20 + 2P. Find the new equilibrium. By how much has the supply curve shifted up at each quantity, and how much of that increase is passed on to buyers?
Show worked solution
New equilibrium: 200−4P=20+2P200 - 4P = 20 + 2P, so 180=6P180 = 6P, giving P=30P = 30 and Q=200−4(30)=80Q = 200 - 4(30) = 80. Price rises from 25 to 30 and quantity falls from 100 to 80. Write both supply curves with price on the left: originally P=Q2−25P = \frac{Q}{2} - 25, now P=Q2−10P = \frac{Q}{2} - 10. At every quantity, sellers now need 15 more per unit, so the supply curve has shifted up (to the left) by 15. Yet the price rises by only 5. Demand slopes downward, so buyers cut their purchases from 100 to 80 units (a movement along the demand curve), and sellers cannot pass the whole cost increase on. Demand itself has not shifted.

Problem 6: Both curves shift at once

Difficulty: Medium

Cheaper battery technology lowers the cost of producing e-bikes, while higher fuel prices make e-bikes more attractive to commuters. (a) What can you say for certain about the new equilibrium price and quantity of e-bikes? (b) To see why, use the market from Problem 2 and suppose demand increases to QD=260−4PQ_D = 260 - 4P. Find the new equilibrium if supply becomes QS=110+2PQ_S = 110 + 2P, and again if it becomes QS=170+2PQ_S = 170 + 2P.
Show worked solution
(a) Lower costs shift supply right, and higher fuel prices shift demand right (e-bikes are a substitute for driving). Both shifts raise quantity, so the equilibrium quantity rises for certain. The effect on price is ambiguous: the demand increase pushes the price up and the supply increase pushes it down, so the result depends on which shift is larger. (b) With QS=110+2PQ_S = 110 + 2P: 260−4P=110+2P260 - 4P = 110 + 2P, so 150=6P150 = 6P, P=25P = 25 and Q=160Q = 160. Both curves shifted right by 60 units, so the price is unchanged and quantity rises by 60. With QS=170+2PQ_S = 170 + 2P: 260−4P=170+2P260 - 4P = 170 + 2P, so 90=6P90 = 6P, P=15P = 15 and Q=200Q = 200. The larger supply shift makes the price fall. The general pattern: when both curves shift, one of price or quantity is always ambiguous. Demand and supply both increase: quantity rises, price ambiguous. Both decrease: quantity falls, price ambiguous. Demand increases and supply decreases: price rises, quantity ambiguous. Demand decreases and supply increases: price falls, quantity ambiguous.

Problem 7: Reading a shift from a graph

Difficulty: Medium

A graph of the market for fresh strawberries shows the equilibrium moving from point A (price 4 euros per kg, quantity 200 tonnes) to point B (price 5 euros per kg, quantity 180 tonnes). Assume only one curve shifted. (a) Which curve shifted, and in which direction? Suggest a plausible cause. (b) Use points A and B to estimate the price elasticity of demand with the midpoint method. (c) What happened to growers' total revenue?
Show worked solution
(a) Price rose while quantity fell. A demand shift moves price and quantity in the same direction, so this must be a supply shift: supply decreased (shifted left). A plausible cause is bad weather that damaged the harvest, or higher wages for pickers. (b) Demand did not shift, so A and B both lie on the same demand curve and can be used to estimate its elasticity. Midpoint changes: %ΔQ=180−200(180+200)/2=−20190≈−10.5%\%\Delta Q = \frac{180 - 200}{(180 + 200)/2} = \frac{-20}{190} \approx -10.5\% and %ΔP=5−4(5+4)/2=14.5≈22.2%\%\Delta P = \frac{5 - 4}{(5 + 4)/2} = \frac{1}{4.5} \approx 22.2\%. So ϵD≈−10.5%22.2%≈−0.47\epsilon_D \approx \frac{-10.5\%}{22.2\%} \approx -0.47: demand is inelastic over this range. (c) Revenue rose from 4×200=8004 \times 200 = 800 to 5×180=9005 \times 180 = 900 thousand euros (price is per kg and 1 tonne is 1,000 kg). This matches the total-revenue test: with inelastic demand, price and revenue move in the same direction.

Problem 8: Consumer and producer surplus

Difficulty: Medium

A market has demand QD=90−PQ_D = 90 - P and supply QS=2P−30Q_S = 2P - 30. Find the equilibrium, then calculate consumer surplus, producer surplus and total surplus.
Show worked solution
Equilibrium: 90−P=2P−3090 - P = 2P - 30, so 120=3P120 = 3P, P∗=40P^* = 40 and Q∗=90−40=50Q^* = 90 - 40 = 50. Find where each curve meets the price axis. Demand: QD=0Q_D = 0 at P=90P = 90 (the choke price). Supply: QS=0Q_S = 0 at P=15P = 15 (the lowest price at which anything is supplied). Consumer surplus is the triangle below the demand curve and above the price: CS=12×50×(90−40)=1,250CS = \frac{1}{2} \times 50 \times (90 - 40) = 1{,}250. Producer surplus is the triangle above the supply curve and below the price: PS=12×50×(40−15)=625PS = \frac{1}{2} \times 50 \times (40 - 15) = 625. Total surplus =1,250+625=1,875= 1{,}250 + 625 = 1{,}875. This is the largest total surplus the market can generate. Problems 10, 11, 12 and 14 use this market to measure how much each intervention reduces it, and Problem 15 opens it to trade.

Problem 9: Elasticity along a straight-line demand curve

Difficulty: Medium

For the demand curve in Problem 2, QD=200−4PQ_D = 200 - 4P, calculate the point price elasticity of demand at P=25P = 25, P=35P = 35 and P=10P = 10. What does the pattern tell you about slope and elasticity?
Show worked solution
Point elasticity is ϵD=dQdP⋅PQ\epsilon_D = \frac{dQ}{dP} \cdot \frac{P}{Q}, and here dQdP=−4\frac{dQ}{dP} = -4 everywhere on the curve. At P=25P = 25: Q=100Q = 100, so ϵD=−4×25100=−1\epsilon_D = -4 \times \frac{25}{100} = -1 (unit elastic). At P=35P = 35: Q=60Q = 60, so ϵD=−4×3560≈−2.33\epsilon_D = -4 \times \frac{35}{60} \approx -2.33 (elastic). At P=10P = 10: Q=160Q = 160, so ϵD=−4×10160=−0.25\epsilon_D = -4 \times \frac{10}{160} = -0.25 (inelastic). The slope is constant but the elasticity is not, because the ratio P/QP/Q changes along the line. Demand is unit elastic at the midpoint of the line (P=25P = 25 is halfway between the choke price of 50 and zero), elastic above it and inelastic below it.

Problem 10: Price ceiling: shortage and deadweight loss

Difficulty: Medium

In the market from Problem 8 (QD=90−PQ_D = 90 - P, QS=2P−30Q_S = 2P - 30, equilibrium P∗=40P^* = 40, Q∗=50Q^* = 50), the government imposes a price ceiling of 30. Calculate the shortage, the quantity actually traded, consumer surplus, producer surplus and the deadweight loss.
Show worked solution
The ceiling is below the equilibrium price, so it binds. At P=30P = 30: QD=90−30=60Q_D = 90 - 30 = 60 and QS=2(30)−30=30Q_S = 2(30) - 30 = 30. The shortage is 60−30=3060 - 30 = 30 units, and only 30 units are traded, because buyers cannot buy more than sellers offer. At Q=30Q = 30, the most a buyer would pay for the last unit comes from demand: P=90−30=60P = 90 - 30 = 60. The price that just covers the last seller's cost comes from supply, P=15+Q2P = 15 + \frac{Q}{2}: 15+15=3015 + 15 = 30. Consumer surplus, assuming the 30 units go to the buyers who value them most, is a trapezoid between demand and the price of 30: CS=12×[(90−30)+(60−30)]×30=1,350CS = \frac{1}{2} \times [(90 - 30) + (60 - 30)] \times 30 = 1{,}350. Producer surplus: PS=12×30×(30−15)=225PS = \frac{1}{2} \times 30 \times (30 - 15) = 225. Deadweight loss is the triangle between demand and supply over the 20 units no longer traded: DWL=12×(50−30)×(60−30)=300DWL = \frac{1}{2} \times (50 - 30) \times (60 - 30) = 300. Check: 1,350+225=1,575=1,875−3001{,}350 + 225 = 1{,}575 = 1{,}875 - 300. Consumers as a group gain here (from 1,250 to 1,350) while producers lose 400. In practice the loss is larger if some units go to buyers who value them less, or if people spend time queuing.

Problem 11: Price floor: excess supply and deadweight loss

Difficulty: Medium

In the same market (QD=90−PQ_D = 90 - P, QS=2P−30Q_S = 2P - 30), the government instead sets a minimum price of 50. Calculate the excess supply, the quantity traded, consumer and producer surplus, and the deadweight loss. How much would it cost the government to buy the unsold output at the minimum price?
Show worked solution
The floor is above the equilibrium price of 40, so it binds. At P=50P = 50: QD=90−50=40Q_D = 90 - 50 = 40 and QS=2(50)−30=70Q_S = 2(50) - 30 = 70. Excess supply is 70−40=3070 - 40 = 30 units, and only 40 units are sold, because sellers cannot sell more than buyers want. Consumer surplus: CS=12×40×(90−50)=800CS = \frac{1}{2} \times 40 \times (90 - 50) = 800, down from 1,250. Producer surplus on the 40 units sold, assuming the lowest-cost sellers make the sales: at Q=40Q = 40 the supply price is 15+402=3515 + \frac{40}{2} = 35, so PS=12×[(50−15)+(50−35)]×40=1,000PS = \frac{1}{2} \times [(50 - 15) + (50 - 35)] \times 40 = 1{,}000, up from 625. Deadweight loss over the 10 units no longer traded: DWL=12×(50−40)×(50−35)=75DWL = \frac{1}{2} \times (50 - 40) \times (50 - 35) = 75. Check: 800+1,000=1,800=1,875−75800 + 1{,}000 = 1{,}800 = 1{,}875 - 75. Buying the 30 unsold units at the floor price would cost the government 30×50=1,50030 \times 50 = 1{,}500, and producing units that no buyer wants at that price adds to the efficiency cost. A minimum wage is the labour-market version of this problem.

Problem 12: Per-unit tax: incidence, revenue and deadweight loss

Difficulty: Hard

In the market QD=90−PQ_D = 90 - P, QS=2P−30Q_S = 2P - 30, the government levies a tax of 6 per unit on sellers. Find the price buyers pay, the price sellers keep, the quantity traded, the tax revenue and the deadweight loss. How is the burden of the tax split, and would the split change if the tax were levied on buyers instead?
Show worked solution
Sellers now supply according to the price they keep, P−6P - 6: QS=2(P−6)−30=2P−42Q_S = 2(P - 6) - 30 = 2P - 42. New equilibrium: 90−P=2P−4290 - P = 2P - 42, so 132=3P132 = 3P and buyers pay PB=44P_B = 44. Sellers keep PS=44−6=38P_S = 44 - 6 = 38. Quantity: Q=90−44=46Q = 90 - 44 = 46. Tax revenue =6×46=276= 6 \times 46 = 276. Deadweight loss =12×6×(50−46)=12= \frac{1}{2} \times 6 \times (50 - 46) = 12. Burden: buyers pay 44−40=444 - 40 = 4 more per unit (two thirds of the tax) and sellers keep 40−38=240 - 38 = 2 less (one third). At the original equilibrium, ϵD=−1×4050=−0.8\epsilon_D = -1 \times \frac{40}{50} = -0.8 and ϵS=2×4050=1.6\epsilon_S = 2 \times \frac{40}{50} = 1.6, so the buyers' share is ϵSϵS+∣ϵD∣=1.62.4=23\frac{\epsilon_S}{\epsilon_S + |\epsilon_D|} = \frac{1.6}{2.4} = \frac{2}{3}: the less price-responsive side bears more. Check with surplus: CS=12×46×(90−44)=1,058CS = \frac{1}{2} \times 46 \times (90 - 44) = 1{,}058 and PS=12×46×(38−15)=529PS = \frac{1}{2} \times 46 \times (38 - 15) = 529, and 1,058+529+276=1,863=1,875−121{,}058 + 529 + 276 = 1{,}863 = 1{,}875 - 12. Levying the tax on buyers gives the same result. Demand in terms of the price sellers receive becomes QD=90−(P+6)=84−PQ_D = 90 - (P + 6) = 84 - P, and 84−P=2P−3084 - P = 2P - 30 gives PS=38P_S = 38, so buyers pay 38+6=4438 + 6 = 44 in total. Who is legally required to pay the tax does not decide who bears it; relative price responsiveness does.

Problem 13: Per-unit subsidy: who gains and what it costs

Difficulty: Hard

In the market from Problem 2 (QD=200−4PQ_D = 200 - 4P, QS=50+2PQ_S = 50 + 2P, equilibrium P∗=25P^* = 25, Q∗=100Q^* = 100), the government pays sellers a subsidy of 6 per unit. Find the price buyers pay, the price sellers receive including the subsidy, the quantity traded, the cost to the government and the deadweight loss.
Show worked solution
Sellers now supply according to the price they receive including the subsidy, P+6P + 6: QS=50+2(P+6)=62+2PQ_S = 50 + 2(P + 6) = 62 + 2P. New equilibrium: 200−4P=62+2P200 - 4P = 62 + 2P, so 138=6P138 = 6P and buyers pay PB=23P_B = 23. Sellers receive 23+6=2923 + 6 = 29. Quantity: 200−4(23)=108200 - 4(23) = 108. Split of the benefit: buyers pay 2 less than before and sellers receive 4 more. Sellers capture two thirds because supply is the less price-responsive side here (quantity supplied changes by 2 per unit of price, quantity demanded by 4). Cost to the government: 6×108=6486 \times 108 = 648. Gains: consumer surplus rises by 12×(100+108)×2=208\frac{1}{2} \times (100 + 108) \times 2 = 208 and producer surplus by 12×(100+108)×4=416\frac{1}{2} \times (100 + 108) \times 4 = 416, a total of 624. Deadweight loss =648−624=24= 648 - 624 = 24, which is the triangle 12×(108−100)×6\frac{1}{2} \times (108 - 100) \times 6: the 8 extra units cost more to produce than buyers value them.

Problem 14: Quota versus price ceiling

Difficulty: Hard

Return to the market QD=90−PQ_D = 90 - P, QS=2P−30Q_S = 2P - 30. Instead of a price ceiling, the government limits output to 30 units with a production quota, and the quota licences are held by producers. Find the market price, the quota rent, consumer surplus, producer surplus and the deadweight loss. Compare the outcome with the price ceiling of 30 in Problem 10.
Show worked solution
With only 30 units available, the price is what buyers will pay for the 30th unit: P=90−30=60P = 90 - 30 = 60. The supply price (marginal cost) of the 30th unit is 15+302=3015 + \frac{30}{2} = 30. Quota rent, the gap between price and marginal cost on each licensed unit, is (60−30)×30=900(60 - 30) \times 30 = 900, and it goes to the licence holders. Consumer surplus: 12×30×(90−60)=450\frac{1}{2} \times 30 \times (90 - 60) = 450. Producer surplus including the rent: 12×30×(30−15)+900=225+900=1,125\frac{1}{2} \times 30 \times (30 - 15) + 900 = 225 + 900 = 1{,}125. Deadweight loss: 12×(50−30)×(60−30)=300\frac{1}{2} \times (50 - 30) \times (60 - 30) = 300. Check: 450+1,125=1,575=1,875−300450 + 1{,}125 = 1{,}575 = 1{,}875 - 300. Comparison: both policies cut the quantity to 30, so the deadweight loss is the same, 300. What differs is who gets the rectangle of 900 between the prices of 60 and 30. Under the ceiling, consumers keep it, because they pay 30 (consumer surplus 1,350, producer surplus 225). Under the quota, producers keep it, because buyers pay 60. The quantity traded determines the efficiency loss; the price determines how the remaining surplus is shared.

Problem 15: Tariff in a small open economy

Difficulty: Hard

A small country has domestic demand QD=90−PQ_D = 90 - P and domestic supply QS=2P−30Q_S = 2P - 30 for a good it can import freely at a world price of 25. (a) Find domestic consumption, domestic production and imports under free trade. (b) The government imposes a tariff of 5 per unit. Find the new imports, the tariff revenue, and the change in consumer and producer surplus. (c) Calculate the deadweight loss and explain where it comes from.
Show worked solution
(a) A small country takes the world price as given, so the domestic price is 25. Consumption: QD=90−25=65Q_D = 90 - 25 = 65. Domestic production: QS=2(25)−30=20Q_S = 2(25) - 30 = 20. Imports =65−20=45= 65 - 20 = 45. (b) The tariff raises the domestic price to 25+5=3025 + 5 = 30. Consumption falls to 90−30=6090 - 30 = 60, domestic production rises to 2(30)−30=302(30) - 30 = 30, and imports fall to 60−30=3060 - 30 = 30. Tariff revenue =5×30=150= 5 \times 30 = 150. Consumer surplus falls by the trapezoid between the two prices: 12×(65+60)×5=312.5\frac{1}{2} \times (65 + 60) \times 5 = 312.5. Producer surplus rises by 12×(20+30)×5=125\frac{1}{2} \times (20 + 30) \times 5 = 125. (c) Net effect: −312.5+125+150=−37.5-312.5 + 125 + 150 = -37.5, so the deadweight loss is 37.5. It is made of two triangles. The production loss, 12×(30−20)×5=25\frac{1}{2} \times (30 - 20) \times 5 = 25: 10 extra units are now made at home at a cost above the world price. The consumption loss, 12×(65−60)×5=12.5\frac{1}{2} \times (65 - 60) \times 5 = 12.5: 5 units that buyers valued above the world price are no longer bought.

Frequently asked questions

How do you find equilibrium price and quantity from supply and demand equations?

Set quantity demanded equal to quantity supplied and solve for the price, then substitute that price into either equation to get the quantity, and check it in the other. For example, 200 - 4P = 50 + 2P gives P = 25 and Q = 100 (Problem 2).

What is the difference between a change in demand and a change in quantity demanded?

A change in quantity demanded is a movement along a fixed demand curve, caused only by a change in the good's own price. A change in demand is a shift of the whole curve, caused by something else: income, the prices of substitutes or complements, tastes, expectations or the number of buyers. The same distinction applies to supply and quantity supplied.

How do you calculate the deadweight loss of a price ceiling, price floor or tax?

Deadweight loss is the triangle between the demand and supply curves over the units that are no longer traded. With straight-line curves, it equals one half times the fall in quantity times the vertical gap between the demand price and the supply price at the new quantity. For a per-unit tax, that vertical gap is the tax itself.

Who pays a per-unit tax, buyers or sellers?

The side of the market that is less responsive to price bears more of the tax, whichever side is legally required to pay it. When supply is more elastic than demand, buyers bear most of the tax; when demand is more elastic, sellers do. Problem 12 shows that levying the same tax on buyers instead of sellers leaves the prices and the quantity unchanged.

Which courses are these supply and demand problems for?

They match the supply and demand material in first-year university microeconomics and in AP Microeconomics (Unit 2). The equation-based problems suit courses that use linear demand and supply functions, such as IB Economics HL. A-Level and IB SL exams test the same ideas mainly through diagrams, and the solutions describe what happens on the diagram as well as the algebra.

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