Microeconomics guide, Unit 2, step 10 of 28Previous step Next step

Step 10: Consumer and Producer Surplus

By the EconTutorials team. 10-minute read with 6 practice questions.

SyllabusAP Micro 2.6 · Cambridge 2.5

In 30 seconds

Consumer surplus is what buyers gain: the gap between what they were willing to pay and what they actually paid.
Producer surplus is what sellers gain: the gap between the price they receive and the lowest price they would have accepted.
Each is a triangle on the diagram: $ \text{Surplus} = \tfrac{1}{2} \times \text{base} \times \text{height} $. Total surplus = CS + PS, and competitive equilibrium makes it as large as possible.
Taxes and price controls cut the quantity traded and destroy surplus. The lost part is the deadweight loss, and it is bigger when demand or supply is more elastic.

Video lesson coming soonA short animated lesson for this step will appear here.

What consumer surplus means

It is a hot afternoon and you are desperate for a bottle of cold water. You would happily pay $5. The price tag says $1.50. You pay $1.50 and walk away with $3.50 of “bonus” value: the difference between what you were willing to pay and what you actually paid. That $3.50 is your consumer surplus.

Steps 5 to 8 showed you how markets set prices. This step asks a different question: are those outcomes good, and for whom? To answer it, economists measure the gains from trade.

Key termConsumer surplus (CS): the difference between the maximum price a consumer is willing to pay and the price they actually pay; on a diagram, the area below the demand curve and above the market price, up to the quantity traded.

Why a triangle? The demand curve shows how much each buyer is willing to pay. The first buyers value the good highly, so they get a big bonus. Later buyers value it less, so their bonus is smaller. The last buyer, at the equilibrium quantity, values it at exactly the market price and gets no bonus at all. Add up all these bonuses and you get a triangle sitting above the price line and under the demand curve.

Producer surplus: the seller’s side

A farmer would be willing to sell a bushel of wheat for as little as $3, because that covers her cost. The market price is $6. She sells at $6 and gains $3 more than her minimum. That $3 is her producer surplus.

Key termProducer surplus (PS): the difference between the price a producer actually receives and the minimum price they would accept; on a diagram, the area above the supply curve and below the market price, up to the quantity traded.

The supply curve shows the minimum price at which each unit would be supplied, which is its marginal cost. Sellers with low costs gain a lot from the market price; the last seller gains nothing. The total is a triangle below the price line and above the supply curve.

When demand and supply are straight lines, both areas are triangles, and you use the triangle formula. The height is the gap between a price-axis intercept and the equilibrium price.

\[ CS = \tfrac{1}{2} \times Q^* \times (\text{max WTP} – P^*) \qquad PS = \tfrac{1}{2} \times Q^* \times (P^* – \text{min price}) \]

Here “max WTP” (maximum willingness to pay) is where the demand curve meets the price axis, and “min price” is where the supply curve meets it.

Worked example

In the market for phone cases, the demand curve meets the price axis at $24 and the supply curve meets it at $4. Equilibrium is $ P^* = \$12 $ and $ Q^* = 60 $. Find CS, PS and total surplus.

Step 1$ CS = \tfrac{1}{2} \times 60 \times (24 – 12) = \tfrac{1}{2} \times 60 \times 12 = \$360 $

Step 2$ PS = \tfrac{1}{2} \times 60 \times (12 – 4) = \tfrac{1}{2} \times 60 \times 8 = \$240 $

Step 3$ TS = 360 + 240 = \$600 $

Buyers gain $360 of value above what they pay, and sellers gain $240 above their minimum. Together the market creates $600 of net benefit for society.

Total surplus and efficiency

Total surplus (CS + PS) measures the total net benefit a market creates. A key result in microeconomics is that competitive equilibrium maximises total surplus.

Here is why. A buyer willing to pay $12 and a seller with a cost of $4 will trade, creating $8 of surplus. A buyer willing to pay only $3 and a seller with a cost of $7 will not trade, which is correct, because that trade would destroy value. The market price lets every value-creating trade happen and screens out every value-destroying one. Up to Q*, each unit is worth more to a buyer than it costs to make. Beyond Q*, each extra unit costs more than it is worth.

Key termAllocative efficiency: the situation where resources are allocated so that total surplus is maximised, reached at competitive equilibrium where the value of the last unit equals its marginal cost (P = MC).

Deadweight loss: when surplus is destroyed

Anything that stops the market reaching equilibrium destroys some surplus. The surplus that disappears, from trades that would have helped both sides but no longer happen, is called deadweight loss (DWL). Nobody receives it: not buyers, not sellers, not the government.

Key termDeadweight loss: the reduction in total surplus caused by a market distortion such as a tax, a price control or monopoly, shown as a triangle on the diagram.

A tax. A per-unit tax on producers shifts the supply curve up by the amount of the tax. Buyers now pay a higher price $ P_b $, sellers keep a lower price $ P_s = P_b – \text{tax} $, and the quantity traded falls from Q* to $ Q_t $. On the diagram:

Tax revenue is a rectangle: $ \text{tax} \times Q_t $.
Deadweight loss is the triangle between Q* and $ Q_t $, between the old demand and supply curves: $ \tfrac{1}{2} \times \text{tax} \times (Q^* – Q_t) $.

Worked example

Before a $6 per-unit tax, a market trades 500 units. After the tax, it trades 400 units. Find the tax revenue and the deadweight loss.

Step 1$ \text{Revenue} = 6 \times 400 = \$2{,}400 $

Step 2$ \Delta Q = 500 – 400 = 100 $

Step 3$ DWL = \tfrac{1}{2} \times 6 \times 100 = \$300 $

The government collects $2,400, but $300 of surplus simply vanishes: those 100 units would have been worth more to buyers than they cost sellers, yet the tax stopped them being traded.

Price controls. A price ceiling set below equilibrium (for example, rent control) creates a shortage: fewer units are supplied, so trades are lost. A price floor set above equilibrium creates a surplus: buyers purchase fewer units, so trades are lost again. Both create a deadweight loss triangle.

Elasticity matters. This is where Step 8 links in. If demand or supply is elastic, a tax causes a large fall in quantity, so the DWL triangle is wide. If they are inelastic, quantity barely changes and the DWL is small. That is one reason governments prefer to tax goods like cigarettes and petrol: revenue is high and the efficiency loss is relatively low.

Common mistakeCounting tax revenue as part of the deadweight loss. Revenue is not lost to society: it moves from buyers and sellers to the government. Only the triangle of trades that no longer happen is the DWL. Another slip is forgetting the ½ in the triangle formula.

Exam tipWhen asked to shade areas on a tax diagram, label each one: CS above $ P_b $ under demand; PS below $ P_s $ above supply; tax revenue as the rectangle between $ P_b $ and $ P_s $ up to $ Q_t $; DWL as the triangle to the right of $ Q_t $. Examiners also love questions that compare DWL for an inelastic good and an elastic good, so be ready to explain the link with elasticity.

Practise: 6 questions

Try each one on paper first, then check the worked answer.

EasyQ1. You would pay up to $40 for a concert ticket. You buy one for $25. What is your consumer surplus? Show worked answer

$ CS = 40 – 25 = \$15 $
That is the extra value you get above what you paid.

EasyQ2. The demand curve meets the price axis at $20, the equilibrium price is $8 and the equilibrium quantity is 60. Calculate consumer surplus. Show worked answer

$ CS = \tfrac{1}{2} \times 60 \times (20 – 8) = \tfrac{1}{2} \times 60 \times 12 = \$360 $

MediumQ3. A government imposes a $3 per-unit tax. Before the tax, 1,000 units were traded; after it, 850 units. Calculate the tax revenue and the deadweight loss. Show worked answer

Revenue $ = 3 \times 850 = \$2{,}550 $
$ \Delta Q = 1{,}000 – 850 = 150 $
$ DWL = \tfrac{1}{2} \times 3 \times 150 = \$225 $

MediumQ4. A price floor of $22 is set in a market where equilibrium is $20 and 1,000 units. At the floor, only 800 units are bought. At 800 units, the demand price is $22 and the supply price is $16. Calculate the deadweight loss. Show worked answer

Lost trades: $ 1{,}000 – 800 = 200 $ units.
Height of the triangle: $ 22 – 16 = \$6 $.
$ DWL = \tfrac{1}{2} \times 200 \times 6 = \$600 $

MediumQ5. Explain why a tax on a good with very inelastic demand (such as insulin) creates a smaller deadweight loss than the same tax on a good with elastic demand (such as luxury handbags). Show worked answer

DWL $ = \tfrac{1}{2} \times \text{tax} \times \Delta Q $, so its size depends on how much the quantity traded falls.
With inelastic demand (steep curve), buyers keep buying, so $ \Delta Q $ is small and the DWL triangle is narrow.
With elastic demand (flat curve), buyers switch away, so $ \Delta Q $ is large and the DWL triangle is wide.
Same tax, different elasticity, very different DWL.

ExamQ6. In a competitive market, $ Q_d = 100 – 2P $ and $ Q_s = 3P – 30 $. (a) Find the equilibrium. (b) Calculate CS, PS and total surplus. (c) A $5 per-unit tax is imposed on producers, so supply becomes $ Q_s = 3P – 45 $. Find the new quantity, the price buyers pay and the price sellers receive. (d) Calculate tax revenue and the deadweight loss. [8 marks] Show worked answer

(a) $ 100 – 2P = 3P – 30 \Rightarrow 130 = 5P \Rightarrow P^* = 26 $. $ Q^* = 100 – 52 = 48 $. Check: $ 78 – 30 = 48 $ ✓ [2 marks]
(b) Demand intercept: $ Q_d = 0 \Rightarrow P = 50 $. Supply intercept: $ Q_s = 0 \Rightarrow P = 10 $.
$ CS = \tfrac{1}{2} \times 48 \times (50 – 26) = \$576 $. $ PS = \tfrac{1}{2} \times 48 \times (26 – 10) = \$384 $. $ TS = \$960 $. [2 marks]
(c) $ 100 – 2P = 3P – 45 \Rightarrow 145 = 5P \Rightarrow P_b = 29 $. $ Q_t = 100 – 58 = 42 $. Check: $ 87 – 45 = 42 $ ✓. $ P_s = 29 – 5 = 24 $. [2 marks]
(d) Revenue $ = 5 \times 42 = \$210 $. $ DWL = \tfrac{1}{2} \times 5 \times (48 – 42) = \$15 $. The $15 is surplus that neither buyers, sellers nor the government receives. [2 marks]

Check yourself

1. Consumer surplus is best defined as:

CS is the buyer’s “bonus” above the price paid.

2. At competitive equilibrium, total surplus is:

Every value-creating trade happens and no value-destroying trade does.

3. The deadweight loss from a tax is larger when:

Elastic curves mean a bigger fall in quantity, so a wider DWL triangle.

Your score: 0 out of 3

The short version

CS is the triangle under demand and above price; PS is the triangle above supply and below price.
Use $ \tfrac{1}{2} \times \text{base} \times \text{height} $, where the height runs from the price to the axis intercept.
Competitive equilibrium maximises total surplus: this is allocative efficiency.
Taxes, price ceilings and price floors cut the quantity traded and create deadweight loss; for a tax, $ DWL = \tfrac{1}{2} \times \text{tax} \times \Delta Q $.
More elastic demand or supply means a larger DWL, which is why inelastic goods are popular tax targets.

This guide covers the core of the chapter. For the full Chapter 9, with shaded surplus diagrams, the UK sugar tax case study and 15 exam-style questions with a complete answer key, see the book Economics Made Simple.

Step 10: Consumer and Producer Surplus

What consumer surplus means

Producer surplus: the seller’s side

Total surplus and efficiency

Deadweight loss: when surplus is destroyed

Practise: 6 questions

Check yourself

The short version

Further reading on EconTutorials

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