The Effects of Government Intervention in Markets: Study Guide (Microeconomics 2.8)

The benchmark: an efficient market

In Topic 2.7 a shortage or surplus disappeared because the price was free to move. Governments sometimes stop the price from moving, or change the incentives buyers and sellers face. This guide shows what follows.

The benchmark is a perfectly competitive market with no market failures. In Topic 2.6 you saw that its equilibrium maximises total surplus: every unit worth more to a buyer than it costs to produce is traded, and no other unit is. So in such a market, any policy that changes the quantity traded can only lower total surplus. The surplus that disappears, and that nobody receives, is called deadweight loss (DWL). It is the loss to buyers and sellers from trades that no longer happen (or, with a subsidy, from units that cost more to make than they are worth).

Price controls, quantity limits, taxes and subsidies change incentives in every type of market, not only competitive ones. This topic uses a competitive market; you will meet the same policies in other market structures later in the course (Topic 6.4).

Throughout this guide we use the monthly market for refills of cooking-gas cylinders on Brisa, a fictional island. P is dollars per cylinder and Q is thousands of cylinders per month.

• Demand: Qd = 160 − 4P
• Supply: Qs = 2P − 20

Price ($ per cylinder)	20	25	30	34	40
Quantity demanded (thousands)	80	60	40	24	0
Quantity supplied (thousands)	20	30	40	48	60

Equilibrium: $30 and 40 thousand cylinders. Demand meets the price axis at $40 and supply at $10, so consumer surplus is ½ × 40 × (40 − 30) = $200 thousand, producer surplus is ½ × 40 × (30 − 10) = $400 thousand, and total surplus is $600 thousand per month.

Price ceilings

A price ceiling is a legal maximum price. Rent controls and caps on fuel prices are common examples.

• A ceiling above equilibrium (say $35 on Brisa) is non-binding: the market price of $30 is already allowed, so nothing changes.
• A ceiling below equilibrium is binding. Quantity demanded rises, quantity supplied falls, and there is a shortage. The quantity traded is the quantity supplied, because sellers cannot be made to sell more.

Because the price cannot rise to ration the good, something else does: queues, waiting lists, favouritism, or sales on an illegal market above the ceiling. Sellers may also cut quality, because they cannot charge more. Some buyers gain (those who get the good at a lower price), but others go without. A shortage under a ceiling often grows over time, because supply (and often demand) becomes more elastic in the long run: sellers find other uses for their resources, so quantity supplied keeps falling.

Price floors

A price floor is a legal minimum price. Guaranteed minimum prices for farm products are an example; a minimum wage is a floor in a labour market (Unit 5).

• A floor below equilibrium is non-binding.
• A floor above equilibrium is binding. Quantity supplied rises, quantity demanded falls, and there is a surplus. The quantity traded is the quantity demanded.

On Brisa, a floor of $34 gives Qd = 24 thousand and Qs = 48 thousand: a surplus of 24 thousand cylinders. Only 24 thousand are sold.

• CS = ½ × 24 × (40 − 34) = $72 thousand (down from $200 thousand).
• Supply gives $22 at 24 thousand cylinders, so PS = 24 × (34 − 22) + ½ × 24 × (22 − 10) = 288 + 144 = $432 thousand (up from $400 thousand).
• DWL = ½ × (40 − 24) × (34 − 22) = $96 thousand. Check: 72 + 432 + 96 = 600. ✓

Sellers who still sell gain from the higher price, but they sell fewer units, so a floor does not always raise producer surplus. If the government buys the unsold surplus to support the price, that costs taxpayers money too.

Quantity controls

A quantity control (or quota) sets a legal maximum quantity, often through licences: for example, a fixed number of fishing or taxi permits.

Suppose Brisa allows only 30 thousand cylinders per month. At 30 thousand, buyers are willing to pay (160 − 30) ÷ 4 = $32.50, but the supply curve shows sellers would supply that amount for only (30 + 20) ÷ 2 = $25. The price rises to $32.50. The $7.50 gap per cylinder goes to whoever holds the licences. Units between 30 and 40 thousand, worth more to buyers than they cost, are not traded, so DWL = ½ × (40 − 30) × (32.50 − 25) = $37.50 thousand.

Per-unit taxes

A per-unit (excise) tax of t dollars collected from sellers raises their cost of every unit by t. The supply curve shifts up by t (equivalently, to the left).

The tax drives a wedge between two prices:

• the price buyers pay (on the demand curve), and
• the price sellers keep = price buyers pay − t (on the original supply curve).

Then:

• Tax revenue = t × new quantity (a rectangle on the graph).
• Deadweight loss = ½ × t × (fall in quantity), the triangle between the old and new quantities.
• Incidence (who really pays): buyers’ share = rise in the price buyers pay; sellers’ share = fall in the price sellers keep. The two shares add up to t.

Per-unit subsidies

A per-unit subsidy of s dollars paid to sellers lowers their cost of every unit by s, so the supply curve shifts down by s (to the right). Buyers pay less, sellers receive more (price paid + s), and quantity rises.

On Brisa, a $3 subsidy gives supply Qs = 2(P + 3) − 20 = 2P − 14. Setting 160 − 4P = 2P − 14 gives P = $29 paid by buyers, Q = 44 thousand, and sellers receive $32.

• Government cost = 3 × 44 = $132 thousand.
• CS rises to ½ × 44 × (40 − 29) = $242 thousand (+$42 thousand). PS rises to ½ × 44 × (32 − 10) = $484 thousand (+$84 thousand).
• Buyers and sellers gain $126 thousand, but taxpayers pay $132 thousand. DWL = $6 thousand = ½ × 3 × (44 − 40).

The DWL comes from over-production: the extra 4 thousand cylinders cost up to $32 each to supply but are worth as little as $29 to buyers.

Who bears a tax? Elasticity decides

The more inelastic side of the market bears more of a tax (and gains more of a subsidy), because it is less able to walk away.

• At Brisa’s equilibrium, demand elasticity is 4 × 30 ÷ 40 = 3.0 and supply elasticity is 2 × 30 ÷ 40 = 1.5. Supply is less elastic, so sellers should bear more. Worked example 2 confirms they bear two-thirds.
• If demand were perfectly inelastic, buyers would bear the whole tax: the price would rise by the full amount, and quantity would not change.
• If supply were perfectly inelastic, sellers would bear it all.

The same rule explains DWL: the more elastic either curve, the more the quantity falls, so the larger the deadweight loss for a given tax.

Worked example 1: a binding price ceiling

Question. Brisa’s government caps the price of a refill at $25. (a) Is the ceiling binding? Find the shortage and the quantity traded. (b) Calculate consumer surplus, producer surplus and deadweight loss. (c) Who gains and who loses?

(a) $25 is below the equilibrium of $30, so the ceiling binds.

1. Qd = 160 − 4 × 25 = 60 thousand. Qs = 2 × 25 − 20 = 30 thousand.
2. Shortage = 60 − 30 = 30 thousand cylinders.
3. Quantity traded = the smaller amount = 30 thousand.

(b) At 30 thousand, the last buyer is willing to pay (160 − 30) ÷ 4 = $32.50. Assume the cylinders go to the buyers who value them most.

• CS = 30 × (32.50 − 25) + ½ × 30 × (40 − 32.50) = 225 + 112.50 = $337.50 thousand.
• PS = ½ × 30 × (25 − 10) = $225 thousand.
• DWL = ½ × (40 − 30) × (32.50 − 25) = $37.50 thousand.

Check. 337.50 + 225 + 37.50 = 600, the original total surplus. ✓

(c) Consumer surplus rises by $137.50 thousand, so the buyers who get cylinders gain. Producer surplus falls by $175 thousand, so sellers lose. Total surplus falls by $37.50 thousand. Buyers who want a cylinder at $25 but cannot get one lose out completely, and if cylinders are rationed by queues rather than by value, the real loss is larger than this calculation.

Worked example 2: a per-unit tax

Question. Instead, Brisa places a $6 tax on every cylinder, collected from sellers. (a) Find the price buyers pay, the price sellers keep and the new quantity. (b) What share of the tax do buyers and sellers bear? (c) Calculate tax revenue, the new consumer and producer surplus, and deadweight loss.

(a) The new supply curve is Qs = 2(P − 6) − 20 = 2P − 32.

1. 160 − 4P = 2P − 32, so 192 = 6P and P = $32 (paid by buyers).
2. Sellers keep 32 − 6 = $26.
3. Q = 160 − 4 × 32 = 32 thousand. Check on the original supply curve: 2 × 26 − 20 = 32. ✓

(b) Buyers pay $2 more (32 − 30): one-third of the tax. Sellers keep $4 less (30 − 26): two-thirds.

(c)

	Before	After	Change
Consumer surplus	$200 thousand	½ × 32 × (40 − 32) = $128 thousand	−$72 thousand
Producer surplus	$400 thousand	½ × 32 × (26 − 10) = $256 thousand	−$144 thousand
Tax revenue	0	6 × 32 = $192 thousand	+$192 thousand
Deadweight loss	0	½ × 6 × (40 − 32) = $24 thousand

Interpretation. Buyers and sellers lose $216 thousand together, but the government gains only $192 thousand. The $24 thousand difference is the deadweight loss.

Summary of the policies

Policy	Quantity traded	Price	Main side effect	Money for government
Binding ceiling	falls (= Qs)	lower	shortage	none
Binding floor	falls (= Qd)	higher	surplus	none (cost if it buys the surplus)
Quota	falls (= quota)	higher for buyers	gap goes to licence holders	none
Per-unit tax	falls	buyers pay more, sellers keep less	wedge	revenue = t × Q
Per-unit subsidy	rises	buyers pay less, sellers get more	over-production	cost = s × Q

All five create deadweight loss when applied to an efficient competitive market.

Common misconceptions

• “A price ceiling is set above equilibrium.” To have any effect, a ceiling must be below equilibrium. A floor must be above it.
• “A ceiling shifts the demand or supply curve.” Price controls do not shift curves. They hold the price away from equilibrium, causing movements along both curves.
• “Under a ceiling, quantity sold is quantity demanded.” It is quantity supplied, the smaller amount. Under a floor, it is quantity demanded.
• “If the tax is collected from sellers, sellers bear all of it.” Who really pays depends on elasticities, not on who hands the money to the government.
• “Tax revenue is part of the deadweight loss.” Revenue is transferred to the government, not lost. DWL is the surplus nobody receives.
• “A subsidy has no deadweight loss because everyone gains.” Buyers and sellers gain less than the subsidy costs taxpayers.
• “A price floor always helps producers.” Those who sell gain, but fewer units are sold, and producer surplus can fall.

Where this leads

Next, Topic 2.9, International Trade and Public Policy, uses the same tools to analyse tariffs and import quotas. In Unit 6 you will meet markets with external costs and benefits, where a well-chosen tax or subsidy can reduce deadweight loss rather than create it. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate. To review shortages and surpluses first, see the Topic 2.7 study guide.