Unit 8 Supply and demand: Markets with many buyers and sellers

8.12 The effect of a tax

Tobacco was one of the first consumer goods to be taxed in North America in the eighteenth century. In 1951, the US federal cigarette excise tax was increased from 7 cents to 8 cents per pack to help finance the Korean War.1

Governments levy taxes in different ways and for different reasons. They use taxes on income or wealth both to raise revenue to finance public expenditure, and to redistribute resources and reduce inequality. Particular goods may be taxed to raise revenue, or with the aim of changing decisions to buy them. Many countries now tax cigarettes to discourage smoking, but long before the harmful effects on health were known, tobacco taxes were used to raise revenue. Carbon taxes are an important tool for tackling climate change; in this case, the aim is unambiguously to reduce greenhouse gas emissions.

We can use the supply and demand model to assess the impact of a tax on prices, quantities, and government revenue.

Using taxes to raise revenue: The case of salt

For centuries, salt has been used as a preservative, allowing food to be stored, transported, and traded. The ancient Chinese advocated taxing salt to raise revenue, because people needed it, however high the price. Salt taxes were used by ruling elites in ancient India, by the French monarchy and Tsarist Russia, and by the British in India.

Figure 8.23 illustrates how a salt tax might work. Initially the market equilibrium is at point A. Suppose that a sales tax of 30% is imposed on the price of salt, to be paid by the suppliers. The marginal cost of supplying each unit of salt increases by the amount of the tax, so the supply curve shifts: the price is 30% higher at each quantity.

In this diagram, the horizontal axis shows the quantity of salt, and the vertical axis shows the price of salt. Coordinates are (quantity, price). There are three lines. A downward-sloping line is labelled Demand. An upward-sloping line starts at a lower vertical axis value and is labelled Market supply. These lines intersect at the point A (q-star, p-star). Another upward-sloping line lies above the Market supply curve at all points and is labelled Market supply with tax. It is steeper than the market supply curve and intersects the demand curve at the point B (q1, p1), which represents a lower quantity than q-star and a higher price than p-star. The tax paid to the government is the difference between p1 and the price corresponding to the original Market supply at q1, denoted p0.
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Figure 8.23 The effect of a 30% salt tax.

The initial equilibrium: In this diagram, the horizontal axis shows the quantity of salt, and the vertical axis shows the price of salt. Coordinates are (quantity, price). There are two lines that intersect at the point A (q-star, p-star). A downward-sloping line is labelled Demand. An upward-sloping line starts at a lower vertical axis value and is labelled Market supply.
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The initial equilibrium

Initially, the market equilibrium is at point A. The price is P* and the quantity of salt sold is Q*.

A 30% tax: In this diagram, the horizontal axis shows the quantity of salt, and the vertical axis shows the price of salt. Coordinates are (quantity, price). There are three lines. A downward-sloping line is labelled Demand. An upward-sloping line starts at a lower vertical axis value and is labelled Market supply. These lines intersect at the point A (q-star, p-star). Another upward-sloping line lies above the Market supply curve at all points and is labelled Market supply with tax. It is steeper than the Market supply curve and intersects the demand curve at a lower quantity than q-star and a higher price than p-star.
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A 30% tax

A 30% tax is imposed on suppliers. Their marginal costs are effectively 30% higher at each quantity. The supply curve shifts, but not in a parallel manner, because the dollar amount paid in tax increases with the quantity produced.

The new equilibrium: In this diagram, the horizontal axis shows the quantity of salt, and the vertical axis shows the price of salt. Coordinates are (quantity, price). There are three lines. A downward-sloping line is labelled Demand. An upward-sloping line starts at a lower vertical axis value and is labelled Market supply. These lines intersect at the point A (q-star, p-star). Another upward-sloping line lies above the Market supply curve at all points and is labelled Market supply with tax. It is steeper than the Market supply curve and intersects the demand curve at the point B (q1, p1), which represents a lower quantity than q-star and a higher price than p-star.
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The new equilibrium

The new equilibrium is at B. The price paid by consumers has risen to P1 and the quantity has fallen to Q1.

The tax paid to the government: In this diagram, the horizontal axis shows the quantity of salt, and the vertical axis shows the price of salt. Coordinates are (quantity, price). There are three lines. A downward-sloping line is labelled Demand. An upward-sloping line starts at a lower vertical axis value and is labelled Market supply. These lines intersect at the point A (q-star, p-star). Another upward-sloping line lies above the Market supply curve at all points and is labelled Market supply with tax. It is steeper than the market supply curve and intersects the demand curve at the point B (q1, p1), which represents a lower quantity than q-star and a higher price than p-star. The tax paid to the government is the difference between p1 and the price corresponding to the original Market supply at q1, denoted p0.
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The tax paid to the government

The price received by suppliers (after they have paid the tax) is P0. The double-headed arrow shows the tax paid to the government on each unit of salt sold.

tax incidence
The effect of a tax on the surplus of buyers, sellers, or both.

The new equilibrium is at point B, where a lower quantity is traded. Although the consumer price has risen, note that it is not 30% higher than before, because consumers respond to the price increase by buying less salt, and when less salt is produced the marginal cost of production falls. The consumer price, P1, is 30% higher than the price received by suppliers (net of the tax), which is P0. Suppliers receive a lower price than before, they produce less, and their profits will be lower. This example illustrates an important feature of taxes: it is not necessarily the taxpayer who feels its main effect. In this case, although producers pay the tax, the tax incidence falls partly on consumers and partly on producers.

Figure 8.24 compares the total surplus at equilibrium B with the tax (right panel), with the original surplus at A. At B, when the quantity falls to Q1:

  • Consumer surplus falls: Consumers pay a higher price, P1, and buy less salt.
  • Producer surplus falls: Producers supply less and receive a lower net price, P0 .
  • Tax revenue: A tax equal to (P1P0) is paid to the government on each of the Q1 units of salt sold (the green-shaded area).
  • Total surplus (including tax revenue) is lower: The tax causes a deadweight loss equal to the area of the white triangle, which is 1/2 × (Q* − Q1) × (P1P0).
There are two diagrams. In diagram 1, the horizontal axis shows the quantity of salt, and the vertical axis shows the price of salt. Coordinates are (quantity, price). There are three lines. A downward-sloping line is labelled Market demand. An upward-sloping line starts at a lower vertical axis value and is labelled Market supply. These lines intersect at the point A (q-star, p-star). Another upward-sloping line lies above the Market supply curve at all points and is labelled Market supply with tax. It is steeper than the market supply curve and intersects the demand curve at the point B (q1, p1), which represents a lower quantity than q-star and a higher price than p-star. The region enclosed by the Market demand curve, the vertical axis, and the horizontal line at p-star is the consumer surplus in the pre-tax equilibrium. The region enclosed by the Market supply curve, the vertical axis, and the horizontal line at p-star is the producer surplus in the pre-tax equilibrium. The after-tax price received by producers is p0. The region enclosed by the Market demand curve, the vertical axis, and the horizontal line at p1 is the consumer surplus in post-tax equilibrium. The region enclosed by the Market supply curve, the vertical axis, and the horizontal line at p0 is the producer surplus in the post-tax equilibrium. The rectangle enclosed by the points (0, p0), (0, p1), B at (q1, p1), and (q1, p0) is the government revenue raised by the tax. The triangle enclosed by the points A, B, and (q1, p0) is the deadweight loss from the tax.
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Figure 8.24 When the tax is imposed, the surplus from the salt market is:
total surplus = consumer surplus + producer surplus + government revenue

Provided that the revenue is used to benefit society, we can think of total surplus as a measure in monetary terms of the gains generated by trade in the market for salt for society as a whole. Compared to the situation before the tax, some of the surplus has been transferred from consumers and producers to the government, but also the total surplus is lower: there is a deadweight loss. If the revenue is spent on goods and services that enhance the wellbeing of the population, we might nevertheless conclude that this benefit to society outweighs the loss to consumers and producers, even though it reduces the surplus in the particular market that is taxed.

To raise as much revenue as possible, and reduce deadweight loss, the government would prefer to tax a good with low elasticity of demand, so that the fall in quantity is quite small. But this also means that the incidence of the tax falls heavily on consumers. The notorious salt tax imposed by the French monarchy was much resented by the people, and helped to precipitate the French Revolution. In 1930, the artificially high price of salt in British colonial India provoked one of the defining moments of the Indian independence movement: Mahatma Gandhi’s salt march to acquire salt from the Indian ocean. Similarly, in what came to be called the Boston Tea Party, in 1773 American colonists objecting to a British colonial tax on tea dumped a cargo of tea into the Boston harbour.

In many modern economies, institutions for tax collection are well established, with democratic consent. If citizens believe taxes are implemented fairly and used to benefit society, they are accepted as a necessary part of social and economic policy.

In contrast, if the government’s objective is to reduce the consumption of a good that is considered harmful—like tobacco or carbon—the tax will be more effective if demand is elastic so that quantity falls substantially. We discuss some examples in Unit 10.

Exercise 8.13 Tax incidence

Figure 8.24 shows how a 30% tax on the price of salt affects consumer surplus, producer surplus, the price paid by consumers, and the price received by producers.

  1. Use your diagram (or a new diagram) to show how these four variables would change if consumers were more price-inelastic than shown in Figure 8.24.
  2. How would your answer to the previous question change if instead the producers were more price-inelastic than shown in Figure 8.24?
  3. Explain how the relative elasticity of supply and demand determines who bears more of the tax incidence.

Question 8.13 Choose the correct answer(s)

Figure 8.24 shows the demand and supply curves for salt, and the shift in the supply curve due to the implementation of a 30% tax on the price of salt. Based on this information, read the following statements and choose the correct option(s).

  • In the post-tax equilibrium, the consumers pay P1 and the producers receive P*.
  • The government’s tax revenue is given by (P* – P0)Q1.
  • The deadweight loss is given by (1/2)(P1P0)(Q* – Q1).
  • The tax reduces consumer surplus by (1/2)(Q1 + Q*)(P1P*).
  • In the post-tax equilibrium, the consumers pay P1 and the producers receive P0.
  • The government’s tax revenue is (P1P0)Q1.
  • This expression gives the area of the triangle between the supply and demand curves, below AB.
  • This expression gives the area of the trapezium between the horizontal dotted lines through A and B.
  1. Institute of Medicine (US) Committee on Preventing Nicotine Addiction in Children and Youths; Lynch B.S., Bonnie R.J., editors. 1994. ‘Growing up Tobacco Free: Preventing Nicotine Addiction in Children and Youths’. National Academies Press (US) 6 (Tobacco Taxation in the United States).