Taxes | 4 diagrams, micro theory, analysis and evaluation.

Definitions

A tax is a payment to the government. This can raise revenues to cover government spending.

But taxes can have other purposes, for example to correct market failures (such as negative externalities).

For microeconomics purposes, there are two key types of tax:

• Specific tax – the tax is a fixed amount. For example, the firm has to pay a tax of £3 per unit sold. [We will assume the taxes are specific for simplicity].
• Ad valorem (according to value) – this tax is a percentage of the value of the item, e.g. 10%.

For A-level Economics, we often assume firms are the ones paying the tax directly to the government.

But the firms may still try to pass on the tax to the consumers, through higher prices.

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Examples of taxes

• The UK Government introduced a sugar tax in the form of the Soft Drinks Industry Levy (SDIL), raising the cost of added-sugar soft drinks with more than 5g of sugar per 100ml of drink.
• Petrol – the UK fuel duty for petrol costs 52.95 pence per litre
• Cigarette tax in the UK is 16.5% plus £5.89 on a packet of 20 cigarettes.
• A value added tax (VAT) of 20% on most goods and services. Some goods and services do receive reduced VAT rates of 5% or 0%.

For up to date UK tax rates, see the link here.

Sugary drinks are demerit goods – they are overconsumed in the free market. This is because of negative externalities, that is the harm caused by consuming these drinks on third parties, such as increasing rates of obesity leading to higher treatment costs for the NHS, as well as increasing sick days, reducing productivity. There is also an argument that consumers may underestimate the long-term health costs of a decision to consume a sugary drink. 

What are the effects of a tax? I will consider the example of the sugary drinks tax.

Tax – supply shift left and incidence

For A-level Economics, we assume firms are the ones paying the tax.

The tax increases business costs. So the supply curve shifts left from S to S1 – at a given price, supply is less, because of the tax.

The tax is the vertical distance between the old and new supply curves.

This increases the price from p to p1. The equilibrium quantity falls from q to q1.

The total tax revenue is (p1-p2) x q1.

We can also show the “incidence” of the tax. Here, the incidence is the burden of the tax that consumers or producers face.

Producers pay the tax directly, so they obviously face some burden from the tax. However producers may be able to pass on some of the tax to consumers.

Hence, consumers also see higher prices as a result of the tax, so consumers face a burden too.

The consumers face an increase in price from p to p1. So the consumers are in effect paying the red part of the tax revenue.

But the producers, who were receiving price p before the tax, are now receiving price p2 after the tax. While the market price is p1, the firm pays (p1-p2) in tax, leaving them with only p2 per unit.

In this case, the producers have a greater burden or incidence than the consumers.

Tax leads to welfare loss

Suppose the government taxes a market, where there is no market failure.

Then a tax leads to a welfare loss.

The tax reduces consumer surplus and producer surplus. But the tax generates government revenue. The table below shows the exact changes.

When we add up the changes in consumer surplus, producer surplus and tax revenue, overall there is a welfare loss. This is area EFG on the diagram below.

Why is there a welfare loss? The fall in producer surplus and consumer surplus outweighs the rise in tax revenue.

See the question at the end of this article for more on welfare losses.

Tax in presence of market failure – welfare gain: production externality

However, suppose there is a market failure present. Specifically, a market failure which leads to overproduction or overconsumption in the free market. This could be a negative externality in production for example.

Then a tax can increase welfare.

In the diagram below, the free market quantity is q, where MPB=MPC.

But the socially optimal outcome is at q1, where MSB=MSC.

A negative externality in production causes the difference between the marginal private cost and marginal social cost. This leads to a welfare loss due to the market failure, of area ABE.

An example of a negative production externality is the external effect of oil spills. For example, oil spills can damage marine ecosystems, reduce seaside tourism and cause health problems, especially for those involved in the clean up.

To move the market to the socially optimal outcome, we introduce a tax. This shifts the MPC curve to the left until the MPC + tax = MSC.

This moves the equilibrium quantity from q to q1. So social welfare rises by ABE, as a result of the tax.

Taxing away a negative consumption externality

Alternatively, the government could tax goods with negative extenalities in consumption. For example, the sugar tax reduces the cost to third parties such as the NHS from treating obesity and the potential harm to the  wider economy in terms of higher sick days and reduced productivity. It also reduces the damage caused to individuals’ health, particularly for those who undervalue the long-term health costs of having sugary drinks.

As sugary drinks cause a negative externality in consumption, the marginal private benefit is greater than the marginal social benefit, and in the free market there is overconsumption of q-q1. The sugar tax shifts the marginal private cost curve left from MSC=MPC to MPC+tax, meaning the quantity falls from q to q1 and the price rises from p to p1. Thus the tax achieves the socially optimal quantity q1.

The tax revenue can have second-round effects on social welfare. The tax also raises government revenue which could be used to further invest in advertising to reduce demand for sugary drinks.

This could further reduce the health costs and  externalities from sugary drinks. The UK Government forecasted this would raise £500 million per year from the soft drinks industry levy (sugar tax) for the first few years. [In practice, revenue was much lower].

Note the government can also tax goods where the consumers lack information about the potential drawbacks of (over)consumption. For example, the personal health risks from cigarette or sugar consumption.

Tax evaluation 1 – price elasticity of demand

The effect of a tax depends on the price elasticity of demand (PED) for the good being taxed.

If the demand is price-inelastic, then the tax will lead only to a small fall in quantity and a larger rise in price.

This would mean little effect on consumers’ health. Sugar can be addictive and so is likely to have an inelastic PED, meaning the tax on its own may have less direct benefits for consumer health.

The PED could however change over time, as more substitutes may enter the market. So the PED would become more elastic.

Hence the quantity fall, as a result of the tax, would be greater for sugary drinks, improving the effect on consumers’ health and reducing external harm. 

Cost effects

The sugar tax increases costs for firms that produce sugary drinks.

The SDIL levy is even higher when the sugar concentration is above 8g per 100ml, so firms producing very sugary drinks would see even greater cost increases.

This means a lower quantity sold as quantity falls from q to q1.

Because of derived demand, demand for workers would fall, so employment would fall.

Lower quantity sold may mean reduced profits, which may reduce the degree of reinvestment by companies into sugary drinks.

This could mean the quality of sugary drinks does not improve as quickly. Firms that supply inputs for the sugary drinks, such as sugar, would see reduced demand because of derived demand too.

This reduces the profit and investment of sugar producers too.

Firms that buy sugary drinks as inputs, such as for business meetings or for employee benefits, would see higher business costs as a result too. This would reduce firm profits further up the supply chain.

[If you have studied cost and revenue diagrams, you can use one here. A tax would shift marginal cost and average cost upwards, reducing supernormal profits].

Evaluation 2 – cost effect

The effect on firms’ costs depends on whether firms change their products.

Firms may switch to producing non-sugary drinks which do not face the sugar tax.

This means the tax would not increase firms’ costs as much. So there would be less harm to profits and employment in the sugar industry.

For example Coca-Cola could produce more sugar-free Coca-Cola, to avoid the sugar tax.

Some firms are also increasing the use of sugar substitutes, such as stevia, in some soft drinks. So firms’ costs are likely to increase less as firms have shown they can adapt their products.

Inequality and poverty effects

A per-unit tax on sugar may increase poverty and post-tax inequality.

The tax increases the price of the good. Under the assumption that demand is price-inelastic, a higher price means higher total spending on the good by consumers. So consumers pay more for sugary drinks.

This increase in spending, as a result of the tax, takes up a larger proportion of a poorer consumer’s income, compared to the income of a richer consumer.

In other words the sugar tax would be regressive.

Evidence also suggests the poor are less responsive to a price rise compared to the rich when it comes to soft drinks, meaning that the tax has an even more regressive effect. 

Evaluation 3 – inequality effect

The effect on inequality may depend on what the government does with the revenue raised.

For example, some of the revenue could go towards increased welfare payments for those on low incomes.

This would mitigate any effect on inequality, while still incentivising sugar consumers to reduce their consumption (particularly those on high income).

However at the moment the UK Government has a very large budget deficit of 14.5% of GDP in the year ending March 2021.

Hence any tax funds raised are likely to go towards closing the budget deficit rather than increased welfare payments. This means inequality is likely to increase as a result of the tax.

Substitutes and complements

A tax on one good is likely to affect markets for substitutes and complements.

Suppose there is a tax on flights. This shifts flight supply left, increasing the price and reducing the quantity.

Take a substitute like train travel. The rising price of flights increases demand for train travel. This increases the equilibrium price and quantity of train tickets sold, increasing revenue and profits in the rail industry. You can also show this effect on a diagram.

Note this depends on the strength of the relationship between the two goods. In other words, are the goods or services close or weak substitutes or complements? In some cases, flights may be the only option for travelling from remote locations.

Other analysis or evaluation points

• The tax may only affect a small percentage of consumption of the good. Suppose a tax on alcohol only applied to high concentration alcohol. Then that tax may have less of an effect on overall alcohol consumption.
• Other consumer responses e.g. buying goods from abroad to avoid the tax.
• The effect of taxes on quality. For example reduced profits may mean less investment into the product quality.
• Possible other firm responses e.g. closure, moving abroad if the tax is very high.
• The burden or incidence of the tax depends on the elasticities: PED and/or PES. Typically, the more price-inelastic group (out of producers and consumers) faces the greater incidence, as they cannot reduce consumption or production as easily.
• Government failure when using a tax to correct market failure. For example, setting the tax too high can result in a welfare loss. Setting a tax too low may mean a market failure remains. The government may lack the information required to determine the correct level of the tax.

Related posts

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Related questions

Why can a tax cause a welfare loss?

Why is there a welfare loss? The fall in producer surplus and consumer surplus outweighs the rise in tax revenue.

But a more detailed explanation is:

1) First, we know the tax causes a fall in quantity from q to q1.

2) Next, for the quantities from zero to q1, the tax revenue completely replaces the fall in consumer surplus and producer surplus.

3) But for the quantities between q and q1, the tax means these extra quantities are no longer produced or consumed. Hence, no revenue can be raised for the units between q and q1. So, while consumer and producer surplus fall, this cannot be made up for with extra government revenue.

When can a tax cause a welfare gain?

When there is a market failure that leads to overconsumption or overproduction. Then the tax reduces the equilibrium quantity, reducing the extent of market failure.

Possible market failures can include: negative externalities (in consumption or production) or imperfect information (lack of awareness of long-term benefits of consumption).

Note if the tax is too high, the tax can still cause a welfare loss. A tax can “overcorrect” for a negative externality, thus creating a welfare loss from the equilibrium quantity being too low.

How do diagrams change for ad valorem taxes, instead of specific taxes?

The diagrams above assumed specific taxes. This means the supply curve shifts left in a parallel way.

For ad valorem taxes, the only difference is: the supply curve shifts left while rotating anticlockwise. So the supply curve shift is not parallel.

Ad valorem taxes depend on the value or price. So for low prices, the tax is less. But for higher prices, the tax is greater.

But, all the effects of taxes remain very similar, such as the welfare effects.

While it depends on the situation (e.g. if you are asked to draw an ad valorem tax, then draw one), I typically recommend students draw specific tax graphs most of the time.

Ad valorem tax graphs add additional complexity, for no real gain in intuition or welfare effects.

To show complexity in tax diagrams, there are usually much better ways, such as:

1. Showing welfare loss, incidence on a supply-demand diagram.
2. Illustrating the adjustment from the old to the new equilibrium, via the price mechanism, on a supply-demand diagram.
3. Welfare gain in an externality diagram or
4. Cost/revenue diagrams with the effect of a tax.

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