Chapter 13: Government intervention - indirect taxes (1.3)

  • Why governments tax goods

I always ask my students the question my micro teacher at university asked us: “Why do we tax alcohol more than we tax ice cream?!” There are two answers. The first is that governments levy (= put, apply) indirect taxes as a method to create tax revenue. Alcohol will have far lower price elasticity of demand than ice cream so quantity demanded will fall proportionately less for alcohol than ice cream, which means government revenue will be greater. The second reason is that government commonly try to dissuade (= discourage) the consumption of goods which cause damage to society (see Chapter 17). Alcohol causes a great deal of negative effects for non-users, such as accidents due to drunk driving and domestic violence.

  • Specific tax (per unit tax)

The tax has the following effects:

  • The priceincreases (form €10 to €11) and the quantity demandedfalls (from 100,000 shirts to 80,000 shirts)
  • Half of the €2 tax is paid by the consumer and half is paid by the producer. (This is the incidence of tax – a HL concept done further on.)
  • Total government tax revenueis €2 x 80,000 shirts; €160,000
  • Producerrevenue decreases from €1 million (€10 x 100,000) to €720,000 (€9 x 80,000) per month
  • Consumption decreases by 20,000 shirts per month and consumer spending goes from €1 million (€10 x 100,000) to €880,000 (€11 x 80,000).
  • Ad valorem tax

Assume that a VAT of 20% is imposed at an equilibrium price of €11 and a quantity of 80,000. The supply curve shifts disproportionally, from S0 to S+VAT, since the higher the price, the larger the price increase of the 20% VAT.

At higher prices the ad valorem tax shifts the supply curve higher, increasing the distance between S0 and S+vat. At the new equilibrium price of €12, the 20% VAT renders a €2 tax per unit.[1]In other respects we have the same type of outcome as before; the price increases from €11 to €12, quantity demanded decreases from 80,000 to 60,000 shirts, producers’ revenue is €600,000 (€10 x 60,000) and consumer spending is €720,000 (€12 x 60,000).

HL extensions

  • PED – the incidence of tax and government revenue

Both goods’ demand curves will have a marked effect upon whom the main incidence of tax will fall. The lower the PED, the higher the increase in price due to the expenditure tax – and the more of the incidence of tax lands upon the consumer.

Put in formula:

  • Incidence of tax on the consumer = where P is the price to the consumer and T is the tax per unit on the good. The proportional incidence of cigarette tax on the consumer is thus 40/50 which is 80%.
  • Incidence of tax on the producer = 1- which is 1-0.8 or 20%
  • PES and the incidence of tax and government revenue

The final four examples show how PES and PED affect the incidence of tax such that it is 100% on either the producer or consumer.

  • Plotting linear supply and demand curves

Here we will use the previous supply and demand functions from Chapters 4 – 6 to show and calculate the effects of an expenditure tax on goods. You will have to forgive me for including the “invisible elongated” portion of the Q-axis (i.e. the section showing minus values) for reasons of explanatory clarity. For the same reason, I have put a rather hefty tax on this particular good – since a $2 tax would be rather hard to see clearly in a diagram where the starting value is $100.

So, with a equilibrium price and quantity of $100 and 2,000 units, we add a $50 tax:

  • The supply function in Qs = -2,000 + 40P
  • The new supply function needs to be calculated. A $50 tax raises the supply curve S0 by $50 at all quantity levels, thus we need to calculate the new value of ‘c’.
  • The original P-intercept of the supply curve is 50
  • The P-intercept of the supply curve is calculated by ‘c’ / ‘d’
  • We know that the new P-intercept is 100 and that the slope (‘d’) is unchanged – thus we can calculate ‘c’ by solving 100 = -c / 40; -c = 40 x 100 (Rory, I have NO IDEA how to handle the minus value of ‘c’. Jump in and save us.)
  • The new value of ‘c’ is -4,000
  • The new supply function is Qs = -4,000 + 40P

Now is a good time to refresh your memory by calculating the new equilibrium price and quantity. These values have been left blank in figure 13.9 for precisely that reason.

Figure 13.9 Unit tax on a good

New equilibrium quantity is given by solving the simultaneous equation -4000 + 40P=4000 - 20P

  • P; 8,000 = 60P, P = $133.33
  • Qs; -4,000 + 40 x 133.33 = 1,333
  • Incidence of tax

There is an initial clue here that will help you check your figures! Any case where the slope of a (linear) supply curve is less than the slope of a (linear) demand curve, we know who will carry the largest incidence of tax; the consumer. Doodle a few diagrams to see why. (All ‘areas’ in the text below refer to figure 13.10.)

  • Total incidence (areas 2 and 4); at a quantity of 1,333 and tax of $50, the total incidence (e.g. total government revenue is $66,666.
  • Incidence of tax on consumers; the increase in price is $33.33. Consumers will pay $33.33 x 1,333 in tax which is $44,428.
  • Suppliers will pay the remaining $22,217.
  • Consumer and supplier surplus

Go back and revise consumer surplus, supplier surplus and deadweight loss. That will make it easier for you to see the areas in figure 13.10 and follow the calculations. My wonderful classroom neighbour, Brett the Aussie Math Teacher and Ballroom Dancer, tells me that the easiest way to calculate remaining surplus is “…quantity times the relevant P-intercept minus everything else…then divide by two…” Or something like that.

  • Remaining consumer surplus (area 1): ([$200 - $133.33] x 1333) / 2 = $44,435.5
  • Remaining supplier surplus (area 6): ([83.33 – 50] x 1333) / 2 = $22,214.5

Figure 13.10 Consumer and supplier surplus, incidence of tax and deadweight loss

  • Deadweight loss

The deadweight loss is the sum of the net loss of consumer and supplier surplus. These are the two small triangles (areas 3 and 5 infigure 13.10) that are simply “lost” in levying a tax on a good. Looking at the $50 unit tax as the “base of a triangle”, we get ($50 x [2,000 – 1,333]) /2 = $16,675.

Simple worksheet

  1. Assume a supply function of Qs = 200 + 10P and a demand function of Qd = 500 – 5P.
  1. Draw a diagram showing initial equilibrium.
  1. Add a unit expenditure tax of $10 and calculate the new supply function. Draw a new supply curve showingequilibrium price and quantity after the tax.
  1. Calculate the total incidence of tax (government tax revenue).
  1. Calculate the loss of consumer and supplier surplus.
  1. Calculate the deadweight loss.

[1] A brief footnote on my examples above (figures 13.1 and 13.2). Many of you are probably wondering what lunacy possessed me to put first a unit tax – and then a value added tax on top of that! The example of ‘taxing a tax’ looks absolutely bizarre, silly and impractical. Quite naturally, this is exactly what is done in many countries. Petrol prices in Europe, for example, will be comprised of around 80% tax. Say that the base price of a litre of petrol is €0.2 to which a €0.6 unit tax (per litre) is added, and then topped off by a 25% VAT. This brings the final price to €0.8 + 25% = €1.