Indirect taxes

Overview

Revenue from a specific tax as demand becomes more elastic.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Draw and describe in words the effect of a specific tax of £2.00 per unit on a market where equilibrium price is £10.00 and equilibrium quantity is 1,000 units.

   Model answer

   Put price in £ on the vertical axis and quantity per period on the horizontal. Demand slopes down, supply slopes up, and they cross at £10.00 and 1,000 units. The tax shifts supply vertically upward by £2.00 at every quantity, so the new supply curve is parallel to the old one and the vertical gap between them is exactly £2.00. The new equilibrium is higher and to the left, at a price of £11.20 and a quantity of 900 units. Producers keep £11.20 minus £2.00, which is £9.20 per unit.

2. 2

   A specific tax of £2.00 per unit raises the price paid from £10.00 to £11.20 and cuts quantity from 1,000 to 900 units. Calculate the consumer burden, the producer burden and the total tax revenue.

   Model answer

   Price paid by the consumer rises by £11.20 minus £10.00, which is £1.20 per unit. Consumer burden equals £1.20 multiplied by 900 units, which is £1,080. The producer bears the remainder of the tax, £2.00 minus £1.20, which is £0.80 per unit, so producer burden equals £0.80 multiplied by 900 units, which is £720. Total revenue is £2.00 multiplied by 900 units, which is £1,800, and £1,080 plus £720 equals £1,800, as it must.

3. 3

   A specific tax of £2.00 per unit leaves the consumer bearing £1.20 of it. What does that tell you about the relative elasticities of demand and supply in the market?

   Model answer

   The consumer's share is £1.20 divided by £2.00, which is 0.6, so consumers bear 60% of the tax and producers 40%. The side of the market that is less responsive to price bears the larger share, because it has fewer alternatives to fall back on. Consumers bearing the majority therefore means demand is less elastic than supply over this price range. Had supply been the less elastic side, producers would have carried more than half.

4. 4

   Why does a specific tax shift the supply curve in parallel while an ad valorem tax pivots it?

   Model answer

   A specific tax is a fixed sum per unit, so the same cash amount is added at every quantity and the vertical distance between the old and new supply curves is constant. An ad valorem tax is a percentage of the price, so the cash amount collected grows as price grows. At a low price the vertical gap is small and at a high price it is large, so the new supply curve pivots upward about its price-axis intercept rather than moving up in parallel, and the gap widens as you move up the curve.

5. 5

   Value added tax is charged at 20%. Calculate the tax and the gross price on a net price of £40.00, then work backwards to find the net price behind a gross price of £54.00.

   Model answer

   Forwards: tax equals 20% of £40.00, which is 0.20 multiplied by £40.00, giving £8.00. The gross price is £40.00 plus £8.00, which is £48.00. Backwards: the gross price is 120% of the net price, so net equals £54.00 divided by 1.20, which is £45.00. The tax is £54.00 minus £45.00, which is £9.00. Checking, 20% of £45.00 is £9.00, so the figures agree.

6. 6

   Production of a chemical imposes a marginal external cost of £3.00 per unit. What rate of tax corrects the market, and why exactly that rate?

   Model answer

   A tax of exactly £3.00 per unit is required. Marginal social cost lies £3.00 above marginal private cost at every unit, so a specific tax of £3.00 shifts the private supply curve vertically upward by £3.00 until it coincides with marginal social cost. The firm now faces the full cost of its own activity, which is what internalising the externality means, and it chooses the output at which marginal social cost equals marginal social benefit. A tax above £3.00 would over-correct and cut output below the social optimum.

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