Friday, 24 November 2017

Tax Incidence

Every Chancellor likes to pull a rabbit out of their hat during the budget, and this Chancellor is no different.  Like any good showman, he left his rabbit until the very end.  He announced he would be abolishing stamp duty on all properties purchased by first time buyers below £300,000.  This was announced as a measure to help first time buyers.  It took most economists worth their salt about 10 seconds to realise that this measure would not help first time buyers, but would simply lead to higher prices, and real effect was a transfer of resources from the tax payer to home owners.  Of course, the OBR (who are economists and worth their salt) had already pointed this out in their blue book accompanying the budget.

Most economists would be quick off the mark here because it is one of the first lessons taught in Econ101 that the formal incidence of a tax and the effective incidence of a tax are completely independent.  The formal incidence of a tax is a question of who is legally responsible for paying a tax.  The effective incidence of a tax is asking who actually ends up paying for the tax after all is said and done.  Governments can change the formal incidence of a tax as much as they like, but it will have no impact on the effective incidence of a tax. 

This is something that can demonstrated through one of the most common economic models, supply and demand.  Let's start by thinking of the market for widgets.  Suppose that the demand curve for widgets is described by the following equation: p = 100-q.  Suppose that the supply curve is described by p= 3q.  The price moves until the number of units consumers want to consume is the same as the number of units suppliers are willing to supply, which will be where the demand and supply curves meet.  This is where 3q = 100-q, or 4q = 100, or q=25, which implies a price of p=75.

Now suppose that the government imposes a tax on the sale of widgets in the amount of £10 per widget.  At first we will suppose that buyers are responsible for declaring their widget purchases and paying the tax.  Provided we are careful about our terms, we can work out what will be the effect of this on the market for widgets.  To be consistent, we will always ensure that p represents the amount of money handed over to the supplier by the purchaser.  So consumers now take into account that for every unit they purchase, they will have to hand over £10 to the government.  This will shift the demand curve down by exactly £10, so it becomes p+10 = 100-q => p = 90-q.  think about it like this: whatever the price consumers hand over to the seller, p, they know they know they must hand over an additional 10 to the government, so wherever p used to appear in their demand curve, we replace it with p+10.  So now let's find the equilibrium again, and this will be where 90-q = 3q, which is where 4q=90, which is where q=22.5, so the price handed over to the supplier is p=67.5. Note that this is what the supplier receives for each unit, while the buyer pays 10 more than this, so the price paid by the buyer is p+10=77.5.  So for buyers, the price has only gone up by £2.50, while for sellers it has gone down by £7.50.  Despite formally being responsible for the whole tax, buyers effectively only pay 25% of it, while the sellers pay 75%.

What would happen if the formal responsibility for paying the tax were reversed, and sellers had to report transactions and pay the tax?  In that case, demand would return to its pre-tax relationship, p=100-q, but sellers would take account of their responsibility to hand over £10 for every transaction.  So whatever the price paid, p, they would be aware that they would only receive p-10, and they would respond accordingly.  So their supply curve becomes p-10=3q=> p = 10+3q.  Once again, we can find the equilibrium in the market after the tax is imposed by finding the intersection of demand and supply: 100-q=10+3q => 4q=90 => q=22.5.  Substituting this quantity into the demand curve or the post tax supply curve, we see that the transaction price must be p=77.5.  This is the whole price paid by the consumers for each unit, but the suppliers have to hand over £10 out of this figure to the government.  So the net price received by the suppliers for each unit will be £67.50.  So comparing to the no-tax benchmark, the price paid by the consumers went up by £2.50, while the price received by the suppliers went down by £7.50.  The consumers pay 25% of the tax and the suppliers pay 75%.  The effective division of the tax is exactly the same when the sellers are formally responsible for paying as it is when the buyers are formally responsible for paying. This is what economists mean when they say that the effective incidence of a tax is independent of the formal incidence of a tax.

But we can go further than that.  Why did most of the tax burden fall on the suppliers?  To get the intuition here it is useful to look at supply and demand on a diagram.  In the diagram below we have graphed supply and demand.  The grey line shows the pre-tax equilibrium.  The dashed black lines show the post tax price paid by the consumer and price received by the supplier. 
The impact of the tax is that the new equilibrium must be where the price paid by the consumer is £10 more than the price received by the supplier.  Effectively it drives a wedge between supply and demand.  Because the supply curve is steeper than the demand curve, this wedge involves a larger price fall for the supplier than price rise for the purchaser.  This is actually a general result.  The more inelastic side (i.e. the side with the steeper curve) of the market will pay more of the tax.  How much more of the tax they pay is in proportion to how much steeper their curve is.

In the UK housing "market", the supply curve is incredibly steep.  It is almost vertical.  This is the key problem in this "market" and why prices have risen so high.  So although buyers are formally responsible for paying stamp duty, the effective incidence is such that virtually all of it is actually paid by the seller in the form of lower prices.  If you cut stamp duty, sellers don't have to pay so much of the tax, and the means through which this happens is higher prices.

So whenever the chancellor announces a tax cut remember that the benefits don't necessarily accrue to the party officially paying the tax.  They will accrue to the people who are actually paying the tax, and they won't always be obvious.  One needs to think about what is being taxed and whether the buyers or the sellers are on the more inelastic side of that market.

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