More on Tax Incidence

Monday, September 24, 2001

We have seen that when government passes a law to assign statutory incidence to some economic agent, that agent would like to avoid having to actually pay the tax. Through tax shifting, the agent with the statutory incidence can pass the actual burden onto someone else. The agent that actually has to end up paying the tax is bearing the economic incidence of the tax.

If possible, the agent with statutory incidence would like to shift the entire burden of the tax onto someone else; usually he cannot. How successful is an agent in foisting off a tax on someone else? No surprise that we covered elasticity right before doing tax incidence.

Elasticity = Ability to Dodge a Tax

Earlier, I cast elasticity as the responsiveness of an agent. Someone that has an elastic curve is very flexible and can react to a price change. For an elastic demander, this means they can easily find some other substitute for the now more expensive item. I am an elastic demander for cola drinks because I really don't care if I get Pepsi or Coke. If Pepsi were to raise their price per can by $0.25 tomorrow, i'd only buy Coke. For an elastic supplier, this means they can easily increase or decrease output to take advantage of high or low prices. Suppose all of a sudden the price people are willing to pay for an Explorer drops but the price they are willing to pay for a Escort increases. If Ford designs their factories to be able to quickly change between Explorer and Escort production, Ford could be considered an elastic producer.

Being inelastic means you don't have many options. An inelastic demander has a hard time finding substitutes for the more expensive item. An inelastic supplier has a hard time changing how much product he's offering for sale. People who need a specific medicine are inelastic demanders of that medicine - they won't buy more than they need if it's cheap and they won't buy less if it's expensive; the amount they buy is pretty much independent of the price of the medicine. Take Ken Griffey Jr. 1989 Upper Deck baseball cards. Upper Deck produced a fixed amount of these back in 1989, so the number in existence cannot change. This is a perfectly inelastic supply: no matter how high the price goes, there will never be more produced.

It makes sense to think that someone who is more flexible ought to be able to dodge tax incidence better than someone who is not flexible. Let's look at some very extreme cases.

Our first diagram shows a perfectly elastic supply curve and a somewhat elastic demand curve. Here we assign statutory incidence to the demanders - so their curve shifts left. What happens? Well, the suppliers are supremely flexible, so we expect them to bear none of the burden of the tax. Demanders attempt to substitute away to nontaxed goods, which would ordinarily cause prices to fall (less people fighting for the goods). But our super responsive suppliers can roll with this and cut back on their production at will (less people fighting for less goods). Consumers end up paying the same price (and also the tax!), so suppliers bear none of the economic incidence of the tax.

Our second diagram shows a perfectly inelastic supply curve and a somewhat elastic demand curve. Here we assign statutory incidence to the demanders - so their curve shifts left. What happens? Well, the suppliers are totally stuck, so we expect them to bear all of the burden of the tax. Demanders attempt to substitute away to nontaxed goods, which do in fact cause prices to fall (how much? by the entire amount of the tax!). Our helpless suppliers can do nothing about how much stock they have to sell. Since suppliers want to sell everything, they are forced to slash prices and hold a fire sale; so suppliers bear all of the economic incidence of the tax.

Case three is a perfectly elastic demand curve and a somewhat elastic supply curve. Here we assign statutory incidence to suppliers - so their curve shifts left. Suppliers would like to try and cut back on supply to raise prices, passing along the burden of the tax to demanders through that higher price. Unfortunately, our super flexible demanders instead switch to a substitute and the suppliers get no rise in price. Our suppliers' efforts to raise prices have been thwarted by a perfectly elastic demand curve.

Case four is a perfectly inelastic demand curve and a somewhat elastic supply curve. Here we assign statutory incidence to suppliers - so their curve shifts left. Suppliers would like to try and cut back on supply to raise prices, passiing along the burden of the tax to demanders through that higher price. In this case, demanders are totally unable to find any substitutes and for some reason must buy the same quantity regardless of price. Our suppliers' efforts to raise prices work fantastically, passing the entire tax through to demanders as a higher price.

To recap:

So far it looks like our initial guess is holding true - the more flexible guy (read: more elastic) is good at dodging the burden of the tax and shifts it onto the less flexible (read: more inelastic) guy. The next step is to ask what happens in a less extreme case.

In case five, neither curve is perfectly elastic or perfectly inelastic. But when we look at supply and demand, we can easily tell that demand is less elastic than supply. Here we assign statutory incidence to suppliers - so their curve shifts left. Suppliers would like to try and cut back on supply to raise prices, passiing along the burden of the tax to demanders through that higher price. In this case, demanders find it difficult, but not impossible to find any substitutes and are stuck buying almost the same amount as before. Our suppliers' efforts to raise prices work very well, but not as well as when the demanders were perfectly inelastic.

Although it is hard to see on my small diagram, the price increase is not the full tax amount. Here the less elastic demanders absorbed the majority of the economic tax incidence through a higher price, but they still had a small degree of flexibility. Even this small degree of flexibility allowed them to dodge a tiny bit of the economic tax incidence - the slightly lower quantity (quantity dropped from Q1 to Q2) captures this. Suppliers would have loved to see a situation where they got to sell the same amount (or more) of goods at higher prices, but instead they have to settle for selling slightly less for the higher price.

A very good diagram to look at in Mankiw is Figure 6-9 on P.133. On the next page, Mankiw says exactly what we have worked through: "A tax burden falls more heavily on the side of the market that is less elastic." (P.134)

A very interesting thing you ought to look at in the book is on P.129-131, where Mankiw looks at How Taxes on Buyers Affect Market Outcomes and How Taxes on Demand Affect Market Outcomes. The punch line here is that "Taxes on buyers and taxes on sellers are equivalent." (P.131) This makes sense when you consider tax shifting behavior. Everybody wants to dodge a tax, not just the agent who happens to have statutory incidence under the law. When suppliers and demanders square off and try to be the best at dodging the tax, does it matter where the tax started? No, it only matters where the tax ends up.

When you want to know what a tax will do:

If you have all of that, you can look at the market and tell how much the post-tax equilibrium quantity and price differ from the pre-tax equilibrium price and quantity.

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