Env-Econ 101: Who pays a tax? (Part 2)

In part 1 of 'Who pays a tax?' we explored the case of simple per unit sales tax on sellers.  That is, for every unit sold the seller must pay $X to the government.  The net effect of the tax on sellers is to increase the price that buyers pay, but not necessarily by the full amount of the tax.  Buyers pay part of the tax and sellers pay part.  In part 2, we will:

1. Look at a per unit tax on buyers and compare it to the case of a tax on sellers.
2. Look at what affects the distribution of the burden of the tax.

Consider again our simple case of a competitive GAS market (on the right).   Instead of taxing the sale of GAS, the government will now tax the purchase of GAS.  In other words, buyers now must pay the purchase price to the seller and then pay an additional fee to the government.  The effect of such a tax in the market is to decrease the maximum willingness to pay of the buyer by the amount of the tax.  For example, if the buyer is willing to pay at most $5 for the first gallon of GAS and the government slaps a $1 per gallon tax on GAS, the buyer is now only willing to pay $4 for the first gallon of gas. 

Graphically (look to the right) the tax has the effect of shifting the demand curve down by the amount of the tax.  At the new willingness to pay (P*-tax), buyers have a problem: sellers don't want to sell the amount buyers want to buy.  That is, there is a shortage.  Anytime there is a shortage in a market, there is upward pressure on the price (think Wii at Christmas).  But for the price to rise, buyers must be willing to absorb part of the tax. 

The new equilibrium occurs when the price (less the tax) rises to the point where the amount buyers want to buy exactly equals the amount sellers are willing to accept (right).  Adding the tax back in, the buyer now pays a price higher than the previous market equilibrium--but not higher by the full amount of the tax.  Some of the tax is passed through to the seller.   

In fact, in this simple linear world, the split of the tax between the buyer and the seller is identical regardless of who pays the tax in practice. Staying consistent with part 1:  What is the net effect of the tax on buyers? 

1. The price buyers have to pay increases, but not by the full amount of the tax (except for a special case).
2. The price sellers are willing to accept decreases, but not by the full amount of the tax (except for a special case).
3. The total amount of GAS sold in the market falls.

A tax on buyers is equivalent to a tax on sellers. 

So the obvious question arises, what determines who pays how much of a tax?  or put another way, why does price sensitivity matter for the burden of a tax?  Well, if buyers are not price sensitive, then the burden of the tax falls more on the buyer.  In econogeekspeak we call this inelastic demand.  If buyers are price sensitive (demand is elastic--think rubber band), then the tax can't be passed through and the seller bears more of the burden.  On the flip side, if sellers are price insensitive (inelastic supply) then the seller will bear more of the burden.  If sellers are price sensitive, buyers will bear more of the burden.  It all depends on the relative sensitivity of prices for the buyer and seller.

Graphically we can depict price sensitivity by the slope of the supply or demand function.  The steeper the slope to less price sensitive the buyer or seller.  The graph at the right looks at four cases for the burden of tax placed on a seller. 

Only two cases are clear cut.  If buyers are price insensitive and and sellers are price sensitive (top right panel), the buyer will bear the burden of the tax.  If sellers are price insensitive and buyers are price sensitive (bottom left panel), sellers will bear the burden.  In cases where both are sensitive or both insensitive, the results are unclear and depends on the relative sensitivities.  In the three cases mentioned above, gas, liquor and cigarettes, buyers are price insensitive relative to sellers, so buyers bear the burden of the tax.

So what makes buyers insensitive to price changes?  Three main things:

1. the unavailability of close substitutes,
2. goods taking up a small portion of income
3. addiction. 

I would argue that gas falls in category 1, Liquor in 2 (and sometimes 3) and cigarettes in 3.  Why then would the government choose to tax goods for which consumers are price insensitive and as a result place the burden on the tax on consumers?  I'll let you decide whether that's a rhetorical question or not.

Comments

[robertdfeinman]

Either I'm misunderstanding or you inverted part of your verbal discussion. A tax imposed on the buyer should lower demand and create a surplus not a shortage. [see text next to second diagram.]

What you only hinted at was the moral aspect of taxation, that is "sin" taxes which are designed specifically to lower consumption. Where this idea goes wrong is when the government then plans to use the revenue for "good things". If the tax is successful then consumption will drop and the good things will be underfunded. This creates a conflict of interest for the government. Perhaps sin taxes should never be allowed to be allocated for specific uses because of this.

Another example is the promotion of gambling as a way to fund education. This isn't an explicit tax (although it does take money from the public and give some of it to the government). Lottery promotion has gotten more aggressive, the proportion going to education has declined and worst of all, the money has become a substitute for allocated general funds resulting in no net gain for education funding.

All of which shows that government should use laws to promote social policy, not economic forces.

[Devon Whittle]

Thank you very much for these posts, I find them a very interesting refresher on microeconomics.

I was just wondering, does the burden of the tax fall the same way whether it is placed on consumer or producer in practice as well as in theory?

So is the reason the government decides to put the tax on one of the other purely political with maybe consideration of who it is easier to collect tax from?