The Economic Incidence of a Tax--Part 2

A few days ago I began discussing the economic incidence of a tax. Closely related to this is the deadweight loss of a tax. On February 22 I wrote: "The deadweight loss comes from the reduction in economic activity caused by the tax. If the gain from a transaction between a buyer and a seller is $5, but the government imposes a $6 tax on the transaction, it will cause the transaction to disappear."

The main harm done by taxes is this deadweight loss. Taxes tend to reduce economic activity. Now the government programs funded by the tax might increase economic activity, or make citizens and residents better off in some way. If tax revenue is used to pay for a legal system, which by its existence reduces crimes by a sufficient amount, the gain from having the legal system will exceed the deadweight loss incurred by the taxes necessary to pay for the legal sytem. (By legal system I mean things like police, prosecutors, public defenders, prisons and courts.)

I presume that no one doubts that we need a legal system. However, it is conceivable that an increase in taxes imposed to pay for an expansion of the legal system (such as building a new courthouse or hiring more police) could cause a deadweight loss sufficiently large to be greater than the value to society of the expansion of the legal system. A new federal courthouse is to be built near where I live. Already the city has condemned property and thereby put many businesses out of business or forced them to move. The federal government is going to pay for the new courthouse, so local residents are not concerned about the deadweight loss of the taxes needed to pay for the new courthouse. Only a small part of those taxes will be raised locally. But the loss is there, and I don't think the new courthouse will make the area safer. But I digress.

Today's topic is the incidence of a tax. Suppose there is no tax on the production and sale of a good. If markets are perfectly competitive, then each buyer will spend dollars on the good until the value (to the buyer) of one additional unit of the good just equals its price. Each seller will be willing to supply additional units of the good to the market until the cost of providing one additional unit just equals the price of the good. If the price of bananas is 45 cents a pound, then I will buy pounds of bananas per month until the value to me of one more pound of bananas per month is just equal to 45 cents. I purchase more bananas than this, the value to me of each additional pound of bananas will be less than 45 cents.

Lets keep the price of bananas at 45 cents per pound and suppose the government imposes a tax of 10 cents per pound on bananas. And suppose the the government requires me, and other buyers, to pay this tax. In order for me to keep buying the same number of bananas per month the price would have to decline to 35 cents per pound. But if this happens, the seller of the last pound of bananas that I purchase will only get 35 cents for that pound, even though it costs him to 45 cents to provide me with that pound of bananas. Hence, the price cannot go down all the way to 35 cents per pound. What will tend to happen is that the price of bananas will decline a little bit, say to 40 cents per pound. Buyers, in this case, will pay 40 cents plus 10 cents in taxes--at total of 50 cents per pound--for each pound of bananas. Hence they buy fewer bananas. Sellers will supply fewer bananas to the market because they will not supply those bananas that cost it more than 40 cents per pound to supply. So the tax causes sellers to receive a smaller amount for each unit of their product, and buyers to pay a higher amount to purchase each unit of the product.

When there was no tax, the value to each buyer of the last pound of bananas purchased per month was 45 cents per pound. The cost to each seller of the last pound supplied was also 45 cents per pound. With the 10 cent tax per pound, the value to each buyer of the last pound of bananas purchased per month will exceed the cost to each supplier of supplying his last pound supplied by 10 cents. Each buyer will buy pounds of bananas until the value of the last pound per month is 50 cents, and suppliers will supply bananas until the cost of supplying the last pound is 40 cents. 50 minus 40 cents is 10 cents.

This gives us the information we need to calculate the incidence of the 10 cent tax on bananas. Before the tax was imposed, buyers paid 45 cents per pound for bananas, but now they pay 50 cents. So the incidence of buyers is 5 cents. The incidence of a tax on buyers is the increase in the amount that the buyer has to pay because of the tax. The incidence on sellers is also 5 cents in this example, because before the tax each seller received 45 cents per pound of bananas, but now they receive only 40 cents for each pound. The incidence of a tax on a seller is the decrease in price per unit of output received by the seller because of the tax.

The incidence of a tax is often expressed as a percentage. In this example buyers pay 50% of the tax and sellers pay 50% of the tax (because 5 cents is 50% of 10 cents). The tax is not always equally shared by buyers and sellers. What actually happens depends on how sensitive the demand for the taxed good is to price, as well as how sensitive the supply of the taxed good is to price. (We call these items the elasticity of demand and the elasticity of supply, respectively.) In general, the more sensitive to price the demand for the good is, the smaller the incidence on buyers. Likewise, the more sensitive supply is to price, the smaller the incidence is on sellers.

Interestingly enough, there are conditions under which the sensitivity of supply to price is so great that it is not possible for the price received by sellers to decline. This is a long-run or long-term possibility and the industries in which this can happen are called constant-cost industries. If an industry is a constant cost industry, then the incidence of any tax imposed upon it will fall entirely on buyers.

Suppose an industry is a constant cost industry. Suppose all the producers in this industry are really rich. The government decides to tax them because they are rich. Suppose the people who buy the good are either poor or are typically people with low incomes. The incidence of the tax then will fall entirely or almost entirely on people who are poor, even though by statute the "rich" are suppose to pay the tax. The economic incidence of a tax does not depend upon the statutory incidence of the tax. You can tax the rich and by doing so make the poor worse off.

There are also examples where it is the behavior of buyers that causes incidence to fall entirely or nearly entirely on sellers and in which the buyers are "rich" and the sellers are "poor". A good example of this is the luxury tax. Luxurious goods are not necessarily produced by the rich for rich, they can be produced by the poor for the rich. But by its very nature a luxury good or service is not a necessity. People do not have to have it. If it is taxed, the quantity of the good or service demanded declines greatly, causing the amount produced to decline and incomes of producers to decline because price declines. Consider a tax on employing domestic help. Since this is not a necessity, households that employ housekeepers, nannies, and cooks will tend to greatly reduce their employment of domestic employees, or conspire with them not to pay the tax. This is why so many nominees to cabinent positions have "nanny" tax problems.