Paul Krugman and Robin Wells. Microeconomics. Third Edition. Chapter 7 Taxes. Copyright 2013 by Worth Publishers

1. Taxes: overview Taxes can be imposed on demanders (consumers) or suppliers (producers) So, to analyze taxes, we need a pre- and post-tax demand curve (for a tax imposed on demanders) or a pre- and post-tax supply curve (for a tax imposed on suppliers) Taxes can be shifted (at least partially) from producers to consumers, and from consumers to producers. So, in general, both producers and consumers end up sharing the burden of the tax. In principle, it doesn t matter who has the initial burden consumers or producers! The share of the tax paid by producers and consumers depends (among other things) on the elasticities of supply and demand. Taxes drive a wedge between the price that consumers pay and the price that producers receive. Taxes entail a deadweight loss (reduction in surplus, due to reduction in output) but not taxing may also involve a loss.

First consider equilibrium in the absence of any tax: equilibrium P = 80, equilibrium Q = 10,000

2. A tax imposed on producers The pre-tax supply curve shows the minimum price the firm will accept (in the absence of taxes) in order to produce each level of output, given the firm s costs. The post-tax supply curve will be the same as the pre-tax supply curve, except that it will be shifted up by the amount of the tax: The tax is just another cost for the employer, so now the employer will want to get a price at each level of Q that not only pays for its (other) costs, but also pays for the tax. So the post-tax supply curve will be higher than the pre-tax curve, and the vertical distance between the two curves is equal to the size of the tax. (Note that this is a decrease in supply!)

So consider a tax of $40 put on suppliers. post-tax supply curve The pre-tax supply curve is S 1. The post-tax supply curve is $40 higher, i.e., S 2. pre-tax supply curve Point E is the pretax equilibrium; points A and B describe the post-tax equilibrium. Per unit sold, at Q = 5000: * consumers pay a price of 100 (point A). * firms collect 100, but must pay 40 in tax (A B). * government receives 40 (A B). * firms get to keep 100 40 = 60 (point B).

Price paid by consumers rises from 80 to 100. pre-tax supply curve Price received by producers falls from 80 to 60. paid by consumers paid by producers So both consumers and producers end up paying a portion of the total tax (40) even though the tax was imposed solely on producers! Thus, producers have shifted some of the tax to consumers. Note also that equilibrium output falls from 10,000 to 5,000. We already know this will mean a decline in total surplus! pre-tax supply curve

A F B E C D surplus before after consumer A+B+C A producer D+E+F F government --- B+E total A+B+C+ A+B+E+F D+E+F deadweight loss --- C+D

3. A tax imposed on consumers The pre-tax demand curve shows the maximum total price that consumers would be willing to pay in order to have each level of output. (In the absence of taxes, this is just the price of the good; in the presence of taxes, this is the price of the good plus the tax.) The post-tax demand curve will be the same as the pre-tax supply curve, except that it will be shifted down by the amount of the tax: The tax is just a part of the cost of the good. The tax doesn t change the total amount the consumer is willing to pay for the good (including the tax as well as the cost of the good itself). But the post-tax demand curve for the good itself will be shifted down by the amount of the tax, relative to the pre-tax demand curve. Only if this is true will consumers end up paying the same amount per unit (for taxes plus the good itself) to get each different level of Q. The only difference is that now, some of what they pay goes to the government as taxes whereas the rest goes to producers for the Q. (Previously, everything consumers spent went to producers.)

pre-tax demand curve post-tax demand curve For example: to get Q = 5000, before the tax, consumers would be willing to pay up to $100 (point A). After the tax of 40, consumers would be willing to pay only 100-40 = 60 for output in order to get the same quantity (Q = 5000): Only if this is true will they still pay only a total of 100 (= 60 for the room, plus 40 for the tax), to get Q = 5000.

A B E F C D surplus before after consumer A+B+C A producer D+E+F F government --- B+E total A+B+C+ A+B+E+F D+E+F deadweight loss --- C+D

4. Tax shifting, tax incidence, and elasticities of supply and demand "Shifting" of the tax means that both sides of the market will usually end up paying some portion of a tax, even if it is imposed on only one side of the market. "Incidence" of the tax refers to the portion paid by each side of the market, after all shifting has been done. The more elastic (price-responsive) side of the market will pay the lower share of the tax; the less elastic side of the market will pay the greater share. Intuition: * If consumers are very price-elastic, producers can't pass on much of the tax to consumers, because consumer demand would drop dramatically. Producers will have to "eat" most of the tax. * If producers are very price-elastic, even a small drop in the after-tax price they get will reduce their output substantially, so the amount of tax they will pay (and their share of the total tax) will be very small.

Original equilibrium at E: P = $2. Supply curve is highly elastic; demand curve is relatively inelastic. E Then $1/gallon tax is imposed on consumers. Post-tax demand curve is $1 below the pre-tax demand curve. post-tax demand pre-tax demand Since demand is relatively inelastic, consumers absorb most of the tax without reducing purchases by very much. Price paid by consumers rises from $2 to $2.95; price received by firms falls from $2 to $1.95.

Here, supply is relatively inelastic and demand is relatively elastic, firms can't pass much of the tax on to consumers. Original equilibrium occurs at point E with price of $6. After the tax: Price paid by consumers rises from $6 to $6.50; price received by firms falls from $6 to $1.50. E

post-tax number of units sold To calculate government revenue from the tax, multiply the size of the tax per unit (e.g., AB in the above diagram) by the post-tax level of output (e.g., 5,000 in the above diagram) This is equal to the area (base x height) of the rectangle above.

Tax revenue = tax rate post-tax output: Higher tax rate must mean less output -- the tax rate/output tradeoff! A "small" tax doesn't change output (Q) by very much. (See (a).) A "large" tax changes output by more. (See (b).) Which tax raises more revenue depends on the responsiveness of supply and demand to amount of the tax. (However, a larger tax always means a greater deadweight loss!)

post-tax demand curve post-tax supply curve

Size of the deadweight loss from a tax depends on the elasticities of supply and demand -- just like the effect of a tax on the change in output and in prices paid by consumer/received by producer. The more elastic is supply and/or demand, the greater the drop in output; hence, the greater the deadweight loss. The greater the tax (= T), the greater the deadweight loss.

4. A few concluding comments about practical matters To minimize deadweight loss, tax products with low elasticities of supply, demand (e.g., sin taxes on cigarettes, booze) Taxes on income from capital may involve large deadweight loss if elasticity of supply of capital is high (e.g., lower returns would mean the investment goes to places outside the USA) Taxes on income from work may involve large deadweight loss if elasticity of supply of labor is high (e.g., females (not males!)) Taxation always involves a deadweight loss (unless elasticity of supply or demand is zero) But not taxing also involves a loss -- less revenue for roads, R&D investment, defense, etc. So the point about deadweight loss is that taxation involves costs, which should be taken into account in designing taxes, and in deciding whether it s a good idea to impose them. A tax makes sense only if its benefits outweigh its costs.