1. Terrel Gallaway: Public Finance 1 Excess Burden u The First Fundamental Theorem of Welfare Economics says that, under ideal conditions, the behavior of producers and consumers will automatically lead to efficiency. u Thus when taxes distort economic decisions, they reduce efficiency and create what is called the excess burden of the tax. u This excess burden is a welfare loss beyond the tax revenue collected. It is also referred to as the welfare cost or deadweight loss. v For example, if I stopped buying beer because of a tax on beer, no taxes would be collected but there would still be a welfare loss.

2. Terrel Gallaway: Public Finance 2 Tax Shifts Budget Constraint u Initially, there are no economic distortions. u Original budget constraint has a slope -(P x /P y ) u After a tax on x less x can be bought. u The new budget constraint has a slope -[(1 + t)P x /P y ]. x y

3. Terrel Gallaway: Public Finance 3 Measuring the Tax Payment u For any level of x, the vertical distance between the two budget constraints shows the tax payment measured in terms of the good y. v Set P y = $1 or let y represent all other goods. u For example, if we hold purchases of x fixed at x 1 then purchases of y would have to fall from y 1 to y 2. y y2y2 y1y1 x1x1 x

4. Terrel Gallaway: Public Finance 4 A Decline in Utility u The tax causes the utility- maximizing bundle of goods to switch from 1 to 2. u Naturally, utility decreases. u The tax revenue collected is equal to the distance between A & B. u Is the decrease in utility greater than the tax revenue collected? 1 2 B A y x

5. Terrel Gallaway: Public Finance 5 Equivalent Variation u Equivalent variation is the amount, if there were no tax, by which income would have to be reduced to yield an equivalent decline in utility. u Such a reduction income is shown as a parallel shift of the budget constraint and is equal to the vertical distance between A and C. u The distance between B & C is the dead weight loss (DWL). u DWL is the difference between what is paid in taxes and an equivalent (in terms of utility) reduction in income A y 1 2 B C x

6. Terrel Gallaway: Public Finance 6 Lump Sum Tax u A lump sum tax is a tax that is paid regardless of a consumer’s behavior. u Significantly it doesn’t change relative prices. Rather, it simply decreases income by the amount of the tax. u Note that reduction in income is identical to the tax collected. (The distance between A& B.) u There is no Deadweight Loss. y A B 1 2 x

7. Terrel Gallaway: Public Finance 7 Why no Lump Sum Taxes? u An example of such a tax is a head tax. u Such taxes are regressive. u If everybody has to pay $100, this is much more of a burden to a poor person than it is to a billionaire. u Margaret Thatcher replaced property taxes with a head tax and was subsequently booted out of office.

8. Terrel Gallaway: Public Finance 8 Wherefore Excess Burden? u Remember, allocative efficiency requires that MRS xy = MRT xy u However, after the tax, the consumer faces a new budget constraint such that utility is maximized where MRSxy = (1 + t x )P x /P y. u For producers, the important thing is price net of taxes. Thus, profit-maximizing producers will still set MRT xy = P x /P y. u Since tx > 0, MRSxy > MRTxy. That is, the necessary condition for allocative efficiency is not satisfied.

9. Terrel Gallaway: Public Finance 9 Intuitive Explanation u As long as consumers are willing to cover the economic costs of producing a good, then economic efficiency dictates that the good should be produced. u However when a tax, rather than production costs, pushes a good beyond a consumer’s price range, then too few resources will be dedicated to the production of a good for which consumers would have been willing to pay. v Basically economists want decisions to reflect opportunity costs rather than the tax structure.

10. Terrel Gallaway: Public Finance 10 Does Quantity Have to Change for There to be Inefficiency? u Before and after the tax on x, the consumption of x is x1. u The excess burden is equal to BC. v Equivalent Variation equals E 1 S v Tax Revenues equal E 1 E 2. v E 2 S is the excess burden v A lump sum tax resulting in the same reduction in utility would raise more revenue. (IC runs tangent to both new BCs) v Tax did change consumption of Y & alter the relative mix of X & Y!

11. Terrel Gallaway: Public Finance 11 Substitution and Income Effects u The move from our initial equilibrium (1) to our new equilibrium (2) can be divided into two parts: v The move from 1 to 3 is the income effect. v The move from 3 to 2 is the substitution effect. x1x1 x y A B 1 2 C D 3

12. Terrel Gallaway: Public Finance 12 SE causes DWL u Excess burden is caused when a tax changes relative prices and the consumer’s MRS--this is exactly what the substitution effect is. u The income effect can offset or mask the substitution effect. u While there is no perceived change in quantity demanded, there is still a deadweight loss. x1x1 x y A B 1 2 C D 3 usus