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## Taxation and income distribution

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**Taxation and income distribution**Today: Some basic tax theory**Begin Unit 4**• Today • Parts of chapter 14 • An introduction to some basic theories related to taxation**Taxation**• Taxes are typically used to finance public projects • Deadweight loss comes with most forms of taxation • This will be discussed in next lecture**Taxation and income distribution**• The US federal tax system has been set up so that people with high incomes have higher average tax rates • Do people consume more leisure with high marginal tax rates? • Usually yes • Public project financing • People with high tax rates probably have high willingness to pay for many public projects**Taxation and income distribution**Table 14.3 Average federal tax rates and share of federal taxes by income quintile (2006)**Some terminology**• Statutory incidence • Who legally has to pay for the tax • Economic incidence • How much does real income change to all parties due to a tax?**Some terminology**• Lump sum tax • A tax that has to be paid no matter how a person behaves • Proportional tax • Average tax rate is independent of income • Progressive tax • Average tax rate increases with income • Regressive tax • Average tax rate decreases with income**Some terminology**• Unit tax • A tax that is paid per unit of a good • Ad valorem tax • A tax that is a percentage of the purchase price**Partial equilibrium models**• With partial equilibrium models, only one market is examined at any one time • Ignores possible spillover effects • Usually easier to analyze than general equilibrium models • Two types of taxes analyzed • Unit tax • Ad valorem tax**Unit tax**• You have likely seen unit taxes before • Econ 1 (or equivalent) • Econ 100A/B (or equivalent) • Either the buyer or seller pays a given dollar amount for each unit sold or purchased**$**0 Partial Equilibrium Models $1.20 $1.40 $1.00 $1.20 S1 S0 D1 D0 Quantity**Ad valorem taxes**• Assume that the consumer pays an ad valorem tax • Example: 6% sales tax (of the net price) imposed on the consumer • The ad valorem tax shifts the demand curve by the same percentage (relative to the horizontal axis)**Ad valorem taxes**Sf Price per pound of food Pr P0 Pm Df Df’ Qm Pounds of food per year Q0 Qr**Tax on gross price? …or net price?**• A tax on the gross price (paid by consumers) lowers the willingness to pay by the percentage of the tax • Example • 25% tax of gross price when demand is P = 4000 – 20Q • New demand after tax is P = (1 – 0.25) (4000 – 20Q) • P = 3000 – 15Q**Tax on gross price? …or net price?**• A tax on the net price (paid by consumers) is more complicated • You need to find the new demand such that when the tax is added, you get the new demand • Example • 25% tax of net price when demand is P = 4000 – 20Q • WTP with the tax is 5/4 of WTP without the tax • In other words, WTP without the tax is 4/5 the WTP with the tax • New demand after the tax is P = (4/5) (3000 – 20Q), which leads to P = 3200 – 16Q**Other types of taxes**• Taxes from working • Income tax • Social Security tax • Hospital insurance tax (Medicare) • Capital taxes • Problem: Mobility of capital may move capital out of the country with taxation • Taxes on profits • Accounting profits • Economic profits**Summary**• High income people pay a higher percentage of their income in taxes • Different forms of taxation exist • Unit tax • Ad valorem tax • Taxes on wages • Capital taxes • Profit taxes**Problem: Ad valorem tax**• Supply: P = Q • Demand: P = 1710 – Q • What is the equilibrium in the absence of a tax? • What is the equilibrium if there is a 10% tax of the gross price?**No taxes**• Set Q = 1710 – Q • Q = 855 • Since P = Q from the supply curve, P = 855**With a tax**• A tax on the gross price implies that the willingness to pay goes down by 10% for each unit • New demand is P = 1539 – 0.9Q • Set Q = 1539 – 0.9Q • Q = 810**With a tax**• What about price? • Price without the tax is 810 • This is the price that suppliers receive • Price with tax is 810/0.9 = 900 • This is the price that consumers pay