Econ 208 Marek Kapicka Lecture 11 Redistributive Taxation Ricardian Equivalence

Where are we? Introduction: A model with no Government The Effects of Government Spending Government Taxation and Government Debt Labor Taxation Taxation and Redistribution Government Debt

Taxation and Redistribution Fiscal policy may aim to change income or consumption inequality Will have an example when It is optimal to reduce income inequality even if A (distorting) flat tax is used There are costs in terms of production

An example: 2 productivity levels Two types of people: Low productivity: wages w L High productivity: wages w H >w L ½ of population is of low productivity, ½ is of high productivity Utility:

Taxes High productivity people are taxed at rate t Low productivity people get a transfer v

Low productivity people Subject to Solution

High productivity people Subject to Solution

Government Budget constraint: Express utility as a function of t only: where k=w H /w L >1

Welfare and Production Assume that the society’s welfare is given by Big and controversial assumption! We have

Welfare and Production Welfare is maximized at Production is decreasing in t:

Conclusions There is a trade-off between efficiency and redistribution What matters: How the government weights the utility of different individuals Distribution of skills in the population

Where are we? Introduction: A model with no Government The Effects of Government Spending Government Taxation and Government Debt Labor Taxation Taxation and Redistribution Government debt

Government Debt 1) The Data 2) Ricardian Equivalence Theorem Gov’t Debt does not matter ! 3) Ramsey Problem Find the optimal debt level if taxes are distortionary and RET fails Read for today, for next week

US Government Debt Privately held debt

US Government Debt As of now: Privately held US gov’t debt is about 70% of GDP Total US gov’t debt is about 100% of GDP US Treasury: monthly statement

US Government Deficits

Consumers Budget constraints Utility

Lifetime wealth Define lifetime wealth as present value of a disposable income Then lifetime budget constraint says that present value of consumption is equal to lifetime wealth

A Consumer Who Is a Lender

A Consumer Who Is a Borrower

Government Current period budget constraint Future period budget constraint Present value budget constraint

Competitive Equilibrium Consumers choose c, c ’, s optimally, given r Government PVBC holds Interest rate such that the credit market clears:

Ricardian Equivalence Suppose the government cuts taxes by $600:

Ricardian Equivalence You should also get a second letter: There is no change in your wealth!! Dear Taxpayer: We are sorry to inform you that the present value of your future tax liabilities has increased by the amount of $600.

Ricardian Equivalence Theorem The Ricardian Equivalence Theorem: If all government spending is held constant, then a change in current taxes leaves the equilibrium interest rate and the consumption of individuals unchanged

Ricardian Equivalence with a Cut in Current Taxes for a Borrower

Implications of Ricardian Equivalence Tax cut is not a free lunch! Timing of gov’t taxes does not matter Deficits do not matter!

Failure of Ricardian Equivalence 1.If people are heterogeneous, they might not be affected equally Some people may receive larger tax cuts than others and their lifetime wealth may change That is, there is a redistribution of wealth across people

Failure of Ricardian Equivalence 2.Debt may not be repaid during the lifetimes of the people who received tax cuts There is a redistribution of wealth across generations Example: Social Security

Failure of Ricardian Equivalence 3.Credit markets are not perfect People may face borrowing limits. In such case, a tax cut will not be saved People may face higher interest rate than government. In such case, a tax cut will increase present value of their resources and increase consumption

Failure of Ricardian Equivalence 4.Taxes are not lump sum If taxes cause distortions, then timing of taxes does matter A government may want to spread the distortions across all periods

Example of RI: George Bush, 1992 George Bush, 1992: change in tax withholding Taxes were deferred until April 1993 Total size: $25 billion Hope: consumers will increase spending Result: consumption didn't change much Didn't know Ricardian Equivalence...

Real Consumption of Durables, 1991–1993

Real Consumption of Nondurables, 1991–1993

Real Consumption of Services, 1991–1993