Econ 208

Marek KapickaLecture 11

Redistributive TaxationRicardian 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 wL

High productivity: wages wH>wL

½ of population is of low productivity, ½ is of high productivity

Utility:LCLCU 2),(

Taxes

High productivity people are taxed at rate t

Low productivity people get a transfer v

Low productivity people

Subject to

Solution

LLLC

LCLL

2max,

vLwC LLL

LLL

LL

LLL

w

vwU

wC

w

vwL

2

High productivity people

Subject to

Solution

HHLC

LCHH

2max,

HHH LwtC )1(

HH

HH

HH

wtU

wtC

wtL

)1(

)1(

)1(22

Government Budget constraint:

Express utility as a function of t only:

where k=wH/wL>1

2)1( H

HH

wtt

Ltwv

HH

HLL

wtU

wtktwU

)1(

)1(

Welfare and Production Assume that the society’s welfare

is given by

Big and controversial assumption! We have

HL UU

HL

HHLHL

wkttw

wtwtktwUU

)1)(1(

)1()1(

Welfare and Production Welfare is maximized at

Production is decreasing in t: k

kt

2

1

222

222

22

)1(

)1()1(

)1(

tww

twttww

twvw

LwLwY

HL

HHL

HL

HHLL

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 14.1-14.2 for today, 14.3-14.4 for next week

US Government DebtPrivately 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

srtyc

tysc

)1('''

)',( ccU

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

r

tt

r

yywe

1

'

1

'

wer

cc

1

'

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

BtG

')1(' tBrG

r

tt

r

GG

1

'

1

'

Competitive Equilibrium

Consumers choose c,c’,s optimally, given r

Government PVBC holds Interest rate such that the credit

market clears: Bs

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