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## Ricardian Equivalence And Credit Market Imperfection Notes

This is an extract of our Ricardian Equivalence And Credit Market Imperfection document, which we sell as part of our Macroeconomic Principles Notes collection written by the top tier of LSE students.

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Ricardian Equivalence and Credit Market Imperfection Topics

• Ricardian Equivalence

• Credit Market Imperfections - Asymmetric information and limited commitment

• Social Security Programs

Ricardian Equivalence

• The Ricardian Equivalence theorem states that a change in the timing of taxes by the government has no effect on consumption

• A tax cut is not a free lunch!
The government present-value budget constraint

• Introduce government to the two-period model
○ Government's current-period budget constraint:
○ Government's future-period budget constraint:
○ So government's present-value budget constraint:

• Total private saving is equal to the quantity of government bonds issued in the current period:

• Credit market equilibrium implies that the income-expenditure identity holds:

Key Points

• Ricardian equivalence

• Government PV budget constraint

• Consumer's wealth

• When might Ricardian equivalence not hold?

• Credit market imperfections

• Asymmetric information

• Limited commitment and collateral

• The financial crisis

• Effect on consumption of tax cut with credit imperfections

Definitions

• Asymmetric information = Would-be borrowers know more about their characteristics than lenders

• Limited commitment = Borrowers may choose to default. Lenders can overcome limited commitment with collateral

• The Ricardian Equivalence theorem states that a change in the timing of taxes by the government has no effect on consumption

Deriving consumer's wealth
○ There are N consumers
○ ∴ T = Nt
○ Government's budget constraint implies:

Formulae

○ ∴ consumer's wealth:

Ricardian equivalence in graphs Consumer's wealth remains the same so the consumption choice remains the same

• ∴ consumer's wealth:

• →

• Collateral constraint:

• Government's budget constraint implies:

• Government's current-period budget constraint:

• Government's future-period budget constraint:

• Lifetime budget constraint for a borrower:

• A tax cut financed by an increase in government bond is met by an increase in private saving

• The market real interest rate remains the same

• Lifetime budget constraint for a lender:

• So government's present-value budget constraint:

• When might the Ricardian Equivalence theorem not hold?

• If the tax burden is not shared equally among consumers then the government can redistribute wealth through tax

• If taxes are distortionary

• i.e. labour income tax reduces incentives to work (recall the simple income tax model)

• If there are credit market imperfections

• If consumers have a different life-span than the government then there can be intergenerational redistribution

• i.e. social security programs Credit Market Imperfections - Asymmetric information and limited commitment

• Credit Market Imperfections and Consumption

• Assume that lenders face a lower interest rate than borrowers

• Government borrows and lends at the interest rate lenders face

• ∴ Ricardian equivalence does not hold, in general

Course Notes Page 30

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