Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 8 A Two-Period Model: The...

Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter 8

A Two-Period Model: The Consumption–Savings Decision and Credit Markets

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 8-2

Chapter 8 Topics

• Consumer’s consumption/savings decision – responses of consumer to changes in income and interest rates.

• Government budget deficits and the Ricardian Equivalence Theorem.

• Social Security.

• Credit market imperfections.


Two-Period Model

• N consumers (not representative)

• Live for two periods (current, future).

• Receive endowment in each period (y, y’).

• Pay lump-sum tax in each period (t, t’).

• Decision: how much to spend as consumption in current period, and how much to save (dissave) to finance future consumption.


Equation 8.1

The consumer’s current-period budget constraint:

If s > 0, consumers save in current period.That is, sacrifice c and consume more c’.

If s < 0, consumers dissave in current period. That is, sacrifice c’ and consume more c, borrow against future income.

If s = 0, consumers consume his endowment net of tax in current period.


Bonds

• If s > 0, consumers are lenders and buy bonds in the credit market.

• If s < 0 , consumers are borrowers and sell bonds in the credit market.

• Abstract from some complications.– No default risk, direct trade in credit markets, and equal

borrowing and lending rates.• A bond issued in the current period is a promise to pay

(1+r) unit of future consumption good. r: real interest rate.

• The relative price of c’ to c is 1 / (1+r).


Equation 8.2

The consumer’s future-period budget constraint:

(1+r)s : interest payment and principal of saving (dissaving) carried forward from last period.


Equation 8.3

Solve the future-period budget constraint for s:


Equation 8.4

Substitute in the current-period budget constraint obtaining lifetime budget constraint:

LHS: PV of lifetime consumption.RHS: PV of lifetime income net of tax.PV: value in terms of current-period consumption goods.1 / (1+r) : relative price of future goods to current goods.Tradeoff between c and c’.


Equation 8.5

Consumer’s lifetime wealth:


Equation 8.6

Simplified lifetime budget constraint for the consumer:


Equation 8.7

Lifetime budget constraint in slope-intercept form:


Figure 8.1 Consumer’s Lifetime Budget Constraint

1. Slope is –(1+r).2. E: endowment point.3. Points on BE are lenders.4. Points on AE are borrowers.5. Optimal bundle is on BC frontier.


Figure 8.2 A Consumer’s Indifference Curves

More is better than less.Diversity is preferred.

MRS c, c’ = - slope of a tangent to IC.

Diminishing MRS c, c’ (convexity of IC)implies desire for consumptionsmoothing.


Table 8.1 Sara’s Desire for Consumption Smoothing

Dislike large difference in consumption between 2 periods.


Equation 8.8

Marginal condition that holds when the consumer is optimizing:

1+r : relative price of c to c’.

Recall Ch.4, MRS l , C = w, where w is relative price of l to C.


Figure 8.3 A Consumer Who Is a Lender

Optimal bundle:

Tangent point betweenBC frontier and IC.


Figure 8.4 A Consumer Who Is a Borrower


An Increase in Current Income for the Consumer

• Current and future consumption increase.

• Saving increases.

• The consumer acts to smooth consumption over time.


Figure 8.5 The Effects of an Increase in Current Income for a Lender


Equation 8.9

Decomposing the change in saving for the consumer:

0y c s


Observed Consumption-Smoothing Behavior

• Aggregate consumption of non-durables and services is smooth relative to aggregate income, but the consumption of durables is more volatile than income.

• This is because durables consumption is economically more like investment than consumption.


Figure 8.6 Percentage Deviations from Trend in GDP and Consumption, 1947–2006


An Increase in Future Income for the Consumer

• Current and future consumption increase.

• Saving decreases.

• Again, these results are explained by the consumer’s motive to smooth consumption over time.


Figure 8.7 An Increase in Future Income


Temporary and Permanent Increases in Income

• As a permanent increase in income will have a larger effect on lifetime wealth than a temporary increase, there will be a larger effect on current consumption.

• A consumer will tend to save most of a purely temporary income increase.


Figure 8.8 Temporary Versus Permanent Increases in Income


Figure 8.11 An Increase in the Real Interest Rate


An Increase in the Market Real Interest Rate

An increase in the market real interest rate decreases the relative price of future consumption goods in terms of current consumption goods – this has income and substitution effects for the consumer.


Figure 8.12 An Increase in the Real Interest Rate for a Lender


Figure 8.13 An Increase in the Real Interest Rate for a Borrower


Table 8.2 Effects of an Increase in the Real Interest Rate for a Lender


Table 8.3 Effects of an Increase in the Real Interest Rate for a Borrower


Equation 8.17

The government’s current-period budget constraint:


Equation 8.18

The government’s future-period budget constraint:


Equation 8.19

The government’s present-value budget constraint:


Equation 8.20: Credit Market Equilibrium Condition

Total private savings is equal to the quantity of government bonds issued in the current period.


Equation 8.21

Credit market equilibrium implies that the income-expenditure identity holds.


Ricardian Equivalence

If current and future government spending are held constant, a change in current tax with an equal and opposite change in the present value of future taxes leave the equilibrium real interest rate and consumption of individual unchanged.

Intuition of RE Theorem

• When consumers receive a tax cut in current period, and this change will be offset by an equal and opposite tax increase in future period, the present value of tax burdens are unchanged, which leaves the consumers’ lifetime wealth unchanged. So the equilibrium optimal consumption bundle and real interest rate all remain the same as before.


Some Issues about RE

• Intergeneration issues

• Different tax rates faced by consumers.

• Assumption of lump-sum taxes.

• Perfect credit market.


Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 8 A Two-Period Model: The...

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