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

Question 1

Intertemporal Decisions

Answer 1

Decisions involving economic trade-offs across time

Question 2

Consumption saving decision

Answer 2

The decision by a consumer about how to split current consumption and savings

Question 3

The government’s financing decision

Answer 3

• Government has to make a choice between current and future taxes
• If the government decreases taxes in the present it must borrow from the private sector to do so, which implies that future taxes will increase to pay off the higher government debt

Question 4

Real interest rate

Answer 4

• The rate at which consumers can borrow and lend

- Determines the relative price of consumption in the future in terms of consumption in the present

Question 5

Consumption smoothing

Answer 5

• The tendency of consumers to seek a consumption path that that is smoother than income
• Affects how consumers respond in their aggregate to changes in government policies or features of their external environment that effect their income streams

Question 6

Ricardian equivalence theorem

Answer 6

States that there are conditions under which the size of the government’s deficit is irrelevant, in that it does not affect any macroeconomic variables of importance on the welfare of any individual

Question 7

Key implication of the Ricardian equivalence theorem

Answer 7

• A tax cut is not a free lunch
• A tax cut may not matter at all, or it may involve redistribution of wealth within the current population or across generations

Question 8

Consumers current period budget constraint

Answer 8

c + s = y - t

• If s > 0, the consumer is a lender on the credit market; consumer buys bonds
• If s < 0, the consumer is a borrower on the credit market; There is a sale of bonds

Question 9

Assumptions about bonds

Answer 9

• Bonds are indistinguishable (Consumers never default on their debts)
• Bonds are traded directly in the credit market (no financial intermediaries)

Question 10

Bond payouts

Answer 10

One bond issued in the current period is a promise to pay 1 + r units of consumption goods in the future, so that the real rate of interest for each bond is r

Therefor the relative price in terms of current consumption is 1 / 1+r

The real rate of interest at which a consumer can lend is the same as the real rate of interest at which a consumer can borrow

Question 11

Consumer’s future period budget constraint

Answer 11

c’ = y’ - t’ + (1+r)s

All of the future disposable income and interest earnings of savings are consumed as the consumer does not live beyond this point

The consumer is a price taker and treats the real interest rate r as given

• If s < 0, the consumer pays the interest and principal on his or her loan and consumes what remains of the future disposable income

Question 12

The consumer’s lifetime budget constraint

Answer 12

s = (c’ - y’ + t’) / (1+r)

c + (c’ - y’ + t’) / (1+r) = y - t

C + c’ / (1 + r) = (y - t) + (y’ -t’) / (1 + r)

Question 13

Consumer’s Lifetime Wealth

Answer 13

we = y - t + (y’ - t’) / (1 + r) = c’ + c’ / (1+r)

Wealth is the PV of disposable income over the consumer’s lifetime

Question 14

Consumer’s lifetime budget constraint in slope-intercept from

Answer 14

c’ + - (1 + r) * c + we * (1+r)

Question 15

Endowment point

Answer 15

The point on a consumer’s budget constraint where consumption is equal to disposable income in each period and savings = 0 in the current period

• Above / left of endowment point, s > 0, consumer is a lender
• Below / right of endowment point, s < 0, consumer is a borrower

Question 16

Properties of consumer’s preferences

Answer 16

• More is always preferred to less
• The consumer likes diversity in his or her consumption bundle
• Current consumption and future consumption are normal goods

Question 17

Consumer optimization

Answer 17

MRS c, c’ = 1 + r

• slope = - slope

Question 18

An increase in current period Income for the consumer

Answer 18

• c & c’ increases
• s increases:
  ds = dy - dt - dc
  but dt = 0 and dy > dc
• Shift budget constraint right by y2 - y1
• Consumer wishes to smooth consumption over time relative to income, so current and future income, and saving increases, so c increases less than y

Question 19

Observed consumption-smoothing behavior

Answer 19

• Aggregate consumption of non-durables and services is smooth relative to aggregate income because if of consumption smoothing, but the consumption of durables is more volatile than income
• This is because durables consumption is economically more like investment than consumption
• Measured consumption is more volatile than theory appears to predict

Question 20

Explanations for the excess variability is consumption

Answer 20

• There are imperfections in the credit market

- When all consumers are trying to smooth consumption in the same way simultaneously, this changes the market price

Question 21

An increase in future income

Answer 21

• Shifts the budget line up by y’2 - y’1
• Lifetime wealth increases from we1 to we2
• c & c’ increase
• s decreases (in the case of expected increases in future income)
  ds = dy - dt - dc
  but dt = dy = 0 and dc > 0
• The increase in c’ is less than the increase in c, because consumer wants to smooth consumption over time and saves less in the current period so that current consumption can increase

Question 22

Temporary and Permanent increases in income

Answer 22

As a permanent increase in income will have a larger impact 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 permanent income

Question 23

Permanent income hypothesis

Answer 23

A primary determinant of a consumer’s current consumption is his/her permanent income, which is closely related to the concept of lifetime wealth in our model

Question 24

Temporary increase in income vs permanent increase in income

Answer 24

Temporary - s increases due to consumption smoothing

Permanent - s need not increase and c can increase as much as or even more than y

graph p 344

Question 25

Increase in the market real interest rate

Answer 25

The budget constraint pivots around the endowment point, shifting the y-intersect up and x-intersect left

Question 26

An increase in the Real interest rate for the lenders

Answer 26

c ?
c’ increases
s ?

Question 27

An increase in the Real interest rate for the borrowers

Answer 27

c decreases
c’ ?
s increases

Question 28

Intertemporal substitution effect

Answer 28

Higher real interest rates lowers the relative price of future consumption in terms of current consumption and this leads to substitution of future consumption for current consumption and therefor an increase in savings

Question 29

Perfect complements

Answer 29

c’ = ac

• No substitution effects

c = we * (1 + r) / (1 + a + r)
= [(y - t) * (1 + r) + (y’ - t’)] / [1 + a + r]

c’ = a * we * (1 + r) / (1 + a + r)
= a * [(y - t) * (1 + r) + (y’ - t’)] / [1 + a + r]

Question 30

Government’s current budget constraint

Answer 30

G = T + B

t = Nt

Question 31

Government’s future budget constraint

Answer 31

G’ + (1 + r) * B = T’

T = Nt’

Pays back debt with no new debt issued

Question 32

The government’s present-value budget constraint

Answer 32

G + G’ / (1 + r) = T + T’ / (1 + r)

Question 33

Conditions of competitive equilibrium

Answer 33

• Each consumer chooses first- and second- period consumption and savings optimality given the real interest rate r
• The government’s present-value budget constraint holds
• The credit market clears - When the net quantity that consumers want to lend in the current period is equal to quantity that government wishes to borrow

Question 34

Credit market equilibrium condition

Answer 34

S^p = B

Question 35

Income - expenditure identity

Answer 35

Y = C + G

Question 36

Neutral

Answer 36

A change in timing of taxes by the government is neutral

By neutral we mean that is equilibrium a change in current taxes, exactly offset in present- value terms by an equal and opposite change in future taxes, has no effect on the real interest rate or the consumption of individual consumers

Question 37

Key-equation of the Ricardian equivalence theorem

Answer 37

t + t’ / (1 + r) = (1 / N) * [G + G’ / (1 + r)]

In equilibrium the individual’s PV share of taxes are equal to his/her share of the PV of Government spending, which tells us it does not matter how the taxes are timed

Substituting in consumer’s budget constraint:

c + c’ / (1 + r) = y + y’ / (1 + r) - (1 / N) * [G + G’ / (1 + r)]

Consumer is unaffected by change in t as it is not in the equation

Question 38

Ricardian equivalence theorem graph

Answer 38

p 359

A current tax cut moves the endowment point, but does not change the budget constraint for the consumer, but the consumer saves the tax cut in order to pay the higher taxes that are coming in the future, which are required to pay of higher government debt

Question 39

Ricardian equivalence and credit market equilibrium

Answer 39

• In aggregate, the real interest rate is determined by the supply and demand for government debt
• If there is a current tax cut, this shifts the supply of government debt to the right, but the demand for government debt shifts to the right by the same amount, so the real interest rate is unaffected

p 360

Question 40

Why might Ricardian equivalence fail in practice

Answer 40

• Redistributional effects of taxes:
  Tax changes affect the wealth of different consumers differently
• Intergenerational redistribution
  Debt issued by the government today is paid off by future generations
• Taxes are not lump sums, they cause distortions
  Change the relative prices of goods in the markets
• Credit market distortions
  The credit market is not perfect eg different borrow and lend rates and collateral