A Two Period Model: The Consumption-Savings Decision and Credit Markets Flashcards
Intertemporal Decisions
Decisions involving economic trade-offs across time
Consumption saving decision
The decision by a consumer about how to split current consumption and savings
The government’s financing decision
- 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
Real interest rate
- 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
Consumption smoothing
- 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
Ricardian equivalence theorem
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
Key implication of the Ricardian equivalence theorem
- 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
Consumers current period budget constraint
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
Assumptions about bonds
- Bonds are indistinguishable (Consumers never default on their debts)
- Bonds are traded directly in the credit market (no financial intermediaries)
Bond payouts
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
Consumer’s future period budget constraint
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
The consumer’s lifetime budget constraint
s = (c’ - y’ + t’) / (1+r)
c + (c’ - y’ + t’) / (1+r) = y - t
C + c’ / (1 + r) = (y - t) + (y’ -t’) / (1 + r)
Consumer’s Lifetime Wealth
we = y - t + (y’ - t’) / (1 + r) = c’ + c’ / (1+r)
Wealth is the PV of disposable income over the consumer’s lifetime
Consumer’s lifetime budget constraint in slope-intercept from
c’ + - (1 + r) * c + we * (1+r)
Endowment point
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
Properties of consumer’s preferences
- More is always preferred to less
- The consumer likes diversity in his or her consumption bundle
- Current consumption and future consumption are normal goods
Consumer optimization
MRS c, c’ = 1 + r
- slope = - slope
An increase in current period Income for the consumer
- 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
Observed consumption-smoothing behavior
- 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
Explanations for the excess variability is consumption
- 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
An increase in future income
- 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
Temporary and Permanent increases in income
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
Permanent income hypothesis
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
Temporary increase in income vs permanent increase in income
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
Increase in the market real interest rate
The budget constraint pivots around the endowment point, shifting the y-intersect up and x-intersect left
An increase in the Real interest rate for the lenders
c ?
c’ increases
s ?
An increase in the Real interest rate for the borrowers
c decreases
c’ ?
s increases
Intertemporal substitution effect
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
Perfect complements
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]
Government’s current budget constraint
G = T + B
t = Nt
Government’s future budget constraint
G’ + (1 + r) * B = T’
T = Nt’
Pays back debt with no new debt issued
The government’s present-value budget constraint
G + G’ / (1 + r) = T + T’ / (1 + r)
Conditions of competitive equilibrium
- 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
Credit market equilibrium condition
S^p = B
Income - expenditure identity
Y = C + G
Neutral
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
Key-equation of the Ricardian equivalence theorem
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
Ricardian equivalence theorem graph
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
Ricardian equivalence and credit market equilibrium
- 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
Why might Ricardian equivalence fail in practice
- 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
