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ECO3020F Term 2 EXAM NotesØ Chapter 90
Ø Chapter 10
Ø Chapter 11
Ø Chapter 12
Ø Chapter 13
Ø Chapter 14
Ø Chapter 16
Ø Chapter 17
Chapter 9 – A Two-Period Model: The Consumption-Savings Decision & Credit Markets
• Extra material (slides) on Budget deficits and disagreements among economists regarding
budget deficits and the size of the fiscal multiplier.
Chapter 10:
• Miskhin ‘Anatomy of a financial crisis’.
• C-Rene ‘Behind the 2008 Capital Market Collapse’.
Chapter 11:
• No Readings.
Chapter 12:
• No Readings.
Chapter 13:
• Economics and Its Discontents.
• Ideological influence in economics and RBC models.
• Blanchard – The Story of Macroeconomics.
• Romer – The Trouble with Macroeconomics 2016
• Muelbauer – Why central bank models failed and how to repair them.
Chapter 14:
• No Readings.
Chapter 16 & 17:
• No Readings.
, CHAPTER 9: A Two-Period Model: The Consumption-Savings Decision & Credit Markets
Intertemporal decisions = decisions involving economic trade-offs across periods of time:
• Consumption-savings decision: involves a trade-off between current & future consumpt.
• Government’s decision: involves a trade-off between current and future taxes concerning
the financing of government expenditure. If the government decreases taxes in the
present, it must borrow from the private sector to do so, which implies that future taxes
must increase to pay off the higher government debt.
Key terms:
• Lifetime budget constraint: Condition that the present value of a consumer’s lifetime
disposable income equals the present value of his lifetime consumption.
• Present value: The value of future goods in terms of current goods.
• Lifetime wealth: The present value of lifetime disposable income for a consumer.
• Endowment point: The point on the consumers budget constraint where consumption is
equal to disposable income in each period.
CONSUMER:
Consumer’s current-period budget constraint: 𝒄 + 𝒔 = 𝒚 − 𝒕 (Equation 9-1)
- If s > 0, then the consumer is a lender on the credit market (he buys bonds).
- If s < 0, then the consumer is a borrower on the credit market (he sells bonds).
Consumer’s future-period budget constraint: 𝒄! = 𝒚! − 𝒕! + (𝟏 + 𝒓)𝒔 (Equation 9-2)
- If s < 0, then the consumer pays the interest + principal amount on his loan, and then
consumes what remains of his future period disposable income.
Consumer’s Lifetime Budget Constraint:
" ! #$ ! %& !
STEP 1: Use Equation (9-2) to solve for s à 𝑠 = '%(
(Equation 9-3)
" ! #$ ! %& !
STEP 2: Substitute s from (9-3) into Equation (9-1) à 𝑐 + '%(
=𝑦−𝑡
𝒄! 𝒚! 𝒕!
STEP 3: Re-arrange à 𝒄 + 𝟏%𝒓 = 𝒚 + 𝟏%𝒓 − 𝒕 − 𝟏%𝒓 (Equation 9-4)
- This is the consumer’s Lifetime Budget Constraint: the PV of lifetime consumption (𝑐 +
"! $! &!
'%(
) equals the PV of lifetime income (𝑦 + '%() plus the PV of lifetime taxes (𝑡 + '%().
𝒕! 𝒕!
The consumer’s lifetime wealth: 𝒘𝒆 = 𝒚 + 𝟏%𝒓 − 𝒕 − 𝟏%𝒓 (Equation 9-5)
𝒄!
Or, 𝒘𝒆 = 𝒄 + 𝟏%𝒓 (Equation 9-6)
Consumer Optimization: Point where IC is tangent to the Budget constraint.
• Slope of the budget constraint = (1 + 𝑟).
• Slope of IC = 𝑀𝑅𝑆"," ! .
∴ Optimal consumption point: 𝑴𝑹𝑺𝒄,𝒄! = 𝟏 + 𝒓 (Equation 9-8)
,LENDER: BORROWER:
• The endowment point is E. • The endowment point is E.
• The consumer choses consumption bundle at point • The consumer choses consumption bundle at point
A, where (𝑐, 𝑐 ! ) = (𝑐 ∗ , 𝑐 !∗ ). A, where (𝑐, 𝑐 ! ) = (𝑐 ∗ , 𝑐 !∗ ).
• Savings = BD à 𝑠 = 𝑦 − 𝑡 − 𝑐 ∗ . • Borrows in period 1 = DB à −𝑠 = 𝑐 ∗ − 𝑦 + 𝑡.
Effect of an increase in Current-Period Income:
Assume, ceteris paribus, current-period income increases from 𝑦' to 𝑦0 .
• Initial endowment point is at 𝐸' . Consumer initially chooses consumption bundle A.
&! &! &! &!
• Lifetime wealth increases from 𝑤𝑒' = 𝑦' + '%( − 𝑡 − '%( to 𝑤𝑒0 = 𝑦0 + '%( − 𝑡 − '%( ! .
• ∆𝑤𝑒 = 𝑤𝑒0 − 𝑤𝑒' = 𝑦0 − 𝑦' .
• Budget constraint shifts right by the amount 𝑦0 − 𝑦' (distance 𝐸' 𝐸0 ).
• Slope of the budget constrain remains unchanged bc the RER is the same.
• New consumption bundle is represented by point B.
- Current consumption increases from 𝑐' to 𝑐.
- Future consumption increases from 𝑐'! to 𝑐0! .
• Increase in current income = AD. Increase in current consumption = AF. AF < AD, thus, the consumer smooths
consumption across both periods instead of consuming it all in the current period.
• Change in savings is given by: ∆𝑠 = ∆𝑦 − ∆𝑡 − ∆𝑐. Because ∆𝑡 = 0, and ∆𝑦 > ∆𝑐 > 0, the increase in current
income causes an increase in consumption in both periods and an increase in savings.
,Effect of an increase in Future Income:
Assume, ceteris paribus, future-period income increases from 𝑦'! to 𝑦0! (e.g., expects higher paying job).
• Consumer initially chooses optimal consumption bundle A.
• Lifetime wealth increases from 𝑤𝑒' to 𝑤𝑒0 à Budget constraint shifts right by the amount 𝑦0! − 𝑦'! .
• Slope of the budget constrain remains unchanged bc the RER is the same.
• Initially, consumer chooses consumption bundle A, but after the rise in 𝑦 ! , he chooses bundle B.
- Current consumption increases from 𝑐' to 𝑐0 .
- Future consumption increases from 𝑐'! to 𝑐0! .
• Increase in future income = AD. Increase in future consumption = AF. AF < AD, thus, the consumer smooths
consumption across both periods instead of consuming it all in the future period.
• Change in savings is given by: ∆𝑠 = ∆𝑦 − ∆𝑡 − ∆𝑐. Bc ∆𝑡 = ∆𝑦 = 0, and ∆𝑐 > 0, this means ∆𝑠 < 0. Therefore,
the increase in future income causes an increase in consumption in both periods and a decrease in savings.
, Temporary vs. Permanent Changes in Income:
- Temporary changes in income à affects only 𝑦 à yield small changes in 𝑤𝑒 and 𝑐.
- Permanent changes in income à affects both 𝑦 and 𝑦 ! à yield big changes in 𝑤𝑒 and 𝑐.
• Consumer’s budget constraint is initially AB, and consumer chooses consump. bundle H on IC 𝐼' .
Temporary increase in income:
• Current income increases from 𝑦' to 𝑦0 à Budget constraint to shift right by the amount 𝑦0 − 𝑦' (distance HL).
• The slope of the budget constraint doesn’t change bc the RER remains unchanged.
• Consumer’s new budget constraint is DE, and consumer chooses consump. bundle J on IC 𝐼0 .
• The increase in current consumption, 𝑐0 − 𝑐' , is less than the increase in current income, 𝑦0 − 𝑦' , so savings
increase due to consumption-smoothing behaviour.
Permanent increase in income:
• The change in current income is equal to the change in future income: 𝑦0 − 𝑦' = 𝑦0! − 𝑦'! .
• Future income increases from 𝑦'! to 𝑦0! à Budget constraint shifts more right by 𝑦0 − 𝑦' = 𝑦0! − 𝑦'! (distance LM).
• The slope of the budget constraint doesn’t change bc the RER remains unchanged.
• Consumer’s new budget constraint is FG, and consumer chooses consump. bundle K on IC 𝐼1 .
o Therefore, if permanent income increases have larger effects on current consumption than temporarily ones.
– If there is a temporary income increase, 𝑠↑ so that consumption does not increase as much as income does.
– However, if there is a permanent increase in income, then saving does not increase, and current consumption
could increase as much as or more than does income.
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