Class notes
ECO3020F: Macroeconomics
- Institution
- University Of Cape Town (UCT)
- Book
- Macroeconomics
Lecture and study notes for term 2 of ECO3020F, Macroeconomics
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MacroeconomicsWeek 8: 2-period model for consumption and savings
- Start by constructing a 2-period model of consumption-savings decisions without ignoring credit
markets
- The omission of credit markets was a big flaw in the macro models prior to the global
financial crisis
- Ricardian Equivalence theorem (NB), BUT valid under certain assumptions
- 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 important or the economic welfare of
an individual
- A tax cut may not matter OR it may involve a redistribution of wealth within the current
population or across generations
- 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
- Credit market imperfection (asymmetric information and limited commitment)
- Inter-temporal decisions involve economic trade-offs across periods of time
Two-period model
- A consumer’s consumption-savings decisions involves a trade-off between current and future
consumption
- By saving, you give up consumption in the present to consume more in the future
- By saving, you acquire assets to sell in the future will allow you to sell in the future
- By dissaving (through borrowing) the opposite will take place
- Borrow today to increase current consumption which results in less consumption in the future
- Real Interest rate is NB: which consumers and the government can borrow and lend, it
determines the relative price of consumption in the future, in terms of consumption in the present
Initial assumptions:
1. N consumers that live for 2 periods - the current and the future (Think of N as a large number)
2. They receive exogenous income (no need for work-leisure decisions)
- (‘) indicates a future period
- Lowercase letters denote variable at the individual level
- Uppercase letters denote aggregate variables
Page 1 of 149
,- The consumer’s current-period budget constraint
- C = consumption
- S = savings
- S > 0 - Consumer is a lender
- S < 0 - Consumer is a borrower
- Y = Real income
- T = Tax
- Y - T = disposable income
Assumptions:
- The financial asset is a bond:
- A bond is a financial instrument that pays/makes a fixed income stream of payment
- Appears in capital market or long term financing
- All bonds are default free
- No risk of defaulting
- BUT in real world: This is not true
- All bonds are traded directly in the credit market
- In reality: This is not true, especially with the focus on consumers
- Consumers do not go directly to the who provide the funds
- Both consumers and the government can issue bonds
- Mostly governments and firms will issue the bonds
- The lending rate = borrowing rate
- NOT THE CASE IN THE REAL WORLD
- Borrowing rate will tend to be higher than the lending rate to account for various risks
- In the real world, these assumptions do not hold.
Budget constraints:
- One bond issued in the current period promises to pay (1+r) units of future consumption
- r = real interest rate
- One unit of current C can be exchanged for 1+r units of future C
- Thus, the relative price of future C in terms of current C is
Page 2 of 149
,The consumer’s future-period budget constraint:
- Future consumption = Future real income - future tax + savings/dissavings
- S: final period where the consumer chooses to finish this period with no assets
- Chooses to consume ALL disposable income + interest rate and principal on savings
- Single lifetime budget constraint:
-Future-period constraint for S:
-S made subject of the formula
- Sub S into the current period budget constraint ( Done below )
Substitute S into the current period budget constraint:
-Manipulate the equation:
-Lifetime budget constraint
OR BETTER:
-Present value of lifetime consumption =
present value of lifetime income -
present value of lifetime taxes
- Lifetime budget constraint
- Present value of disposable income
(second part of the equation)
- We: Lifetime wealth which is the
present value of lifetime disposable
income
Can rewrite lifetime budget constraint as:
- Present value of lifetime consumption = present value of lifetime disposable income (lifetime
wealth)
Page 3 of 149
, Simplify further to:
(Use to graph consumers lifetime
budget constraint)
Graph:
- If C’ = 0, makes c subject of the formula. C
- Current consumption will = We (lifetime wealth)
- Point E: Endowment point
- States that all of the disposable income is being consumed in the present
- Savings = 0
- Allows you to distinguish between the consumers who are lenders and those who are borrowers
- E - B: Consumer is a lender
- E - A: Consumer is a borrower @ E, disposable income in the current income is (y-t) and
consume in the future period of (y’ - t’)
- We (1+r) = what we could be consumed in the future if the consumer saved all his current
disposable income and consumed his lifetime wealth in the future
- We = what could be consumed if the consumer borrowed the max amount possible against future
disposable income and consumed all the wealth in the current period
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