Summary Macroeconomics III

Macroeconomics III:

Week 8
Chapter 9
Introduction to the Two-Period Model:
- Shows us how consumers make intertemporal decisions (economic trade off)
regarding consumption & saving
A consumer’s consumption-savings decision 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 dissaving (through borrowing) the opposite.

Initial Assumptions
1. N consumers that live for 2 periods: the current & the future
2. They receive exogenous income (don’t need to consider work-leisure decisions)

Notation:
lowercase letters= variables at the individual level
uppercase letters= aggregate variables.
prime (‘)= future period.

Budget Constraints:



c= consumption
s= saving
y= real income
t= tax
(y-t)= disposable income

The consumer’s current-period budget constraint:
If s>0, consumer is a lender
If s<0, consumer is a borrower

Assumptions:
• the financial asset= bond
• all bonds are default free
(No risk of default – not like this in real world. E.g. Zambia is defaulting on their bonds
due to Covid)
• all bonds can be traded directly in the credit market
(In reality- it is not true- normally consumers who want to borrow must go through an
intermediary, like commercial bank)
• both consumers and the government can issue bonds

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, (In reality- consumers can’t issue bonds. It is mostly the government & some firms)
• the lending rate=borrowing rate.
(In reality- this does not happen. The borrowing rate tends to be higher than the lending
rate to account for various risks)

bond= financial instrument that makes or pays a fixed income stream of payment. Usually
capital market/ long-term financing

One bond issued in the current period promises to pay 1+r units of consumption in the
future period. So, one unit of current C can be exchanged for 1+r units of future C

r= real interest rate

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So, the relative price of future C in terms of current C is:
1+ r

The consumer’s future-period budget constraint=




There is only s because it is the final period. Consumer decides to finish the period with no
assets. Consumer decides to consume ALL disposable income + interest rate on the principal
amount on savings

Now, we take the current & future budget constraints and write them as a single lifetime
budget constraint=

Solve the future-period budget constraint for s:




Substitute s in the current period budget constraint:
(current period budget constraint= c+s=y-t)




Consumer’s Lifetime Budget Constraint
- Rearrange to obtain the lifetime budget constraint:


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, Or better:



Present value of life time consumption= present value of life time income – present value of
life time tax
Present value of life time disposable income= life time wealth=




we=

Simplified Lifetime Budget Constraint and slope intercept:




C’=
*This is the equation used to graph the consumers lifetime budget constraint

Consumers Lifetime Budget Constraint:
Consumers lifetime budget constraint= blue line
slope= -1+r  determined by the real interest rate (r)




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, we(1+r)= what could be consumed in the future if the consumer saved all their current
disposable income & consumed their lifetime wealth in the future. (Point B) B: If c=0,
c’=we(1+r)

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. (Point A) A: If
c’ =0, c= we (life time wealth) look at equation & you will see



E= endowment point (the consumption bundle if I consume all my Yd in the current & future
period) Allows us to distinguish between a lender & borrower At point E  tells us that you
only consume your disposable income (current & future). At this point s = 0

A consumer’s IC:
1. More is preferred (more consumption (current or future) makes the consumer better
off)
2. Diversity in the consumption bundle (C smoothing dislike for having large
differences in current and future period)
E.g. A consumer has large current consumption & small future consumption
B  consumer has large future consumption & small current consumption
(consumer must be given large Q of small future consumption to give up a small
amount of current consumption)
3. Current & future C are normal goods (if disposable income increases, consumption
(current and future) increases graphically increase in disposable income = shift to
the right of the consumer budget constraint, hence current & future consumption
increases)




Slope of IC=MRS


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