Title: Intermediate Microeconomic Theory
1Intermediate Microeconomic Theory
2Intertemporal Choice
- So far, we have considered
- How an individual will allocate a given amount of
money over different consumption goods. - How an individual will allocate his time between
enjoying leisure and earning money in the labor
market to be used for consuming goods. - Another thing to consider is how an individual
will decide how much of his money should be
consumed now, and how much he should save for
consumption in the future (or how much to borrow
for consumption in the present).
3Intertemporal Choice
- To think about this, instead of considering how
an individual trades off one good for another and
vice versa, we can think about how an individual
trades off consumption (of all goods) in the
present for consumption (of all goods) in the
future. - i.e. two goods we will consider are
- c1 - dollars of consumption (composite good) in
the present period, and - c2 - dollars of consumption (composite good) in a
future period.
4Intertemporal Choice
- So an intertemporal consumption bundle is just a
pair c1, c2. - E.g. a bundle containing 50K worth of goods this
year, and 30K next year is denoted c1 50K, c2
30K. - Endowment now describes how many dollars of
consumption an individual would have in each
period, without saving or borrowing, denoted m1,
m2. - For example,
- An individual who earns 50K each year in the
labor market m1 50K, m2 50K. - An individual who earns nothing this year but
expects to inherit 100K next year m1 0, m2
100K.
5Intertemporal Budget Constraint
- Consider an individual has an intertemporal
endowment of m1, m2 and can borrow or lend at
an interest rate r. - What will be his intertemporal budget constraint?
- What is one bundle you know will be available for
consumption? - What else can he do?
6Intertemporal Budget Constraint
- What is slope?
- Hint How much more consumption will he have next
period if he saves x this period? - To put another way, how much does consuming an
extra x this period cost in terms of
consumption next period. - What will intercepts be?
c2 m2
?
x
x
?
m1 c1
7Intertemporal Budget Constraint
- Intercepts
- Vertical What if you saved all of your period 1
endowment, how much would you have for
consumption in period 2? - Horizontal How much could you borrow and
consume today, if you have to pay it back next
period with interest? - What happens to budget constraint when interest
rate r rises?
8Intertemporal Budget Constraint
- Example
- Suppose person is endowed with 20K/yr
- Interest rate r 0.10
- What will graph of BC look like?
- What if r falls to 0.05?
9Writing the Intertemporal Budget Constraint
- Given this framework, we want to write out the
intertemporal budget constraint in the typical
form -
- We know the interest rate r will determine
relative prices, but like with goods, we have to
determine our numeraire.
10Writing the Intertemporal Budget Constraint
- So intertemporal budget constraint can be written
in two equivalent ways - Future value future consumption is numeraire,
price of current consumption is relative to that.
- How much does another dollar of current
consumption cost in terms of foregone future
consumption? - BC (1r)c1 c2 (1r)m1 m2
- Present value present consumption is numeraire,
price of future consumption is relative to that - How much does another dollar of future
consumption cost in terms of foregone current
consumption? - BC c1 c2 (1/(1r)) m1 m2 (1/(1r))
11Intertemporal Preferences
- Do Indifference Curves make sense in this
context? - What does MRS refer to in this context?
- Do Indifference Curves with Diminishing MRS makes
sense in this context? - What Utility function might be appropriate to
model decisions in this context?
12Intertemporal Choice
- We can again think of analyzing optimal choice
graphically. - What does it mean when optimal choice is a bundle
to the left of endowment bundle? How about to the
right of the endowment bundle?
13Intertemporal Choice
- Similarly, we can solve for each individuals
demand functions for consumption now and
consumption in the future, given interest rate
(i.e. relative price) and endowment. - c1(r,m1,m2)
- c2(r,m1,m2)
- So if u(c1, c2) c1a c2b, an endowment of
(m1,m2) and an interest rate of r, what would be
the demand function for consumption in the
present? In the future?
14Intertemporal Choice
- As we showed graphically,
- If c1(r,m1,m2) gt m1
- the individual is a borrower
- If c1(r,m1,m2) lt m1
- the individual is a lender
- Equivalently,
- If c2(r,m1,m2) lt m2
- the individual is a borrower
- If c2(r,m1,m2) gt m2
- the individual is a lender
15Analog to Buying and Selling
- So instead of being endowed with coconut milk and
mangos (or time and non-labor income) we can
think of being endowed with money now and money
in the future. - Moreover, instead of being a buyer of coconut
milk by selling mangos, we can think of being a
buyer of consumption now (i.e. a borrower) by
selling future consumption.
16Comparative Statics in Intertemporal Choice
- Suppose the interest rate decreases.
- Will borrowers always remain borrowers?
- Will lenders always remain lenders?
17Comparative Statics in Intertemporal Choice
- How does this model inform us about government
interest rate policy? - Why might government lower interest rates?
- Raise interest rates?
18Present Value and Discounting
- The intertemporal budget constraint reveals that
timing of payments matter. - Suppose you are negotiating a sale and 3 buyers
offer you 3 different payments schemes - Scheme 1 - Pay you 200 one year from today.
- Scheme 2 - Pay you 100 one year from now and
100 today. - Scheme 3 - Pay you 200 today.
- Assuming buyers words are good, which payment
scheme should you take? Why? (Hint think
graphically)
19Present Value and Discounting
- This is idea of present value discounting.
- To compare different streams of payments, we have
to have some way of evaluating them in a
meaningful way. - So we consider their present value, or the total
amount of consumption each would buy today. - Also called discounting.
- In terms of previous example, with r 0.10 the
present value of each stream is - PV of Scheme 1 200/(10.10) 181.82
- PV of Scheme 2 100 100/(10.10) 190.91
- PV of Scheme 3 200
- While you certainly might not want to consume the
entire payment stream today, as we just saw, the
higher the present value the bigger the budget
set (assuming same interest rate applies to all
schemes!)
20Present Value and Discounting
- What about more than two periods?
- As we saw, if r is interest rate one period
ahead, PV of payment of x one period from now is
x/(1r). What is intuition? - If you were going to be paid m two years from
now, what is the most you could borrow now if you
had to pay it back with interest in two years? - So what is general form for present value of a
payment of x n periods from now? - What is form for a stream of payments of x/yr
for the next n years?
21Interest Rate and Uncertainty
- So far, we have assumed there is no uncertainty.
- Individuals know for sure what payments they will
receive in the future, both in terms of
endowments and loans given out. - What happens if there is uncertainty regarding
whether you will be paid back the money you lend
or will be able to pay back the money you borrow?