Intermediate Microeconomic Theory

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Intermediate Microeconomic Theory

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Intermediate Microeconomic Theory Intertemporal Choice Intertemporal Choice So far, we have considered: How an individual will allocate a given amount of money over ... – PowerPoint PPT presentation

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Title: Intermediate Microeconomic Theory


1
Intermediate Microeconomic Theory
  • Intertemporal Choice

2
Intertemporal 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).

3
Intertemporal 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.

4
Intertemporal 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.

5
Intertemporal 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?

6
Intertemporal 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
7
Intertemporal 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?

8
Intertemporal 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?

9
Writing 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.

10
Writing 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))

11
Intertemporal 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?

12
Intertemporal 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?

13
Intertemporal 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?

14
Intertemporal 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

15
Analog 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.

16
Comparative Statics in Intertemporal Choice
  • Suppose the interest rate decreases.
  • Will borrowers always remain borrowers?
  • Will lenders always remain lenders?

17
Comparative Statics in Intertemporal Choice
  • How does this model inform us about government
    interest rate policy?
  • Why might government lower interest rates?
  • Raise interest rates?

18
Present 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)

19
Present 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!)

20
Present 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?

21
Interest 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?
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