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ECON 352D1 Lecture Notes - Lecture 6: Intertemporal Consumption, Real Interest Rate, Intertemporal ChoiceExam

Course Code
ECON 352D1
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Econ 352 2018
6. A Real Intertemporal Model with Investment (Ch. 9)
This chapter combines the microeconomic behavior we have studied in the
previous two chapters to build a model that can serve as a basis for analyzing how
macroeconomic shocks affect the economy and that can be used for evaluating the role of
macroeconomic policy.
In previous chapters we have examined the consumer’s static work-leisure
choice and his intertemporal consumption-saving choice. On the firm’s side we have
studied the labor demand decision and production decision. Finally we also examined
the effects of choices by the government concerning the financing of its expenditures
and the timing of taxes. In this chapter we complete the model of the real side of the
economy. That is, the real intertemporal model we construct here shows how real
aggregate output, real consumption, real investment, employment, the real wage,
and the real interest rate are determined at the aggregate level. The intertemporal
aspect of the model refers to the fact that both consumers and firms make intertemporal
decisions reflecting the tradeoffs between the present and the future.
The defining characteristic of investment is that it consists of goods that are
produced currently for future use in the production of other goods and services. For
the economy as a whole investment represents a tradeoff between present and future
consumption. Productive capacity that is used for producing investment goods could
otherwise be used for producing current consumption goods. Nonetheless today’s
investment increases future productive capacity, which means that more consumption
goods can be produced in the future.
To understand the determinants of investment, we must study the
microeconomic investment behavior of a firm, which makes an intertemporal decision
regarding investment in the current period. When a firm invests, it forgoes current
profits so as to have a higher capital stock in the future, which allows it to earn higher
future profits. As we will see, a firm invests more the lower its current capital stock, the
higher its expected future total factor productivity and the lower the interest rate.
A key determinant of investment is the real interest rate, which represents the
opportunity cost of investment. A higher real interest rate implies that the opportunity
cost of investment is larger so investment falls. Movements in the real interest rate are an
important channel by which shocks to the economy affect investment (in the second term
of this course you will see how monetary policy affects the nominal (and real) interest
rate opening a channel that connects the real and nominal sides of the economy).
As in the previous chapters we will work with a model that has a representative
consumer, a representative firm, and a government, and, for simplicity we will
specify our model at the level of supply and demand curves. As before the firm and
the household will take prices as given, which in turn will be determine endogenously at
the aggregate level. In our complete model we will focus on the current period. In this
period the representative consumer supplies labor and demands consumption goods
(consumption), while the representative firm demands labor and supplies (and demands)
goods (investment goods). Finally the government demands goods in the current goods
market (government purchases).

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Econ 352 2018
6.1 The Representative Consumer
Our model has two periods; current-period and future-period. The behavior of the
representative consumer combines the work-leisure choice and the intertemporal
consumption decision, consumption-saving choice, studied so far. That is, the consumer
will make a work-leisure decision in each period (current and future) and he will make a
consumption-saving decision in the current period. As before let’s begin by defining
several aggregate variables,
, as current consumption
, as future consumption
, as private saving (in a two-period model it takes place in the first period)
, as current wage
, as future wage
, as current taxes (lump-sum)
, as future taxes (lump-sum)
, as the (net) real interest rate between the present and the future
, as current dividend income
, as future dividend income
, as current labor supply
, as future labor supply
As always households (the representative consumer) own the (representative)
firms and therefore each period they receive the firms’ profits.
Using the variables that we have just defined we can write the household budget
constraint for each of the two periods as,
Current period:
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wh l T C S

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Econ 352 2018
Future (and last) period:
Since the future period is the last period all wealth available to the consumer in
the future is consumed, i.e. there is no saving (or disaving) in the second period.
Combining the two budget constraints we reach the lifetime budget constraint
for the representative consumer,
where denotes lifetime wealth. This constraint equates the present value of lifetime
disposable income, made out of wages and profits net of taxes, to the present value of
lifetime consumption.
The representative consumer chooses current and future consumption and leisure
to maximize his preferences, subject to (1). Although we cannot depict this
four-dimensional choice in a graph we will use the optimality conditions derived in
previous chapters to characterize the optimal consumption and leisure choices in
both periods.
Notice that with four choice variables and (1) we need three conditions (since
having chosen 3 of the variables the constraint pins down the fourth). The optimal
choices are characterized by the following conditions,
1. The representative consumer is optimizing if he equates the marginal rate of
substitution between leisure and consumption (the rate at which he is willing to
increase leisure at the expense of consumption) and their relative price, the real wage
(the rate at which the market is willing exchange leisure for consumption),
2. A similar condition for the second period,
3. If the consumer behaves optimally, the rate at which he is willing to increase current
consumption at the expense of future consumption, the marginal rate of substitution
between current and future consumption, should be equated to the rate at which the
market exchanges current consumption for future consumption, one plus the interest
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