A Real Intertemporal Model with Investment
For the economy as a whole, investment represents a trade-off between
present consumption and future consumption. Productive capacity that is used
for producing investment goods could otherwise be used for producing current
consumption goods. However, investment today increases the production of
future consumption goods (future productive capacity is increased).
Microeconomic investment behavior of a firm is studied in order to understand
the determinants of investment.
When a firm invests, it forgoes current profits in order to have a higher future
capital stock, which will enable the firm to earn higher future profits.
As a firm invests more:
● the lower its current capital stock
● the higher its future total factor productivity
● the higher the real interest rate
Real interest rate represents investment’s opportunity cost (a higher real
interest rate implies a large opportunity cost for investment, therefore
Also, investment decisions of firms depend on credit market risk as perceived
by lenders. If lenders in the credit market view lending to be risky, then it will
be more difficult for firms to borrow in order to finance investment.
ThePcurrent period budget constraint for the consumer:
c+s = w (h-l)+ -T……………………….(1)
The future period budget constraint for the consumer is:
c= w(h-l)+ -T+(1+r)s …………………(2)
From eqn(1), s = w(h-l)+ -T…………….(3)
Substitute (3) into (2)
c=w(h-l)+’ ’-T(1+r)s …………………….(4)
c+ ❑ = w(h-l)+ -T+ ❑ ……………(5)
Eqn (5) is the consumer’s lifetime budget constraint and it states that the
present value of future consumption is equal to the present value of lifetime
disposable income. The representative consumer’s problem is choos c,c,l and l’ ’
subject to the lifetime budget constraint.
Consumer’s optimal decisions:
● MRS =l,c(in general a consumer optimizes by setting the marginal rate
of substitution of one good for another equal to the relative price of the two goods, w is the relative price of leisure in terms of consumption
● MRS l ,cw ’
● MRS =c,cr (that is the marginal rate of substitution of current
consumption for future consumption equals the relative price of current
consumption in terms of future consumption)
The relative price of good x in terms of good y is the number of units of y that
trade for a unit of x.
Current Labor Supply
Interaction between consumers and the firm in the current labor market and
current consumption goods market (that is, determinants of a consumer’s
demand for current consumption goods and a consumer’s supply of labor).
A consumer’s current labor supply is deteSmined by:
● the current real wage (current N increases as the current real wage
● real interest rate
● lifetime wealth
MRS =l,ccaptures the idea that the substitution of current leisure for current
consumption is captured by the current real wage. Recall, that a change in the
real wage has opposing income and substitution effects on the quantity of
leisure. An increase in the real wage could increase or decrease the quantity of
leisure depending on the size of the income effect.
However, for this model, we assume that the substitution effect is larger than
the income effect such that an increase in the real wage causes leisure to
decrease and the number of hours worked increase.
The quantity of current labor supplied increases when the real interest rate
increases. A consumer can substitute intertemporally by substituting current
consumption for future consumption, but also by substituting current leisure
for future leisure. In substituting leisure , consumer responds to the current
price of leisure relative to the future price of leisure, ❑ .
In this case, w is the price of current leisure in terms of current consumption,
w is the price of future leisure in terms of future consumption, and 1+r is the price of current consumption in terms of future consumption. Therefore, an
increase in r given w, and w increases the relative price of current leisure in
terms of future leisure. If the substitution effect is greater than the income
effect, a consumer wants to consume less current leisure and more future
leisure . Therefore, when r increases, and the substitution effect dominates the
N decreases as lifetime wealth increases. An increase in current nonwage
disposable income results in an increase in the quantity of leisure and a
decrease in the quantity of labor supply. In the intertemporal case, an increase
in lifetime wealth increases current and future consumption. However, in this
case, when there is an increase in lifetime wealth there is an increase in
current leisure, and therefore a decrease in current labor supply.
A key wealth effect is the effect o