If consumption in time period 't' is expressed as a function of Income in time period 't-1, it refers to deductive analysis inductive analysis static analysis dynamic analysis
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Answer:
If consumption in time period 't' is expressed as a function of Income in time period 't-1, it refers to deductive analysis inductive analysis static analysis dynamic analysis
Answer:
f fruit available to it each period; this is its income. Ct and Ct+1 is how much fruit it actually
eats each period. If it chooses to not consume some of its fruit in period t, so that St > 0, it can
enter into a financial contract in which it gives up its fruit today in return for (1 + rt)St units of
fruit tomorrow. In contrast, if it wants to consume more fruit today than it has, it can borrow
some extra fruit, with St < 0, and will have to pay back (1 + rt)St units of fruit to the lender in
period t + 1. The fruit is not storable on its own – if the household wants to save some of its fruit
to eat tomorrow, it has to “put it in the bank” and earn rt
. Finally, the household is a price-taker:
it takes rt as given, and does not behave in any strategic way to try to influence rt
. Thus, from
the household’s perspective rt
is exogenous, though from an economy-wide perspective (as we will
see), it is endogenous.
The household thus faces two budget constraints: one in period t, and one in period t+ 1, which
I assume hold with equality:
Ct + St = Yt
Ct+1 = Yt+1 + (1 + rt)St
These two budget constraints can be combined into one: you can solve for St from either the first
or the second period constraint, and then plug into the other one. Doing so, I obtain what is called
the “intertemporal budget constraint”:
Ct +
Ct+1
1 + rt
= Yt +
Yt+1
1 + rt
In words, the intertemporal budget constraint (“intertemporal” = “across time”) says that the
present discounted value of consumption expenditures must equal the present discounted value of
income. Ct+1
1+rt
is the (real) present value of Ct+1. Why is that? The present value is the equivalent
amount of consumption I would need today to achieve a given level of consumption in the future.
Since saving pays a return of 1 + rt
, the present value of future consumption would have to satisfy:
(1 + rt)P Vt = Ct+1 ⇒ P Vt =
Ct+1
1+rt
.
Households get utility from consumption. Loosely speaking, you can think about utility as
happiness or overall satisfaction. We assume that overall lifetime utility, U, is equal to a weighted
sum of utility from consumption in the present and in the future periods:
U = u(Ct) + βu(Ct+1), 0 ≤ β < 1
β is what we call the discount factor, and it is constrained to lie within 0 and 1. It is a measure of
how the household values current utility relative to future utility. We assume that β must be less
than 1, so that the household puts less weight on future utility than the present. This does not
seem to be a particularly controversial assumption when looking at how people actually behave in
the real world. The bigger is β, the more patient the household is, in the sense that it places a
large value on future utility relative to current.
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