The Recession of 20082009 (let’s be optimistic)
The goal of these notes is to give an understanding of the current recession based on a slight
extension of the models we have already been working through.
The extension basically
involves adding enough additional apparatus to think about
speculative motives
for investment.
TwoSector Model
Thus far we have tried to get by with the simplifying assumption that there is only one sector of
production.
Assuming that all goods are made in the same sector using the same production
process allows all goods to have the same market price,
P
.
Now let’s suppose that there are two sectors of production—one where consumption goods are
produced and one where investment goods are produced.
Let
denote the price of capital or
investment goods.
Think of
P
as now some index of the prices of capital and consumption
goods, as we did when discussing how the GDP Deflator was measured.
We need a separate price of capital to talk about speculative investment because speculative
investment occurs when you buy capital goods today (e.g. stocks—financial claims on physical
capital used by corporations—or houses, nonresidential properties, etc.) with the idea that they
might be worth more in the future even if the productivity of the asset does not increase.
So, for
a given MPK, you might also receive a
capital gain
—a rise in the relative price of the capital
you own as time passes.
The Return to Capital and Speculative Investment
To purchase one unit of capital an investor must pay dollars today.
To compute the expected
return on this purchase we first consider the dollar value of the future output that one can
produce with the capital, , where the
e
superscript denotes the expected value of the overall price
index next period.
Next, we must consider the expected value of the capital itself next year.
Accounting for depreciation, this value is .
The annual rate of return is then the growth in future
dollars relative to the dollars invested minus one,
(1)
.
(Note that, as before, in equilibrium the expected return on physical capital must equal the rate of
return on bonds, the nominal interest rate (
i
).)
Let’s contrast this to our previous expression for the return to capital when there was only one
sector of production,
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.
To most clearly see the difference between (1) and (2), consider the case where there was no
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 Spring '08
 Blanchard
 Economics, Microeconomics, Inflation, Monetary Policy, Fed

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