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Notes on Investment
These notes are meant for you to better understand the relationship between interest rates
(r) and investment decisions (I).
A few things before we begin
:
1)
Remember, investment in this class refers to the purchasing of plant, tools,
machines,
and equipment by firms.
These resources are used as an input into production.
*
I
is a flow variable (measured over time).
*
K
is a stock variable (measured at a point in time).
K
is the capital stock in our
production function.
Formally,
K
is the sum of all past investment decisions (less any depreciation).
2)
The capital stock next period is a function of how much we invest this period.
If
we invest more today, the capital stock tomorrow will be higher.
As an identity (we will see this formula again in the Solow model, please try to
understand it well):
K(t+1) =
(1-
δ
) K (t) + I(t),
where
K(t+1)
is the capital stock next period (in period t + 1),
K(t)
is the capital stock
today (in period t), and
δ
is the depreciation rate on existing capital and
I(t)
is investment
today (in period t).
The equation above say that investing today raises the capital stock tomorrow.
In other
words, if you plan to buy a new machine today, it will be productive for you tomorrow
(the delay is due to the fact that it takes time to build a new plant or install a new machine
or train your workers to use the machine, etc.).
How much capital should a firm have?
In this class, we assume firms optimize.
They are going to set the benefit of purchasing
capital to the cost of purchasing capital.
What is the benefit of purchasing capital?
The extra benefit associated with one more unit of capital is the MPK.
Recall that in last
handout one example of MPK was:
MPK = 0.3 A (L/K)
0.7

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