# Macro economics

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Macroeconomics ECO 403
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LESSON 41
INVESTMENT (Continued...)
The Cost of Capital
Total cost of capital = iPK - ΔPK + δPK
= PK (i - ΔPK/PK +δ)
The cost of capital depends upon the price of capital, the interest rate, rate of
change of capital prices and the depreciation rate.
·
Assuming price of capital goods rises with the prices of other goods, so
ΔPk/Pk = overall inflation rate, š
Since,
r = i - š,
Cost of Capital = Pk(r +δ)
·
To express the cost of capital relative to other goods in the economy.
·
The real cost of capital-- the cost of buying and renting out a unit of capital measured in
terms of the economy's output is:
Real Cost of Capital = (PK / P) (r +δ)
Where
r the real interest rate
PK / P the relative price of capital.
The Determinants of Investment
·
Now consider a rental firm's decision about whether to increase or decrease its capital
stock. For each unit of capital, the firm earns real revenue R/P and bears the real cost (PK
/P) (r+δ).
·
The real profit per unit of capital is
Profit rate = Revenue - Cost
= R/P - (PK /P) (r+δ).
·
Because real rental price equals the marginal product of capital, we can write the profit rate
as
Profit rate = MPK - (PK / P) (r +δ)
·
The change in the capital stock, called net investment depends on the difference between
the MPK and the cost of capital.
­ If the MPK exceeds the cost of capital, firms will add to their capital stock.
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­ If the MPK falls short of the cost of capital, they let their capital stock shrink.
­ Thus:
ΔK = In [MPK - (PK / P )(r + δ)]
­
Where In ( ) is the function showing how much net investment responds to the incentive
to invest.
The Investment Function
·  We can now derive the investment function in the neoclassical model of investment. Total
spending on business fixed investment is the sum of net investment and the replacement of
depreciated capital.
·  The investment function is:
I = In [MPK - (PK / P) (r +δ)] +δ K
·  This model shows why investment depends on the real interest rate.
·  A decrease in the real interest rate lowers the cost of capital. It therefore raises the amount of
profit from owning the capital and increases the incentive to accumulate more capital.
·  Similarly an increase in real interest rate raises cost of capital and leads the firms to reduce
their investment.
Real
interest
rate, r
Investment, I
I  as r  ,hence the downward slope of the investment function. Also, an outward shift in the
investment function may be a result of an increase in the marginal product of capital. e.g. a
technological Innovation
·  Finally, we consider what happens as this adjustment of the capital stock continues over
time.
If the marginal product begins above the cost of capital, the capital stock will rise and
·
the marginal product will fall.
If the marginal product of capital begins below the cost of capital, the capital stock will
·
fall and the marginal product will rise.
·  Eventually, as the capital stock adjusts, the MPK approaches the cost of capital.
·
When the capital stock reaches a steady state level, we can write:
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MPK = (PK / P) (r + δ)
·
Thus, in the long run, the MPK equals the real cost of capital. The speed of adjustment
toward the steady state depends on how quickly firms adjust their capital stock, which in
turn depends on how costly it is to build, deliver and install new capital.
Taxes and Investment
·
Tax laws influence the firms' incentives to accumulate the capital in many ways.
·
Sometimes policymakers change the tax laws in order to shift the investment function and
influence aggregate demand.
·
Here we discuss two of the most important provisions of corporate taxes:
­ Corporate Income Tax
­ Investment Tax Credit
·
Corporate income tax is a tax on corporate profits, and its effect on investment depends on
how the law defines profit for the purpose of taxation.
·
Suppose, at first, the law says:
Profit rate = R/P - (PK /P) (r+δ)
·
In this case, even though firms would be sharing a fraction of their income with the
government, it would still be rational for them to invest if
R/P > (PK /P) (r+δ)
·
But in reality the definition of law is quite different than this.
­  Treatment of depreciation
· Theoretically: current value of depreciation
· Tax laws: depreciation at historical cost
·
The Investment Tax Credit is a tax provision that encourages the accumulation of capital. It
reduces a firms taxes by a certain amount for each unit of money spent on capital goods.
· Since the firm recoups part of its expenditures on new capital in lower taxes, the credit
reduces the effective purchase price of a unit of capital Pk. Thus reducing the cost of capital
and raising investment.
Swedish Investment Funds System
·
Tax incentives for investment are one tool policy makers can use to control aggregate
demand.
·
For example, an increase in the investment tax credit reduces the cost of capital , shifts
investment function upward, and raises the aggregate demand.
·
From mid-50s to mid-70s the govt. of Sweden attempted to control aggregate demand by
encouraging or discouraging investment, through a system called Investment Fund
subsidized investment
·
In case of economic slowdown, the authorities offered a temporary investment subsidy, and
in case of economic recovery, revoked it.
·
Eventually subsidy became a permanent feature of Swedish tax policy.
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