3 Types of Investment Spending

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3 Types of Investment Spending

• Business fixed investment includes the equipment
  and structures that businesses buy to use in
  production.
• Residential investment includes the new housing
  that people buy to live in and that landlords buy
  to rent out.
• Inventory investment includes those goods that
  businesses put aside in storage, including
  materials and supplies, work in progress, and
  finished goods.

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Business Fixed Investment
The standard model of business fixed investment
is called the neoclassical model of investment.
It examines the benefits and costs of owning
capital goods. Here are three variables that
shift investment 1) the marginal product of
capital 2) the interest rate 3) tax rules
To develop the model, imagine that there are two
kinds of firms production firms that produce
goods and services using the capital that they
rent and rental firms that make all the
investments in the economy.
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The Rental Price of Capital
To see what variables influence the equilibrium
rental price, lets consider the Cobb-Douglas
production function as a good approximation of
how the actual economy turns capital and labor
into goods and services. The Cobb-Douglas
production function is Y AKaL1-a , where Y is
output, K capital, L labor, and a a parameter
measuring the level of technology, and a a
parameter between 0 and 1 that measures
capitals share of output. The real rental price
of capital adjusts to equilibrate the demand for
capital and the fixed supply.
Capital supply
Real rental price, R/P
Capital demand (MPK)
K Capital stock, K
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The Cost of Capital
Lets consider the benefit and cost of owning
capital. For each period of time that a firm
rents out a unit of capital, the rental firm
bears three costs 1) Interest on their loans,
which equals the purchase price of a unit
of capital PK times the interest rate, i, so i
PK. 2) The cost of the loss or gain on the price
of capital denoted as -DPK . 3) Depreciation d
defined as the fraction of value lost per period
because of the wear and tear, so d PK
. Therefore the total cost of capital i PK -
DPK dPK or PK (i - D PK/ PK
d) Finally, we want 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 economys output is The Real Cost of
Capital (PK / P )(r d), where r is the real
interest rate and PK / P equals the relative
price of capital. To derive this equation, we
assume that the rate of increase of the price of
goods in general is equal to the rate of
inflation.
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The Determinants of Investment
Now consider a rental firms 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 d). The real profit per unit of capital
is Profit rate Revenue - Cost
R/P - (PK / P )(r d). Because
the real rental price equals the marginal product
of capital, we can write the profit rate as
Profit rate MPK - (PK / P )(r d). 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. If the MPK falls short of
the cost of capital, they let their capital stock
shrink, thus DK In MPK - (PK / P )(r
d), where In ( ) is the function showing how
much net investment responds to the incentive to
invest.
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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 d) dK.
This model shows why investment depends on the
real interest rate. A decrease in the real
interest rate lowers the cost of capital.
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Notice that business fixed investment increases
when the interest rate falls-- 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.
Real interest rate, r
Investment, I
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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 MPK
(PK / P )(r d). 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.
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The Stock Market and Tobin's q
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Summary of Business Fixed Investment
1) Higher interest rates increase the cost of
capital and reduce business fixed investment. 2)
Improvements in technology and tax policies such
as the corporate income tax and investment tax
credit shift the business fixed investment
function. 3) During booms higher employment
increases the MPK and therefore, increases
business fixed investment.
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Residential Investment
We will now consider the determinants of
residential investment by looking at a simple
model of the housing market. Residential
investment includes the purchase of new housing
both by people who plan to live in it themselves
and by landlords who plan to rent it to others.
There are two parts to the model
1)
the market for the existing stock of houses
determines the equilibrium housing price 2) the
housing price determines the flow of residential
investment.
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The Stock Equilibrium and the Flow Supply
The relative price of housing adjusts to
equilibrate supply and demand for the existing
stock of housing capital. The relative price
then determines residential investment, the flow
of new housing that construction firms build.
The Market for Housing
The Supply of New Housing
PH/P
Relative Price of housing PH/P
Demand
Stock of housing capital, KH
Flow of residential investment, IH
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Changes in Housing Demand
When the demand for housing shifts, the
equilibrium price of housing changes, and this
change in turn affects residential investment.
An increase in housing demand, perhaps due to a
fall in the interest rate, raises housing prices
and residential investment.
The Market for Housing
The Supply of New Housing
PH/P
Relative Price of housing PH/P
Demand'
Demand
Stock of housing capital, KH
Flow of residential investment, IH
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Summary of Residential Investment
1) An increase in the interest rate increases the
cost of borrowing for home buyers and reduces
residential housing investment. 2) An increase in
population and tax policies shift the
residential housing investment function. 3) In a
boom, higher income raises the demand for housing
and increases residential investment.
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Inventory Investment
Inventory investment, the goods that businesses
put aside in storage, is at the same time
negligible and of great significance. It is one
of the smallest components of spending-- but its
volatility makes it critical in the study of
economic fluctuations.
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Reasons for Holding Inventories
When sales are high, the firm produces less that
it sells and it takes the goods out of inventory.
This is called production smoothing. Holding
inventory may allow firms to operate more
efficiently. Thus, we can view inventories as a
factor of production. Also, firms dont want to
run out of goods when sales are unexpectedly
high. This is called stock-out avoidance. Lastly,
if a product is only partially completed, the
components are still counted in inventory, and
are called, work in process.
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The Accelerator Model of Inventories
The accelerator model assumes that firms hold a
stock of inventories that is proportional to the
firms level of output. Thus, if N is the
economys stock of inventories and Y is output,
then N b Y where b is a parameter
reflecting how much inventory firms wish to hold
as a proportion of output. Inventory investment I
is the change in the stock of inventories DN.
Therefore, I DN b DY.
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The Accelerator Model of Inventories

• The accelerator model predicts that inventory
  investment is proportional to the change in
  output.
• When output rises, firms want to hold a larger
  stock of inventory, so inventory investment is
  high.
• When output falls, firms want to hold a smaller
  stock of inventory, so they allow their inventory
  to run down, and inventory investment is
  negative.
• The model says that inventory investment depends
  on whether the economy is speeding up or slowing
  down.

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Inventories and the Real Interest Rate
Like other components of investment, inventory
investment depends on the real interest rate.
When a firm holds a good in inventory and sells
it tomorrow rather than selling it today, it
gives up the interest it could have earned
between today and tomorrow. Thus, the real
interest rate measures the opportunity cost of
holding inventories. When the interest rate
rises, holding inventories becomes more costly,
so rational firms try to reduce their stock.
Therefore, an increase in the real interest rate
depresses inventory investment.
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Summary of Inventory Investment
1) Higher interest rates increase the cost of
holding inventories and decrease inventory
investment. 2) According to the accelerator
model, the change in output shifts the inventory
investment function. 3) Higher output during a
boom raises the stock of inventories firms wish
to hold, increasing inventory investment.
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Key Concepts of Ch. 17
Stock market Tobins q Financing
constraints Production smoothing Inventories as a
factor of production Stock-out avoidance Work
in process Accelerator model
Business fixed investment Residual
investment Inventory investment Neoclassical
model of investment Depreciation Real cost of
capital Net investment Corporate income
tax Investment tax credit Stock