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MACROECONOMICS II
INVESTMENT DEMAND
(SPENDING)
1 Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe
INVESTMENT DEMAND (SPENDING)
In macroeconomics, Investment Demand is
important for two reasons:
1) Volatile and hence responsible for much fluctuations in GDP across the business cycle.
2) Because of its link with interest rates, it is a means by which fiscal and monetary policy affects the economy.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 2
INVESTMENT DEMAND (SPENDING)
• Investment spending links the present to the future, in that, it offers the possibility today of raising standards of living in the future.
• Consequently, the average level of Investment spending (by adding to the capital stock) plays a key role in long-run economic growth.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 3
INVESTMENT DEMAND (SPENDING)
Three types of Investment demand can be
identified:
1) Business fixed investment (the K in the production function).
2) Residential investment (new housing).
3) Inventory investment (goods businesses put in storage, including materials and supplies, work-in-progress and finished goods)
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 4
INVESTMENT DEMAND (SPENDING)
• Typically, business fixed investment is
the largest component of investment
spending in an economy.
• Whilst inventory investment is
considerably smaller than the other two.
• Nevertheless, all three are volatile.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 5
INVESTMENT DEMAND (SPENDING)
Before we begin, a note on terminology!
• Investment in macroeconomics is the
flow of spending that adds to the physical
stock of capital.
• Capital stock is the money value of all
buildings, machines, and inventories at a
point in time.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 6
INVESTMENT DEMAND (SPENDING)
Thus, it is worth noting that the theories
that we discuss for all the three types of
investment spending emphasise two
elements:
1. The demand for capital, and
2. Investment as a flow which adds to the level of the capital stock.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 7
INVESTMENT DEMAND (SPENDING)
Business Fixed Investment: The
Neoclassical Approach
• Here we go beyond the simple investment function, I = I (r), to examine the role of output, financial constraints and taxes in determining investment.
• We also look at how policy affects investment.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 8
INVESTMENT DEMAND (SPENDING)
• The neoclassical model examines the
benefits and costs to firms of owning
capital goods.
• Two simply our analysis we assume two
firms, Production Firms and Rental
Firms.
• In reality, most firms act as both.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 9
INVESTMENT DEMAND (SPENDING)
• Production firms produce goods and
services using capital they rent.
• Rental firms make all the investment in
the economy; they buy capital and rent it
out to production firms.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 10
INVESTMENT DEMAND (SPENDING)
• The typical production firm rents out capital
in order to produce goods and services, and
weighs the benefits and costs associated with
this decision.
• The firm rents capital at R and sells goods at
a market price P.
• The real cost of production is defined as R/P.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 11
INVESTMENT DEMAND (SPENDING)
• The real benefit of capital is the marginal
product of capital, MPK, which is the
increase in output produced by using 1
more unit of capital.
• We know from microeconomic theory,
that the MPK declines as more capital is
used in production.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 12
INVESTMENT DEMAND (SPENDING)
• As a profit maximizing firm, it aims to equate the benefits to costs, or equate the marginal product of capital to the rental price of capital (cost of capital).
• As long as the value of the marginal product of capital is above the real rental price of capital, it pays the firm to add to its capital stock.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 13
INVESTMENT DEMAND (SPENDING)
In the next slide we illustrate equilibrium in the market for rental capital.
• The marginal product of capital determines the demand curve; it slopes downwards because the MPK is low when the level of capital is high.
• At any point in time the supply of capital is fixed, so the supply is vertical
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 14
INVESTMENT DEMAND (SPENDING)
What influences the equilibrium real rental
price?
• We begin by considering a typical
production function:
• Y is output, A measures technology, K is
capital input, L is labour input.
• ; measures capital’s share of Y
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 16
1LAKY
10
INVESTMENT DEMAND (SPENDING)
• The MPK can defined as
• In equilibrium:
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 17
1
K
LAMPK
1
K
LA
PR
INVESTMENT DEMAND (SPENDING)
• The expression below identifies the
variables that determine the Real Rental
Price of Capital.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 18
1
K
LA
PR
INVESTMENT DEMAND (SPENDING)
1) The lower the stock of capital, the higher the real rental price of capital.
2) The greater the amount of labour employed, the higher the real rental price of capital.
3) The better the technology, the higher the rental price of capital.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 19
INVESTMENT DEMAND (SPENDING)
The Cost of Capital
• We now consider the case of Rental firms.
As with Production firms, we consider the
benefits and costs of owning capital.
• The benefits come from the revenues
earned by renting out capital, and thus
receives a rental price of R/P.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 20
INVESTMENT DEMAND (SPENDING)
• In respect of the costs, we like to think of
the firm as financing the purchase of
capital by borrowing.
• However, for each period of time that the
Rental firm rents outs a unit of capital, it
bears three costs.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 21
INVESTMENT DEMAND (SPENDING)
1. When the firm borrows to buy capital, it
must pay interest on the loan. If PK is the
purchase price, then iPK is the interest cost.
(note the interest cost will be the same even
if the firm doesn’t borrow).
2. Because the price of capital can change
while the firm rents out, there could be a
gain or loss ( ), here representing cost.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 22
KP
INVESTMENT DEMAND (SPENDING)
3. While the capital is rented out, it
suffers depreciation. If is the rate of
depreciation, then the cost of
depreciation is .
• The total cost of renting out can
therefore be given by (see next slide)
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 23
KP
INVESTMENT DEMAND (SPENDING)
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 24
)(
KKK
KKK
PPiPC
PPiPC
INVESTMENT DEMAND (SPENDING)
• The cost of capital depends on the price
of capital, the interest rate, the rate at
which capital prices are changing, and
the depreciation rate.
• To make our lives even easier, we
assume that the prices of capital goods
rises with the prices of other goods.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 25
INVESTMENT DEMAND (SPENDING)
• In that case, we can redefine the rate of
change in the price of capital as the
inflation rate, hence
• We also know that the real rate of
interest can be defined as
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 26
K
K
P
P
ir
INVESTMENT DEMAND (SPENDING)
In that case the cost of capital, C, can be
defined as:
This states that the cost of capital depends
on the price of capital, the real interest
rate and the rate of depreciation.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 27
)( rPC K
INVESTMENT DEMAND (SPENDING)
We can also express the cost of capital
relative to other goods in the economy:
Real Cost of Capital =
This states that the real cost of capital depends
on the relative price of a capital good, the real
Interest rate and the rate of depreciation.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 28
)(
rP
PK
INVESTMENT DEMAND (SPENDING)
The Determinants of Investment
Now we consider the situation in which the
rental firm decides whether to increase or
decrease the capital stock.
We know that for each unit of capital, the firm
earns real revenue and bears real cost. The real
profit per unit of capital is:
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 29
INVESTMENT DEMAND (SPENDING)
Profit Rate = Revenue – Cost
Profit Rate =
Because in equilibrium,
the profit rate can be stated as:
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 30
)(
r
P
P
P
R K
MPKPR
INVESTMENT DEMAND (SPENDING)
Profit Rate =
The Rental firm makes a profit if the
marginal product of capital is greater than
the cost of capital. It makes a loss if the
opposite holds.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 31
)(
r
P
PMPK K
INVESTMENT DEMAND (SPENDING)
• Thus we see that whether a Rental firm adds to the capital stock or allows it to depreciate depends on whether owning and renting out capital is profitable.
• The change in capital stock is defined as net investment.
• The same conclusion applies to a firm that both uses and owns capital.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 32
INVESTMENT DEMAND (SPENDING)
• In other words, whether a firm actually
buys its own capital or leases it, the
cost of capital (rental cost) is the right
measure of the opportunity cost.
• Remember, resources have alternative
uses!
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 33
INVESTMENT DEMAND (SPENDING)
• That is, for such a firm additions to the
capital stock depends on whether it is
profitable or not. In other words,
whether the marginal product of capital
exceeds the cost of capital.
• In the regard we can express the change
in the capital stock as:
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 34
INVESTMENT DEMAND (SPENDING)
Where (...) is the function showing how
net investment responds to the incentives to
invest.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 35
)]([
rP
PMPKIK K
n
nI
INVESTMENT DEMAND (SPENDING)
We can now write an expression for the
investment function:
Total spending on business fixed investment is
the sum of net investment and the replacement
for depreciated capital.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 36
KrP
PMPKII K
n
)]([
INVESTMENT DEMAND (SPENDING)
The model now shows how investment
Relates with the interest rate. A reduction in
real interest rate lowers the cost of capital.
This increases the profit from owning
capital and thus causes capital to increase.
By similar reasoning, a rise in the real interest rate
raises the cost of capital, reducing profitability and
hence causing a decline in capital.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 37
INVESTMENT DEMAND (SPENDING)
For the reasons stated earlier, the investment
function/schedule, relating investment to the
interest rate slopes downwards.
The model also shows that any event that raises
the MPK (improvement in technology increases
the profitability of investment and causes the
investment schedule to shift outward.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 38
INVESTMENT DEMAND (SPENDING)
Finally we consider what happens when the
capital stock is adjusting.
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.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 40
INVESTMENT DEMAND (SPENDING)
Eventually, as the capital stock adjusts, the
marginal product of capital approaches the cost
of capital. When the capital stock reaches a
steady-state level, we can write:
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 41
)(
rP
PMPK K
INVESTMENT DEMAND (SPENDING)
Thus, in the long run, the marginal product of
capital 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.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 42
INVESTMENT DEMAND (SPENDING)
Other Determinants of Investment
• An increase in the size of the economy
moves the entire MPK schedule to the right.
This rightward shift increases the demand
for capital at any given cost of capital (rental
cost).
• This may expressed in the form:
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 43
),(* YrcgK
INVESTMENT DEMAND (SPENDING)
Expected Output
But in the expression (reproduced below):
the level of output must be the level of output at
some future period, during which the capital will
be in production. For some investments the future time
at which output will produced is a matter of weeks or
months away, but for others this could be years away.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 44
),(* YrcgK
INVESTMENT DEMAND (SPENDING)
• From this the notion of permanent
income is relevant to investment as well.
• The firm’s demand for business fixed
capital, which depends on the normal or
permanent level of output, thus depends
on expectations of future output levels,
rather than the current level of output.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 45
INVESTMENT DEMAND (SPENDING)
Taxes
• In addition to interest rate and depreciation, the cost of capital is affected by taxes.
• The two main tax variables are the corporate tax and investment tax policy.
• A corporate tax is essentially a proportional tax on profit. An investment tax policy may allow firms to deduct from their taxes a fraction of their investment expenditures each year.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 46
INVESTMENT DEMAND (SPENDING)
Taxes
• Corporate taxes generally tend to affect the desired stock of capital negatively, such that an increase in the corporate tax rate will adversely impact on investment spending by the firm.
• On the other hand the investment tax policy reduces the cost of capital, hence this has a positive impact on investment spending by firms.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 47
INVESTMENT DEMAND (SPENDING)
The Effects of Fiscal and Monetary Policy
on the Desired Stock of Capital
• We have seen that the desired capital stock increases when the expected level of output rises and when the cost of capital falls.
• The cost of capital falls when the real interest rate and the rate of depreciation fall and when investment tax credits (investment tax policy) rises.
• An increases in the corporate tax reduces the desired capital stock.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 48
INVESTMENT DEMAND (SPENDING)
The Effects of Fiscal and Monetary Policy
on the Desired Stock of Capital
• These conclusions imply that monetary and fiscal policy affect the desired capital stock.
• Fiscal policy exerts an effect through both the corporate tax and investment tax credit.
• Fiscal policy through its effect on the IS curve, which in turn affect interest rates can affect overall demand for capital.
• Monetary policy affects capital demand by affecting the market interest rate.
Macroeconomics 2 Lecture Material Prepared by Dr. Emmanuel Codjoe 49