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CHAPTER 16
INVESTMENT SPENDING
Chapter Outline
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The Stock Demand for Capital and the Flow of Investment
The Desired Capital Stock: an Overview
Expected Output
Taxes and the Rental Cost of Capital
The Effects of Fiscal and Monetary Policy on the Desired Capital Stock
The Stock Market and the Cost of Capital
The q Theory of Investment
From Desired Capital Stock to Investment
Capital Stock Adjustment
Investment Subsectors – Business Fixed, Residential and Inventory
Business Fixed Investment
The Timing of Investment
Irreversibility and the Timing of Investment Decisions
Residential Investment
Monetary Policy and Residential Construction
Inventory Investment
The Accelerator Model
Anticipated versus Unanticipated Inventory Investment
Inventories in the Business Cycle
Just in Time Inventory Management
Investment and Aggregate Supply
Investment Around the World
Working With Data
Changes from the Previous Edition
There are no major changes to Chapter 16 in this edition.
Learning Objectives
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Students should know the three categories of investment (business fixed, residential, and inventory
investment) and how each category is affected by changing economic conditions.
Students should understand the role of housing and inventory changes as economic indicators.
Students should know that the desired capital stock increases with increases in output and decreases
with increases in the rental cost of capital.
Students should know that the rental cost of capital increases with increases in the nominal interest
rates, the rate of depreciation, and most likely with the corporate income tax, but decreases with
increases in inflationary expectations and investment tax credits.
Students should understand why the effects of temporary investment tax credits on investment are
different from the effects of temporary tax changes on consumption.
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Students should be able to distinguish between the real and nominal interest rates, and know that the
real rate of interest is most important for investment decisions (except for housing investment, which
is affected by both the real and nominal rates).
Students should be familiar with the discounted cash flow analysis and know that this analysis is
consistent with the neoclassical theory of investment.
Students should know that the accelerator model implies that the level of investment depends on the
change in output, and that the expected level of output is more important than the actual level of
output.
Students should know that business fixed investment generally responds with long lags to changes in
the level of output.
Students should know how monetary and fiscal policy affect investment.
Students should understand the role of investment in economic cycles and in future economic growth.
Accomplishing the Objectives
Although gross investment spending averages only about 15% of total Canadian GDP (it has been
rising lately), it deserves a great deal of attention, since it is the most volatile of the major components of
GDP and greatly influences economic cycles. Furthermore, since it adds to a nation's productive capacity,
it affects aggregate supply and contributes to long-term growth.
A good understanding of how investment responds to fiscal and monetary policy measures is very
important. As not all investment is affected by policy measures in exactly the same way, we distinguish
between three categories of investment (in order of magnitude): business fixed investment, residential
investment and inventory investment. The distinction between gross and net investment is essential, since
only net investment adds to the existing capital stock. The difference, namely depreciation, is determined
not only by wear and tear but also by usefulness. For example, while outdated computers may still work,
they may nonetheless be replaced by newer, more efficient ones to increase office productivity. It should
also be noted that we should concern ourselves with more than just private net investment, which is
defined as the addition to the existing capital stock in the private sector. Government spending on the
infrastructure (highways, schools, etc.) and investment in human capital are also very important for future
productivity.
The theory of investment is the theory of the demand for real capital. Firms use capital, along
with labour, in the production process. The level of business fixed investment is determined by the speed
with which firms adjust their actual capital stock to a desired level and by the rental cost of capital. Since
investment is undertaken for future production, expected output determines the level of the desired capital
stock. Therefore the notion of permanent income (or output) introduced in Chapter 15 is relevant not only
to consumption but also to investment. Firms plan their capital stock in relation to expected permanent
output, and current output affects the demand for capital only insofar as it affects firms' expectations
about the future. The desired capital stock generally becomes larger as the level of (expected) output
increases and smaller as the rental cost of capital increases. In other words, firms generally want to have
more capital if they expect to produce more or if the use of capital has become cheaper. Additions to the
capital stock (net investment), as a percentage to the existing capital stock, tend to be fairly small;
therefore even a small increase in the desired capital stock has a significant impact on the level of
investment spending.
As we can see in Figure 15-3, an increase in expected output will increase the desired capital
stock and shift the marginal product schedule (the demand for capital) to the right. The demand for capital
is downward sloping since the law of diminishing marginal product applies: if progressively more capital
is employed while labour is kept constant, the increase in output arising from employing an additional
unit of capital will decline.
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The rental cost of capital (rc) should not just be seen as the market interest rate (i); we also have to
consider the expected rate of inflation (e) and the rate of depreciation (d). Therefore we get
rc = i - e + d.
But the rental cost may also be affected by the corporate income tax and investment tax credits.
Due to complexities in tax laws, the effect of a change in the corporate income tax is fairly ambiguous
and largely depends on whether an investment is debt- or equity-financed. We assume here that the rental
cost of capital tends to rise with an increase in the corporate income tax rate (at least in the short run). An
investment tax credit allows a firm to deduct a certain fraction of its investment spending from its taxes,
reducing the rental cost of capital. An investment credit can therefore be seen as a government subsidy for
investment.
Monetary policy affects investment spending via the desired capital stock through its effect on
market interest rates. However, there can be long lags. For one, business fixed investment largely depends
on long-term interest rates, which tend to change fairly slowly. In addition, planning investment projects
and ordering and installing new machines for production is often a lengthy process.
As we have seen, fiscal policy can also work through changes in investment tax credits or the
corporate income tax rate. The timing of an investment tax credit is very important, since temporary
investment tax credits can be very effective in stimulating investment. When a temporary investment tax
credit is given, firms speed up planned investment to take advantage of it. Yet, offering investment tax
credits cannot be seen as a simple policy tool, since uncertainty about the timing and duration of the
credits can actually increase the instability of investment spending.
When making investment decisions, firms often use the discounted cash flow analysis. According
to this analysis, an investment project is profitable and should be undertaken if the net present discounted
value (which is the flow of expected net returns from an investment project for each year discounted at
the appropriate cost of capital) is positive. Since an investment decision has to be made today, any
revenues to be received (or costs to be paid) in the future need to be discounted to calculate their present
value. A decrease in the interest rate (and therefore in the rental cost of capital) will increase the net
present value of an investment project and more projects will be undertaken.
Residential investment (housing) is distinguished as an asset by its long life. For this reason the
existing housing stock is fairly large and investment in new housing adds only minimally to it. Thus we
can assume that, at any given time, the supply curve of housing stock is vertical. A vertical supply curve
implies that gross investment is equal to depreciation and net investment is zero. Demand for housing is
negatively affected by higher mortgage rates and the yield produced by alternative investments and it is
positively affected by wealth. The supply of and demand for the existing housing stock determine the
asset price of housing. New housing cannot be built immediately, but lags are generally short, since it
takes less than a year to build a house. However, since builders incur expenses before they can sell the
house, mortgage interest rates and the availability of funds greatly affect the housing sector.
Since housing is very interest sensitive, it is often seen as an important leading economic
indicator that responds fairly quickly to changes in monetary policy. Factors other than interest rates (such
as the effects of weather) must, of course, also be taken into account when interpreting data on housing
starts. It is important to note, however, that the housing market is affected not only by the real interest rate
but also by the nominal interest rate, since the availability of financing is an important factor. For
example, an increase in the nominal interest rate of 1% can easily increase a homebuyer's mortgage
payments by several hundred dollars a month and render him or her ineligible for a loan.
Inventory investment tends to fluctuate much more than the previous two categories and is
different from the others in that it may be undesired. The accumulation of inventories arises from the
difference between output and final sales and occurs because firms cannot always match the level of
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production to the level of sales. Furthermore, some inventories may be an unavoidable part of the
production process. Firms have a desired ratio of inventories to final sales, and this ratio depends on
expected sales, the market interest rate, the cost of ordering and the speed with which new orders arrive.
It is important to distinguish between desired and undesired inventory changes, since they have
different implications for aggregate demand. An increase in desired inventories is initiated when firms
expect their sales to increase in the future. This can be an indication that the economy will continue to
grow. An increase in undesired inventories, however, is the result of decreasing consumer demand and
can be an indication that the economy is entering a downturn.
The role that inventories play in business cycles results from both desired and undesired
inventory accumulation. In a recession, firms may deliberately cut back production to bring inventories
back in line with sales. Such behaviour will accentuate a recession. On the other hand, in an upswing
firms tend to increase production to increase their inventories in preparation for higher expected sales.
Such behaviour contributes to economic growth. Business fluctuations could be reduced substantially if
inventories could be kept more closely in line with sales. Much of inventory investment can be explained
by the accelerator model.
It is also important to note that there are significant differences in the fraction of GDP that is
devoted to investment across countries. These investment ratios are determined by the demand for capital
and the supply of saving. The fairly low rate of investment in Canada is a source of concern to many,
since high rates of investment tend to be associated with a high growth performance.
Suggestions and Pitfalls
Instructors, who mentioned the role of housing and inventory changes as economic indicators in
Chapter 1, have already laid the groundwork for the more detailed presentation here. Since many students
have become familiar with the decision-making process that goes into the purchase of a house through
their own family experience, they may be particularly interested in discussing this topic first. But many
students are also interested in how actual investment decisions are made by businesses and are eager to
discuss the virtues of the discounted cash flow analysis and the role that internal financing plays in a
firm's investment decision.
A discussion of the reasons why a booming stock market may be good for investment also usually
generates considerable interest. It should be pointed out that the state of a firm's balance sheet rather than
the cost of capital is most often the determining factor in a firm's investment decision. This is particularly
important when lending institutions practice credit rationing. Credit rationing tends to affect smaller and
medium-sized firms much more than larger firms since larger firms have greater access to financial
resources through internal funds, the stock market, or better connections to banks. It should also be noted
that even if internal funds are available, current market interest rates are always important in determining
the profitability of an investment project, since they represent an opportunity cost.
The detailed presentation of the net present discounted value is deferred to Chapter 18. Some
instructors may, however, want to provide some numerical examples and intuitive reasoning to show how
changes in the interest rate may affect a firm's decision to invest. A good way to introduce students to the
concept of the present value is to ask them to evaluate the following investment project:
costs
revenues
Year 0
$510
$0
Year 1
$220
$440
Year 2
$242
$363
Year 3
$266
$532
If the market interest is not given up front, students have a tendency to just add up the numbers
and compare total revenues with total costs. If they do this they will conclude that the investment is
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profitable since net revenues seem to be 1,335 – 1,238 = + 97. However, instructors should point out that,
since there are costs up front, the firm might have to borrow funds to finance the investment project. This
can lead into a discussion of the net present discounted value. The net present value should then be
calculated for different interest rates, i1 = 10% and i2 = 5%:
NPV = -510 + (440 – 220)/(1 + 0.1)1 + (363 – 242) /(1 + 0.1) 2 + (532 – 266) /(1 + 0.1) 3
= -10 ==> unprofitable for i1 = 10%.
NPV = -510 + (440 – 220)/(1 + 0.05)1 + (363 – 242) /(1 + 0.05) 2 + (532 – 266) /(1 + 0.05) 3
= +40 ==> profitable for i2 = 5%.
This way it can be established that, as the interest rate decreases, more investment projects will be
undertaken.
Before the more technical aspects of this chapter are discussed, it is also helpful to once again
make the distinction between gross investment and net investment. Furthermore, instructors should point
out that not only the amount of physical capital but also government spending on infrastructure and
investment in human capital are important forms of investment that help to increase productivity.
The theory of business fixed investment, particularly the derivation of the equation for the desired
capital stock from a Cobb-Douglas production function, is not always easy for students to understand.
However, since they should already be familiar with this production function from Chapter 3, the material
can be reenforced here. From the production function:
Y = AKN1-,
the marginal product of capital (MPK) can be derived as
MPK = Y/K = AK-1N1- = Y/K.
Since cost minimizing firms employ capital up to the point where the marginal product of capital
is equal to the marginal cost of capital (rc), it follows that
MPK = rc ==> Y/K = rc ==> K* = Y/rc.
which shows the optimal capital stock (K *). Similarly, it can be shown that the optimal amount of labour
can be derived as
N* = (1 - )Y/w, where w is the wage rate.
Note that the equation for the desired levels of capital (or labour) is derived under the assumption
that labour (or capital) is held fixed. This is, of course, not realistic. If labour can be substituted for capital
and vice versa, we should expect that the desired stock of capital will increase as the cost of labour (the
wage rate) increases. At the same time, the desired stock of labour will increase as the rental cost of
capital increases. The desired level of both capital and labour will increase as expected output increases.
To familiarize students with the accelerator model, one can use the following three simple
equations:
(1) K*t = aYt
(2) It = (K*t - Kt)
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(3) Kt = K*t -1
Equation (1) states that the desired capital stock is proportional to output; Equation (2) states that
the level of investment depends on the difference between desired and actual capital stock; and Equation
(3) states that this year's actual capital stock is last year's desired capital stock.
The assumption that the capital/output ratio a in Equation (1) is fixed is quite unrealistic. For
example, the desired capital stock derived from the Cobb-Douglas production function is
K* = Y/rc
which would imply that
a = /rc.
In this case the capital/output ratio is influenced by the cost of capital. However, labour can
generally be substituted for capital, which suggests that the desired capital/output ratio can also be
affected by changes in the wage rate. Here, however, we want a very simple model that, if manipulated
correctly, can show us that the level of investment depends on the change in output. This can easily be
done with the three equations above since it follows that
It = (K*t - Kt) = (K*t - K*t-1 ) = (aYt - aYt-1 ) = a(Yt - Yt-1 ) = k(Y).
In Chapter 11 we encountered the expenditure multiplier, which shows that a change in
autonomous investment will induce a larger change in the level of output. If we combine this accelerator
model with the multiplier principle, we can easily explain how economic cycles occur. As long as the
economy grows at an increasing rate, the level of investment will rise, since the level of investment
depends on the change in output, that is
I = k(Y).
But this makes the change in investment positive, which stimulates output further through the multiplier
process, that is,
Y = (I).
This expansion will go on until the economy reaches its full potential and begins to grow more
slowly due to shortages. But as soon as output grows at a slower rate than before, the level of investment
will decrease. In other words, as Y becomes smaller (even though it is still positive), the level of I will
decrease, which will make the change in investment (I) negative. An economic downturn will ensue,
since a negative I implies a negative Y due to the multiplier principle Y = (I). The next upswing
will occur only if a large increase in autonomous investment exceeds the negative level of induced
investment. Then total investment will rise again and income will start another upswing.
Students with a weak math background are likely to have difficulties deriving this result, but its
implications for inventory cycles should make intuitive sense. As previously stated, firms like to have an
optimal level of inventory, based on expected output. As long as expected output (Y) is increasing, the
desired level of inventory (I) will increase and the change in desired inventory (I) will be positive. This
means that production is expanding and the economy is booming. But as the economic cycle nears its
peak, the demand for goods may drop, while firms continue to expect an increase in sales. Thus we will
have an undesired increase in inventories and firms will respond by cutting production. This will have a
negative impact on national output and the economy may enter a recession.
It is also worthwhile to discuss the concepts of crowding out and crowding in. Students have
learned in previous chapters that expansionary fiscal policy leads to an increase in interest rates which, in
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turn, leads to a decrease in investment spending. In other words, public spending crowds out private
investment. But they have also seen that an increase in government spending will lead to an increase in
income through the multiplier process. In this chapter we learn that if the growth in income in one period
is larger than the growth in income in the previous period, the level of investment spending will actually
increase. In other words, private investment is "crowded in." This provides a good opportunity to discuss
the circumstances in which expansionary fiscal policy may actually stimulate rather than discourage
investment spending.
This issue is very controversial and has stirred up many debates among economists and policy
makers. The positive relationship between the level of investment and the change in output and the
inverse relationship between the level of investment and the interest rate (which affects the rental cost of
capital) have been established. Thus the crowding-in and crowding-out effects always take place
simultaneously. Whether investment is positively or negatively affected depends on the situation at hand.
It is therefore a difficult task to empirically verify how much the overall level of investment is actually
affected by an increase in government spending. Generally, when the economy is in a recession there is
little upward pressure on interest rates, so we can expect an increase in investment as the economy is
stimulated. But if the economy is already in a boom, an increase in government spending will not greatly
stimulate output but will instead be reflected in higher interest rates, so investment should be affected
negatively.
Students often see the rental cost of capital simply as the market interest rate. But instructors
should point out that the rental cost of capital also depends on other variables, including the rate of
inflation, the rate of depreciation, the corporate income tax, and investment tax credits. The effects of
various policy measures can then be discussed in more detail. For example, students should be asked to
compare the effects of a permanent and a temporary investment tax credit on current aggregate demand
and the long-term capital stock.
When discussing fiscal policy, it is also important to point out that investment spending is
determined by expected permanent output, just as consumption is determined by permanent income.
However, temporary investment tax credits have a much greater effect on current investment spending
than temporary income tax changes have on current consumption. Investment tax credits are therefore
often thought of as an important (but fairly complex) stabilization tool.
To again stress the importance of investment, Table 16-3 should be discussed. Students should be
asked whether they are worried about the fairly low level of Canadian investment as a fraction of GDP.
What does this imply for the future and what can be done about it? Can the government stimulate
investment enough to sustain a high economic growth rate over a fairly long period? How should this be
done? The recent growth in the Canadian economy that was largely fueled by investment in computer
technology can serve as a good example. Such topics should create some interesting classroom
discussion.
Finally, it should be stressed again that investment decisions depend on several factors. These are:
sales expectations, the cost of capital (which in itself depends on nominal interest rates, expected
inflation, rate of depreciation, the corporate income tax, and investment tax credits), the cost of other
inputs (wages), the degree of capital utilization, credit availability, and the time it takes to plan, order, and
install new capital equipment.
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Solutions to the Problems in the Textbook
Discussion Questions:
1. Even if the economy has achieved the desired capital stock some (gross) investment still must take
place to keep the capital stock at this level. The level of investment has to be sufficient to cover
depreciation (due to wear and tear or because capital becomes obsolete).
2. High-tech capital (such as computers) becomes obsolete at a very fast rate and therefore needs to be
replaced much earlier if firms want to stay competitive. Therefore the rate of depreciation will
increase if more is invested in high-tech machines.
Human capital also depreciates since knowledge tends to become outdated (new theories are
advanced and new discoveries are made continuously). Thus knowledge needs to be updated. Who
for example, wants to be treated by a physician who hasn't kept up with new advances in medical
technology? Similarly, since one can also think of health as human capital, we can see that, as we
grow older, our stock of health tends to depreciate. But the more we invest in health, that is, the
healthier we live and the more preventive measures we take, the slower this stock of human capital
will depreciate.
3. The interest rate cannot simply be considered as the rental cost of capital but is also an opportunity
cost. Retained earnings can be used to invest in new machinery but also to make a loan to someone
else. In other words, at any time retained earnings can be "financially invested," that is, given to
someone in need of funds (the government, for example), in which case these funds would earn
interest. For example, if the yield on a government bond or a commercial paper is much higher than
the expected rate of return on an investment in real capital, a firm may not want to undertake this
investment and "invest" in a government bond.
4. The price of a share of stock in a company should, in an efficient stock market, be equal to the price
of a claim on the capital in the company. Tobin’s q is an estimate of the value the stock market places
on a firm’s assets relative to the cost of producing those assets. In other words, it can be thought of as
the ratio of the market value of a firm to the replacement cost of capital. The replacement cost of
capital is a measure for the marginal cost of capital. If q is greater than 1, then a firm should add
physical capital, since for each dollar’s worth of new machinery the firm can sell stock for q > 1
dollars. But this means that the marginal product of capital exceeds its marginal costs.
5. A sudden increase in the demand for a firm's product will increase expectations of future sales and
induce a firm to increase its desired capital stock. This will require an increase in net investment. The
speed with which the capital stock is increased to its new desired level depends on whether the firm
believes that the increase in sales is permanent or temporary and on the cost to the firm of adjusting
the capital stock to its new desired level quickly.
6. Large firms have easier access to credit than small firms, since large firms tend to have an established
and good credit rating. Therefore, small firms are often limited in their investment opportunities by
their retained earnings. But if we have many more small firms than large firms, we may observe
larger output fluctuations over the business cycle. This is due to the fact that small firms will invest
less in a recession than they otherwise might have because credit is not available to them and profits
are down. On the other hand, in a boom these small firms are likely to invest more than they would
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otherwise, since profits are high and they want to compensate for the lack of investment during the
past downturn.
7.a. When profits are high, more internal funds are available for firms. Firms generally will use these
funds for financing new capital investments, even at times when outside funding is not easily
obtainable. Higher profits may come from increased sales. This may make entrepreneurs more
optimistic about future sales and encourage them to increase investment spending. Higher profits also
mean higher dividends and thus higher stock values. But if stock values are high, firms are more
inclined to raise new funds for additional investment. It should be noted, however, that higher profits
and the availability of internal funds should not distract from the fact that the cost of capital still is an
important factor in investment decisions. Any interest that could be earned on such funds has to be
seen as an opportunity cost.
7.b. Credit rationing by banks occurs since banks realize that while a cautious entrepreneur may be
deterred from investing when interest rates are high, a more reckless entrepreneur may still invest in
spite of high rates. Entrepreneurs who are more reckless are also more likely to fail and default on
their loans. Therefore in times of tight funds, rationing credit may be a more effective way for banks
to ensure profits than increasing the interest rate on loans. Credit rationing may also occur for other
reasons.
8. The flexible accelerator model tries to explain the speed at which firms adjust their capital stock over
time. The larger the gap between the desired and actual capital stock is, the higher the level of the
firm’s investment spending on machinery. Much, but not all, inventory investment can be explained
with the help of this accelerator model. The level of inventory investment is based on changes in
output and therefore sales expectations.
9. Unanticipated inventory accumulation occurs when the demand for a product is lower than was
expected. Firms generally respond by decreasing their level of production and a recession may be
imminent. However, a planned inventory increase generally occurs when firms expect an economic
upturn and want to be ready for the anticipated increase in the demand for their product.
10. The level of net investment is the addition to the capital stock, that is, IN = K. A low level of net
investment implies slow growth in the capital stock and hence future productive capacity. A low rate
of capital accumulation generally implies lower future living standards.
11. In the long run (when the AS-curve is vertical), monetary policy will not affect the real interest rate.
However, it will affect inflation and therefore the nominal interest rate. The nominal interest rate (i n)
is determined by the real interest rate (ir) plus the inflation rate (), that is,
in = ir + 
But if the nominal interest rate increases, the nominal cost of borrowing funds for investments rises
and some borrowers may no longer qualify for loans because of perceived cash flow problems. Banks
may actually limit credit when nominal interest rates increase, because they feel that borrowers still
interested in loans may be high credit risks. This is particularly true for residential investment, since
housing is very sensitive to real and nominal interest rates. A higher rate of inflation may also have a
negative impact on stock market values due to increased uncertainty about the future. But a decrease
in stock values may make it more difficult for firms that want to raise funds for investment projects
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through issuing new stocks. Expectations about inflation also may affect the timing of investments.
As a result, the level of investment may be affected by monetary policy despite the fact that real
interest rates have not changed.
Application Questions:
1. The rental cost of capital (rc) is equal to the real interest rate (r) plus the rate of depreciation (d), with
the real interest rate defined as the nominal interest rate (i) minus the expected inflation rate (e):
rc = = r + d = i - e + d.
A car rental firm would want to know how fast its cars will depreciate (or what is needed to keep the
stock of cars at the original level) and what the costs are of having funds tied up in owning the cars.
In order to make a profit, a car rental firm would charge more per car than the interest it could get (or
has to pay) on the funds tied up plus the depreciation rate times the value of the car. Since the rental
firm charges a nominal price and is charged a nominal interest rate by a bank for any funds that are
borrowed, the charge would be
P > (i + d)V,
with V = the value of the car.
For example, if the current market interest rate is 10%, the rate of depreciation is 20%, and the value
of the car is $10,000, then the car rental company would charge at least
(0.1 + 0.2)(10,000) = (0.3)(10,000) = 3,000
per year or roughly $8.22 dollars per day. If we further assume that the car is rented only half of the
time, then the costs would go up to $16.44 per day. Since the $16.44 charge does not include any
other costs to the firm or any profits, we should expect the actual price for a car rental to be higher.
2.a. If the net present discounted value (NPV) of a project is positive, the project is profitable. Assuming
that Year 1 is the present year, the net present value of the project can be calculated in the following
way:
NPV = R1 + R2/(1 + r) + R3/(1 + r)2
At an interest rate of r = 5% we get
NPV = - 200 + 100/(1.05) + 120/(1.1025) = - 200 + 95.24 + 108.84 = 4.08 > 0.
This means that the project is profitable and should be undertaken.
2.b. Using the same equation as in 2.a. but with an interest rate of r = 10%, we get
NPV = - 200 + 100/(1.1) + 120/(1.21) = - 200 + 90.91 + 99.17 = - 9.92 < 0.
This means that the project is unprofitable and should not be undertaken.
3.a. A temporary investment tax credit should have a positive effect on investment for the period to which
it applies. In the long run, however, we should not see a significant effect on investment arising from
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a temporary investment tax credit. The desired capital stock depends mainly on a firm's estimate of
future or permanent output and a temporary investment tax credit should not affect the firm's desired
long-run capital stock.
3.b. A temporary investment tax credit will increase the number of current projects, since firms will invest
in projects that they otherwise might have delayed. Firms may also initiate some marginal projects
that were unprofitable under previous conditions. Therefore the level of investment in the year that
the tax credit is imposed will increase. Since so many projects are undertaken during the current year,
fewer projects will be undertaken the following year, when the tax credit is no longer in effect. Thus
the level of investment in the second year will be lower than it would have been otherwise.
3.c. While a permanent tax credit does not induce firms to accelerate investment projects, it may
encourage them to undertake marginal investment projects that might not previously have been
profitable. We should therefore see an overall increase in the level of investment, both in the first year
of the tax credit and beyond. The effect of a permanent tax credit on investment in the long run will
be greater than that of a temporary tax credit.
4.a. The total value of the outstanding shares is $25 million. Therefore Tobin’s q has the following value:
q = (value of all shares)/(replacement cost of capital) = 25/18 > 1.
But a value of q that is greater than 1 implies that the value of the marginal product of capital is
greater than its marginal cost. Therefore the firm should invest.
4.b. With a replacement cost of $25 million, q = 1. Therefore net investment should be zero. But there
should still be some gross investment to replace the capital stock that depreciates.
With a replacement cost of $28 million, q < 1. In this case, the firm should “disinvest,” that is, let
its capital stock depreciate but not replace it.
5.a. From K* = (Y)/rc ==> K* = [(0.3)(5)]/(0.12) = 12.5
==> the desired capital stock is valued at $12.5 trillion.
5.b. From K* = [(0.3)(6)]/(0.12) = 15
==> the desired capital stock is now valued at $15 trillion.
5.c. From I1 = (K* - K) ==> I1 = (0.4)(15 - 12.5) = (0.4)(2.5) = 1
==> in the first year, net investment will be I1 = $1 trillion, and the new capital stock will be
K1 = $13.5 trillion.
From I2 = (K* - K) ==> I2 = (0.4)(15 - 13.5) = 0.6
==> in the second year, net investment will be I2 =$0.6 trillion and the new capital stock will be
K2 = $14.1 trillion.
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Additional Problems:
1. Explain why the stock of existing housing would decline if no more new houses were built.
There will always be some depreciation, as existing houses burn or are torn down. If no new houses are
built (gross investment is zero), the housing stock will decline (net investment will be negative).
2. Low interest rates should encourage firms to invest. So why did Canada have a low level of
investment spending during the 1930s when interest rates were very low?
During the 1930s the economy was in a deep recession. Therefore, in spite of low interest rates,
businesses were reluctant to invest. The level of investment depends not only on the interest rate but also
on changes in income, that is, the sales expectations of businesses. In the 1930s, most businesses did not
expect sales to increase.
3. "Firms will undertake investments as long as the value of the marginal product of capital is
below the rental cost of capital." Comment on this statement.
If this were true, then the last unit of capital employed would cost more than the value of the increase in
output. Competitive firms minimize costs when the rental cost of capital is equal to the value of additional
output produced as one more unit of capital is added. Otherwise it would pay for the firm to use more (if
the value of the marginal product of capital exceeded the rental rate) or less (if the value of the marginal
product of capital were less than the rental rate) capital in the production process.
4. "Investment is pro-cyclical in the flexible accelerator model." Comment on this statement.
Assuming away depreciation and the real time required to make adjustments to the capital stock, the
desired capital stock (K*) is proportional to real output, where a is the capital-output ratio, that is,
K*t = aYt .
If investment makes up part of the difference between the actual and the desired capital stock, then
It = [K*t - Kt-1] ==> It = a[Yt - Yt-1].
Therefore, we can see that if output is growing, the level of investment is positive. But if output is falling,
investment is negative. This means that investment in the accelerator model is pro-cyclical, that is, it
follows output. Note, however, that as long as output is increasing at an increasing rate, investment will
increase. On the other hand, if the increases in output become smaller, the level of investment will
decline.
5. Why is the level of investment inversely related to the level of the interest rate? Can you think
of any consumer spending that may also depend on the interest rate? Explain your answer.
When calculating the present discounted value of an investment, the interest rate is in the denominator.
Thus a decrease in the interest rate increases the net present value of an investment. As more investment
projects become profitable, the level of investment rises. Also, the neoclassical theory predicts that the
desired capital stock increases as the interest rate, and therefore the rental cost of capital decreases, that is,
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K* = Y/rc.
Durable consumption goods, such as cars and appliances, are often purchased on credit. Therefore,
spending on durable goods is influenced by interest rate changes, which affect the overall costs of
purchasing these goods. But, as we have seen in the previous chapter, one can interpret the purchase of a
durable good as an “investment.”
6. "Restrictive monetary policy has a negative effect on investment." Comment on this statement.
If inflationary expectations are held constant, monetary restriction will raise both real and nominal
interest rates, at least in the short run. Since the level of investment is inversely related to the real interest
rate, investment will fall. Business fixed investment and housing investment will fall as the returns
generated by projects have to compete with the much higher costs of funds. Inventory investment will
also fall as firms find it more expensive to warehouse raw materials and finished goods.
In the long run, restrictive monetary policy will not have any effect on real interest rates, but will
lower nominal interest rates due to a lower inflation rate. When nominal interest rates are lower, more
people may qualify for mortgage loans and therefore housing investment will increases. A lower inflation
rate may also have a positive impact on stock values. But higher stock values may enable more
corporations to issue new stocks to finance more investment projects. Thus monetary policy may affect
investment even if it does not affect the real interest rate.
7. Which of the following two policy measures would affect GDP more and why: a temporary
investment tax credit for businesses or a temporary income tax cut for individuals? Explain
your answer.
A temporary investment tax credit should have a positive effect on investment for the period in which it
applies. Firms may decide to accelerate projects that they would have undertaken later. They also may
initiate some marginal projects that would otherwise not have been profitable. But in the long run, we
should not see a significant effect on investment from a temporary investment tax credit. On the other
hand, if the government temporarily decreases income taxes, consumption will not be significantly
affected according to the permanent income hypothesis (unless liquidity constraints exist). Therefore the
economy will not be stimulated at all by a temporary income tax cut.
8. Which would stimulate the economy more: a $50 billion tax cut financed by a $50 billion
spending cut, or a temporary tax credit of 15% on each productive investment undertaken next
year? Explain your answer.
According to the balanced budget theorem, a decrease in taxes and government spending by $50 billion
would actually decrease national income. A temporary investment tax credit, which has a positive effect
on the economy, is therefore much more beneficial. A temporary tax credit would make marginal
investment projects profitable. Some firms would also undertake projects earlier to take advantage of the
tax credit. Temporary investment tax credits can be used successfully to stimulate economic activity.
9. “Firms are more likely to invest if current GDP increases.” Comment on this statement.
The level of desired capital stock generally depends on the level of expected future (or permanent) output.
But if the desired capital stock is above the actual capital stock, firms will invest. Entrepreneurs will
invest more if they feel optimistic about the future and expect their sales to increase. If they are
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pessimistic about the future and have low sales expectations, they will invest relatively little. Current
output affects capital demand only to the extent that it affects expectations about future output.
10. For a given nominal interest rate, how does an increase in the expected rate of inflation affect
the level of investment?
The rental cost of capital is defined as rc = i - e + d. This means that an increase in the expected rate of
inflation (e) decreases the rental cost of capital (rc). But a decrease in the rental cost of capital increases
the level of investment, as more investment projects become profitable. A decrease in rc also increases the
desired capital stock K* = (Y)/rc and therefore encourages investment.
11. Comment on the following statement:
“The discounted cash flow analysis is inconsistent with the neoclassical theory of investment.”
The neoclassical theory of investment states that the level of desired capital stock increases with an
increase in expected output (sales) and a decrease in the rental cost of capital. In practice, firms base their
investment decisions on the discounted cash flow analysis. An investment project is evaluated by
calculating its net present discounted value. If a firm expects an increase in sales, the cash flow associated
with any investment project will be larger and the net present discounted value of the investment will rise.
At the same time, if the rental cost of capital decreases, then the net present discounted value of the
project increases and the firm is more likely to undertake the investment. The decision making of firms
using this discounted cash flow analysis is therefore consistent with the neoclassical theory of investment.
12. Assume your firm buys a new computer system at a cost of $12,600 that will save you $5,600
after one year, $4,840 more after the second year and another $4,000 after the third year. Then
the computer will become outdated and no further saving will accrue. Is this a worthwhile
investment if we assume that there is no inflation and that the market rate of interest remains
at i = 10% over these three years?
The net present discounted value of your investment is
NPV = - 12,600 + 6,600/(1+ 0.1) 1 + 4,840/(1+ 0.1)2 + 4,000/(1+ 0.1)3
= - 12,600 + 6,000 + 4,000 + 3,000 = + 400 > 0.
Since the net present discounted value of your investment is positive, it is profitable and you should
undertake this investment.
13. Evaluate the following project, assuming that the market interest rate remains at i = 10%.
costs
revenues
Year 0
$3,700
$0
Year 1
$605
$2,640
Year 2
$363
$2,420
Year 3
$0
$400
The investment should be undertaken, since the net present discounted value of this investment is
positive. It can be calculated as follows:
NPV = -3,700 + (2,640 – 605)/(1 + .1)1 + (2,420 - 363)/(1 + .1)2 + 400/(1 + .1)3
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= - 3,700 + 1,850 + 1,700 + 300 = 150 > 0
Since NPV > 0, this investment is profitable and should be undertaken.
14. Would you undertake the following investment project? Why or why not?
costs
revenues
Year 0
$3,993
$0
Year 1
$4,840
$3,630
Year 2
$3,630
$4,840
Year 3
$0
$3,993
This problem does not list an interest rate so, under normal circumstances, we cannot solve the problem.
But if we simply add up the costs and the benefits, we can see that both sums are equal. Since the costs
occur earlier than the benefits, we can conclude that the project is unprofitable, since we could have
invested the funds we spent at any positive interest rate. For example, if the market interest rate was i =
10%, then the net present value would be:
NPV = - 3,993 + (3,630 - 4,840)/1.1 + (4,840 - 3,630)/1.21 + 3,993/1.331
= - 3,993 - 1,100 + 1,000 + 3,000 = - 1,093
Since NPV < 0, this investment is not profitable and should not be undertaken.
The investment project is unprofitable at any positive real interest rate. But it is conceivable that
the real interest rate is actually negative, if the rate of inflation is greater than the nominal interest rate. In
this case, the project would be profitable. At high rates of inflation it makes sense to borrow money and
pay it back later with money that has lost some of its purchasing power.
15. Is inventory investment pro-cyclical? Why or why not?
During periods of economic expansion, firms increase production to meet sales and add to inventories,
since the desired stock of inventories increases with output. But when the boom reaches its peak and
economic growth and sales slow, inventories rise involuntarily until firms cut back production. This may
actually contribute to the upcoming recession. Before growth resumes after the recession, firms may want
to increase their inventories to be ready for the increase in demand for their product. When demand picks
up, inventories serve to fill the demand until sales can be met through increased production. Inventory
investment is usually not pro-cyclical but more counter-cyclical, that is, during recessions it rises and
during booms it falls.
16. Briefly explain how inventory cycles relate to the multiplier-accelerator model that states that
the level of investment is positively related to the change in income.
According to the multiplier-accelerator principle, any economic disturbance will lead to business cycles.
A change in investment will bring about a larger change in national income, but the level of investment is
proportional to the change in income. This can be expressed as follows:
It = [K*t - Kt-1] ==> It = a[Yt - Yt-1]. ==> I = k(Y), with k = a.
The multiplier principle states that the change in investment will cause a larger change in national
income, or Y = (I). (Note that  is the expenditure multiplier and different from the a mentioned
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above.) As long as the economy is growing at an increasing rate, the level of investment will go up,
stimulating growth even further. As the economy peaks, however, a reduction in the growth rate of
income will reduce the level of investment, which will lead the economy into a recession. If, for example,
firms expect an economic upswing, they will increase inventories since they expect future sales to
increase. They will step up production, which will stimulate the economy. When the economy approaches
its full potential, bottlenecks will occur, so prices and interest rates will increase. While actual sales may
still increase (since the economy is still growing), they may fall below expected sales, so there may be an
unwanted increase in inventories. Firms will then cut production, which may eventually cause layoffs and
possibly a recession.
17. "Even though the economy may still be growing, a decrease in the growth rate of income may in
itself be sufficient to lead the economy into a recession." Comment on this statement.
The multiplier-accelerator principle implies that any economic disturbance can lead to economic cycles.
A change in investment will bring about a larger change in national income, but the level of investment is
proportional to the change in income. As long as the economy grows at an increasing rate, the level of
investment will also increase which will further stimulate the economy. However, a reduction in the
growth rate of income will reduce the level of investment. If the level of investment decreases, the change
of investment becomes negative. This will be multiplied to produce an even larger negative change in
output and the economy will go into a recession. For example, we can explain inventory cycles in the
following way: If firms expect an economic upswing, they will let inventories grow since they expect
future sales to increase also. To increase inventories they will have to step up production, which will
stimulate the economy. When the economy approaches its full potential, then bottlenecks will occur, and
prices and interest rates will increase. While actual sales may still increase (since the economy is still
growing), they may fall below expectations, so there will be an unwanted increase in inventories. Firms
will then cut their production level which may eventually cause some layoffs and a reduction in spending,
that is, the economy enters a recession.
18. Comment on the following statement:
"Continued high budget deficits will adversely affect the construction industry."
If the government finances an increase in spending by borrowing from the public, the budget deficit
increases. As the demand for credit increases, interest rates increase as well. This negatively affects the
housing sector, which is highly interest sensitive. Higher mortgage interest rates not only lead to a
decrease in the demand for new houses, but may also deter some housing developers from financing new
projects.
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