INVESTMENT NOTES
8.1 Categories of investment
Before developing any theories investment choices by people it is
important to define what is meant by investment.
Investment: is the formation of real capital, tangible or intangible,
that will produce a stream of good and service in the future. Investment
undertaken in an economy is classified according to the following
categories:
- Business fixed Investment which include plant and machinery, office
buildings . - Residential Construction Investment which includes houses and
significant additions to house ( that require building permit) - Changes in firm‘s Inventories –as they provide revenue in the future,
not today. - Purchases of Durable Goods by Households for example cars, fridges.
- Government purchases of investment Goods and Building for example
roads Hospital, harbours, - Investment in Human Capital for example schooling university study,
apprenticeships etc. - Knowledge which. Includes things we know about scientific and other
areas. - The national income accounts only measure 1,2,3 and 5 as investment
and it is not clears how well they measure 2 and 5 )eg. Additions not
requiring permits and durables purchased by government departments|. The
national accounts do not measure 6 or 7
Investment Affects Future Output
The capital is a very important used to produce output and the level of
investment ultimately determines the level of the capital stock and thus
the growth of output. The relationship between investment and the
capital stock can be expressed in the following way:
Where In,t is net investment at time t.
This implies that if . In,t increase then kt+1 increase and thus
Yt+1>Yt, that is output should increase . Not that the notation used
above assumes that investment undertaken today not really become
productive until the future. This is usually the assumption we sue in
modern macroeconomics.
Investment Fluctuates A Lot
- A well established fact of modern economies
is that 1 fluctuates a lot more C or Y ( we can also see that Y
fluctuates more than C, probably because of the large fluctuations in I
which helps to make up Y). - Furthermore, inventory investment, which makes up only a small
percentage of GDP, is extremely volatile and in a recession more than
half the fall in spending for a typical industrialized country comes
from a decline in inventory investment as firms rundown their inventories.
As a result, if we want to explain fluctuations in output, then we need
to understand what causes fluctuations in an economy‘s investment
behaviors. this has been recognized for quite a long time, including by
Keynes himself who put it down to ―animal spirits‖, or that fluctuations
of firm‘s investments is due to seemingly random fluctuations in firm‘s
expectations about future profitability, there is likely an element of
truth in this view, since we have seen that people‘s consumption choices
depend on future income, but it is in some sense a pessimistic view
since it essentially says that investment is what it is and that is all
we can say . For the rest of the lecture we shall study three categories
of investment and in the process see if Keynes was right.
8.2 Business Fixed Investment
Many people are intensely interested in business fixed investment and it
not difficult to understand why; it constitute the basic equipments used
by firms to produce output whether it be computers, factories, machine
tools or offices. We will learn about the most common theory develop to
explain this form of investment.
Neoclassical theory of Investment
Our next theory of aggregate investment is the one currently used by
economists. An important underlying assumption of the accelerators model
is that firms do not change their production techniques In effect they
employ the same proportions of capital and labour independents of their
affected by output, but on the basis of cost-benefit decision. That is,
firms may have a desired output level they wish to produce, given the
price the output can be sold at, but the bundle of inputs they use will
depend on their relative costs and benefit so as to maximize the profits
of firms.
The Formal Model
We will now write the basic idea described a above as a formal model .
To begin with define the following variables:
Y= the quantity of output produced by the firm
K= the quantity of capital used by the firm
L= the quantity of labour used by the firm
F(…] = the production which related how the inputs capital and labour
are used to produce output.
Next, we need to specify the key assumption used by the model:
- Firms act to maximize their profits where profits equal revenue less
costs. If firms maximize profits by hiring labour and capital, then the
amount they choose to hire will satisfy the condition MB = MC for each
factor, or in this case their MRP equals their cost Let,
W= the marginal nominal wage paid to employees.
R= the marginal nominal ―rental‖ cost that films incur in using capital
Py= price the firms receive for their output.
P= the aggregate price level.
Where it is important to note that the implicit or explicit cost of cost
of using capital is not simply the actual price of the capital, since
the capital can be resold. The cost of using the using the capital is
the implicit (or explicit (or explicit if rented from another firm) cost
of renting the capital over the period it is used ( we will discuss this
is more detail soon) which we are calling R( eg. if we build a dam and
use it to produce electricity then the capital cost per unit of
electricity is not the total cost of the dam, fraction of it relating to
what
portion of it was use to produce the unit electricity). Given our
assumption, we know that the logical implication is that capital labour
are employed up to the point where.
Py x MPL= W or MPL= WPy and PY x MPK = MPK =RPy .And we will now explore
more about the MB and the MC of using capital
Marginal Benefit of Using Capital
The real benefit of using capital is given by the MP that the production
firms earns from the output it produces using the capital. It is also
worth noting that the MP of the factors, and hence the MPK depends in
general on the actual quantities of the factors used. That is, MPK = Y/
k = f [k, L]/ k
Where it is clear that the level of output depends on both L and K, in
many cases economists assumes diminishing returns to the factors of
production, or that as we increase the amount of a factor used output
increase but at a diminishing rate. We will use this assumption here.
From following the logical implications of our assumptions we have
deducted that there are three things that will influence the marginal
benefit of using capital:
- Stock of capital of labour – eg the higher the stock of capital, the
lower the MPK. This is just the assumption of diminishing returns to the
factors of production. - Quantity of labour used – eg, the higher the quantity of labour used,
the higher the MPK. - State of the production Technology- eg the better, the technology the
higher the MPK.
Marginal Cost of Using Capital.
We know that the real cost of using capital is not just the capital ,
but is instead a fraction of this relating to the period over which the
capital is used, which we have called the reakl rental cost ( or R/P bove).
This is made up of the following factors:
- Foregone Interest Earnings ( or interest costs)- say the nominal
rate of interest is i then ipk is the interest cost, or the foregone
interest cost, where PK is the purchase price of capital . This is
fact gives you the fraction of the actual purchase price of the
capital which is relevant for the period for which is used to
produced things. - Valuation losses or Gains-ie PK may go up ( valuation gains ) or go
down (valuation losses) Let – ∆pk = cost of gains or loss - Wear and tear of capital hired out- ie . the capital depreciates in
values when rented out purely from its being used to produce good
and services . let & = the rate of depreciation
This implies that δPK is the nominal depreciation cost
From 1-3) we now have the total cost of renting out one unit (or using)
capital for producing output for one period from 1-3
Nominal cost of capital =ipk – PK+ pk = pk (i- PK/PK+ )
And to summarize, the nominal cost of capital depends on:
- The price of capital
- The interest rate.
- The rate at which capital prices are changing.
- The depreciation rate.
What we have worked out is perfectly correct, but we will invoke one
more assumption to simplify the expression for the cost capital. For
simplicity, assume that the price of that goods increase at the same
rate the inflation rate. This can be characterized mathematically as,
PK/PK = P/P = the inflation rate
We also know that r=i-π (ie. The real interest rate is approximately
equal to the nominal interest rate less the inflation rate – this should
really be the expected inflation rate, but how do we get real cost of
capital = Pk/p(r + )
This tells us that we can expect that real cost of capital to depend upon
- The relative price of the capital good
- The real interest rate
- The depreciation rate
PROFIT Rate of capital
Now we know that the determine both the MB and the MC of using and thus
owing capital we are now in a position to answer the basic question of
how mush capital should firms in total use and own. The answer to this
is that it all depends on the profit rate of capital, which equal,
profit rate =revenue –cost= MPk- (pk/p)r+δ)
There are three cases to consider.
- MPK> cost of capital means there are potential profits a firms could
earn by increasing its capital stock k and the amount of net investment
is positive (ie. Kt+1>Kt). - MPK < cost of capital means the firms is making losses on the last
units of capital it is using and it could increase profits by reducing
its capital stock k and the amount of net investment is negative (ie
kt+1<kt) - MPK = cost of capital means the firms is maximizing the amount of
profit it can earn from using capital and does not want to change its to
capital stock , or reduce it through depreciation depends upon the
profit rate or the different between the MPK and the cost of capital.
Note that unlike the accelerators theory shows us what determines that
optimal or desired capital stock , it is the amount of capital where MB=
MC , or no more profit can be made from changing firm‘s amount of capital
8.3 Investment and the Capital Stock
A Logical conclusion from the neoclassical theory of investment is that
both net gross investment of firms are a negative function of r because
the cost of capital is positively affected by changes in r which
negatively affected the profit rate of capital we can show this
relationship graphically as:
And a change in any other variable that affected by MB or MC OF using
and owing capital MPK , say from a technological innovation, cause a
rightward shift in the investment schedule. The amount of investment
that is undertaken depends on whether or not firms are using and owning
the optimal amount of capital amount of capital, that is , whether or
not the profit rate is zero or non-zero. In the long run equilibrium,
with the profit rate we would expect that the amount of the net
investment is zero with gross investment being positive and just
offsetting the amount of depreciated capital each period. Once a firm is
in its long – run state only a change in R or MPK, or some other
variable, will cause net investment demand. This will cause net
investment to stop being zero and the capital stock will adjust to get
back to a new long – run equilibrium situation
Effects of Tax Laws
We have focused on a few key variables which affect the amount of
investment undertaken but in reality anything which affects the cost or
benefit or using capital will affect the amount government taxes let r
be the tax rate on firms‘ revenues. Then the after tax profit rate of
capital equal , profit rate =(1 –r ) Mpk –(PK/P)( r+δ) so that we can
see that the tax reduces the profits earned from capital by reducing the
MB of using and owing capital. For example, three common policies which
affect investment are.
- Taxes on income earned from owing capital.
This is simply the company tax isn‘t directly levied on capital income
but on a company‘s profits, which include income and cost from all
factors, but some proportion of its incidence is on income earned from
capital and we can think of it this way . An increase in the company tax
will effectively increase r and hence decrease i . This sort of policy
will discourage the accumulations, - Investments tax credits
This is a policy where firms ‗tax liabilities are reduced by how much
they spend on new capital during a year .This effectively lowers r
reducing the cost of capital and causing and increase in I. This sort of
policy will encourage the accumulation of K
Tax Treatment of Department Depreciation
Corporate profits are taxed and profits are just revenue minus costs.
Part of the Cost of production of firms is depreciation on capital so
that firms are allowed to Include depreciation of their capital as a
cost when calculating the amount of Profit to be taxed but depreciation
of their capital as a cost when calculating the a amount of profit to be
taxed but depreciation the true cost of depreciation in period of high
inflation which overstate the profits being made this means a tax is
levied even if the economic profit is Zero , which effectively increase
r reducing I and discouraging the accumulation of capital . The third
type of policy is a factor because obviously the IRD to say something
about the treatment of depreciation for firms that have to file tax returns.
8.4 Residential Investment.
Another type of investment dear to the hearts and wallets of many
Kenyans, as wall as involving large expenditures, and one which varies
strongly with the business cycle, is residential investment what we want
to know is that factors determine investment in residences and how they
do so.
8.4.1 Neoclassical Model of Residential Investment
The neoclassical model of residential investment directly uses an
important conceptual thinking about capital. : the existing capital and
investment but is made explicit in the mode learn about . The idea I s
that there are two part to the housing market ; the mark existing stock
of house which determine the equilibriums housing prices and the new
housing which determine the flow of residential investment . Note that
this is a new housing which determines the flow of investment. Note that
this is a for all forms of capital but we are using it explicitly here
in our model,
8.4.2 The formal model
First off, define the following variables:
PH= the going price of housing in an economy.
P= the price going of housing in economy.
KH= stock of residential capital or housing
IH=investment in housing.
Determining the equilibrium price PH/P- the market for Existing house as
normal market the relative price of housing PH/P is determined jointly
by den supply. The stock of houses is fixed in the short tern and so the
supply curve of houses is vertical. If we invoke the assumption of the
law of demand then the housing is of the Norman downward sloping from in
the relative price of
housing. Given a fixed population the demand for housing can change if
the relative pricing of housing change. It is easy to see why using
example. Say for example PH/P then the quantity demanded falls because.
- People live in small house
- People share residences
- Homelessness
8.4.3 Determining investment –the supply of new housing
We know that the supply that of housing does change does over time . we
also know that the costs of building new houses is made of up of
materials, hiring labour and hiring capital ( tools , machines
etc).these form the MC of building new housing. We will assume the law
of supply that extra quantities of new housing is more expensive because of
diminishing returns to the factors of production used by the firms. That
is , the existing resources become more expensive as firms bid up their
prices to get them ; additional factors requires higher payment s to
induce them to supply their services, or the additional factors are just
as existing resources used. The
MB for firms or developer from building new housing is the relative
price of housing. to induce construction firms to build new house the MB
, or relative price o housing has to higher than the MC this tells us
that supply of new housing curve sloping in the relative price of new
housing .The supply of new housing can be characterized graphically as
follows:
Changes in he Demand for and supply Housing
We now have formal model of the residential housing. Any change in the
relative price of housing curves movement a long the existing curves as
per normal supply and demand curves any other change involves a shift of
a curve which will have other flow on effects. We look at one particular
example. Say a country‘s population increase either because of an
increase in the reproduction because of higher net immigration. this
causes the following sequence of things to 1
1) Demand for housing curve shifts outwards
2) PH/P to clear the housing market.
3) Supply of a new housing increase, increasing the future stock of
housing this cause a fall in PH/P although it will still be higher than
the original level.
The change in the demand for housing can be characterized graphically as
follows:
There are many other things that can affected the demand for housing
rate ( ie because it affects mortgage costs, or the opportunity cost of
holding housing )‘ the tax deductibility of interest payment ( ie if
these exist they increase from owing house better technology ,
expecially in builing materials and techniques as it lowers the cost of
supply new houses and thus shifts the supply down incomes of people ( ie
how much income people have affect their damand and host of other factors.
Summary
1) Demand for housing increases when the population increase
(immigration are better of( higher real gdp) per capital growth)
2) Prices act to ration out scarce resources.
3) We never really get to an ―equilibrium‖, in the static meaning of
equilibrium, because shocks are always occurring! but our economic
reasoning tells us what effects the shocks will have and in which
direction economic variables will change in response to them.
8.5 Inventory investment
The last category of investment that we will study is inventory
investment. It is not that large compared to the other forms of
investment, but as mentioned at the beginning of this topic there is a
strong relationship between changes in inventory investment and changes
in output over the business cycle.
8.5.1 Reasons for holding inventories
Before developing a theory of inventory investment we will study the
reasons why inventories are held. Knowing the reasons for holding
inventories will help us understand better the factors which influence
the level of inventory investment. There are four reasons for holding
inventories:
1) Production smoothing: often it is cheaper to produce goods at a
steady rate, than to continually alter production runs. This means that during slow periods inventories build up and during boom periods inventories are run down.
2) Inventories as a factor of production: films carry inventories of
spare parts incase a machine breaks down, so that the entire assembly
line does not come to a stop. E.g. car assembly factory.
3) Stock out avoidance: to avoid lost sales and profits when sales may
be unexpectedly high e.g. a book retailer may carry multiple copies of a
book if they are not sure how popular the book will be.
4) Work in process: partly completed productions are counted as
inventories e.g. cheese making where cheeses are aging.
An important point to notice about all of these reasons is that have a
short-term focus and not a long-term focus as with the other forms of
investment. This suggests that they will not be so heavily influenced
buy short-run changes in relative prices but will instead be tied
closely to output. Another point to note is that reason 1.is not likely
to be an important reason why inventories fluctuate during business
since this sort of inventory investment goes up as output goes down
whereas inventory investment as a whole goes down as output goes down.
This means 2.-4 must be the main cause of fluctuations in inventory
investment during a business cycle.
