Investment can be defined in this context as additions to
the capital stock and therefore measured as .

In periods of economic expansion, investment increases, often by more than the
increase of GDP and vice versa in times of economic decline. This correlation
does not imply causation, however this essay will show that the theories
underpinning the statement are not as convincing as the theories that
contradict it.  

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The simplest economic theory underpinning the statement that
investment is independent of economic growth is one of perfect competition
within the market, making the prices of the goods sold exogenous, as firms are
price takers. It is also assumed that there are no adjustment costs, the
interest rate is constant and there is no depreciation of capital. Firms aim to
maximise profit, and so profit maximisation is the constraint for their
investment decisions:


The cost of the investment is a function of the level of
investment, where

C(I) .

By solving this constraint problem, the firm holds their optimal level of
capital, when the following equation holds.

A Cobb-Douglas production function can then be substituted
in to solve for the level of investment ‘I’, to achieve the firms optimal level
of capital ‘ This function will be independent of economic
growth because investment only depends negatively on the interest rate r (the
opportunity cost of investment), negatively on the price of investment and
positively on the price of the final output goods. This model assumes that the
firm does not face any credit constraints to so can fund an investment project
of any size. This initial model is a simplification of reality, so provides
little more than a basis to work from to illustrate the factors that actually
influence a firms investment decisions.


A more realistic extension of this economic theory is the
Tobin’s Q model, which is widely used as a resource for making investment
decisions. In this model, we again assume that there is perfect competition. However,
we now incorporate adjustment costs (a) such as training workers to use new
machinery, which usually take the form of a quadratic, and depreciation (),
to make the model more realistic. This means that the cost function of the investment
project takes a form such as:  .

The inclusion of depreciation of capital means that: .


A simplifying assumption we make in this economic theory is
a linear production function (,
allowing constant marginal product, although not that realistic it allows us to
calculate a simpler investment function. Therefore, firms want to maximise:



When differentiated with respect to investment, the first
order condition is:



This can be rearranged to find the investment function:


This can also be written as ,
where the fraction marginal q is enough alone to guide investment decisions, as
a firm will invest until q reaches 1. This equation for investment shows us
many factors that affect the optimal level of investment. Firstly, as
adjustment costs increase the level of investment will decrease. Secondly, as
the price of the additional capital goods  decreased relative to the price level of the
goods produced P, the level of investment will increase. Also, as the real
interest rate and the rate of depreciation increase, the level of investment
will decrease. Finally, the marginal product of capital  affects the optimal level of investment, which
is the additional output resulting from an additional unit of physical capital
from investing (Carlin and Soskice, 2006).The marginal product of output would
be affected by many factors, for example, an increase in demand, uncertainty
due to an event like Brexit and technological progress, for this reason q is a
forward looking variable.


Q, the average of q, is a far more observable value. It can
be calculated by the market value of the firm divided by the purchase price of
the additional capital goods. This value of Q alone is enough for a firm to
decide whether or not they should invest. If Q is more then 1, it means that
the market perceives the firms to be more valuable than just the sum of their
assets, implying the firm is efficient so should invest. Despite scale seeming
to be more important to investment decisions than Q, if Q is calculated using
forecasts of a firms earning as opposed to share prices to find the market
value of the firm, Q is far more successful at tracking investment behaviour
(Carlin and Soskice, 2006). This is likely due to the fact that if market value
is measured by share prices, it can be affected by many other factors, other
than the actual value of the firm.


Although economic growth is not in the Tobin’s Q model, it
is indirectly affecting the value of Q through the market value term because of
its affect on the marginal product of output. Current and expected economic
growth can have many implications, for example, low economic growth may lead to
uncertainty or high economic growth may lead to increased demand and these
factors then go into the calculation of Q. The marginal product of output is
measured by the expected profit streams generated by investment and these
profit streams will inevitably be affected by economic growth somehow. Hence, although
an indirect affect, aggregate investment is not completely independent of
economic growth in the Tobin’s Q model.


Furthermore, there are far more realistic economic theories
that contradict theories supporting the statement that investment is independent
of economic growth. This economic theory is one of imperfect competition;
meaning prices are now endogenous, which is far more realistic in the majority
of markets. When the firm increases their capital stock, supply increases and
this causes the price to fall. The firm wants to find the level of capital,
which maximises profit. Therefore, firms choose investment to maximise:

From here the first order condition can be derived as:

Then using the simplification that ,
and the demand curve for a firm with endogenous prices being: where ”
is the elasticity of demand and ‘n’ is the number of firms in the market. The
optimal level of capital is:

Using ,
the optimal level of investment would satisfy:



This is an extension of the accelerator model, because
investment depends on expected demand, which a firm will partially base upon
expectations of economic growth.


The accelerator model can also be derived by saying that there
is an optimal capital output ratio that will be a function of the interest
rate: .

So therefore, .

This would also imply that:

So if  and assuming the interest rate is constant ”,
we arrive at the conclusion that:


The accelerator model implies that economic growth increases
investment which then contributes to economic growth as investment is included
in aggregate demand, and so on, causing a cyclical, multiplier effect (Carlin
and Soskice, 2006).


The theory that assumes imperfect competition leading to the
accelerator model holds strong next to empirical evidence, which has found the
scale of output and cash flow for a firm, which are often affected by economic
growth to be very significant, contradicting theories claiming that investment is
independent of economic growth. The cash flow of the firm is important
partially because it will affect the extent to which the firm will face credit
constraints. Data from the recent recession strongly supports economic growth
as a determinant of investment because despite interest rates falling by 5%
between 2007 and 2017 (Bank
of England, 2017) as the graph below shows, UK gross fixed capital
formation, which is investment minus disposables, still declined significantly
following the 2007 recession, suggesting that economic growth had an affect on
aggregate investment.

gross fixed capital formation, Office for National Statistics, 2012)


Furthermore, statistical evidence produced by Hassett and
Hubbard supports the analysis that cash flow and sales, often strongly
influenced by economic growth, are more strongly correlated to investment
decisions than average q is to investment decisions (Caballero,1999)


In conclusion, from this analysis of economic theories of
both perfect and imperfect markets, whether indirectly or directly, economic
growth, or expectations of it will have an affect on a firms investment
decisions and therefore aggregate investment. The theory underpinning the
statement that aggregate investment is independent of economic growth is not
realistic and not supported by empirical data. The theories that acknowledge
that investment is not independent of economic growth are far more realistic. Tobin’s
Q is especially useful to firms as it provides an observable method to guide firms
as to whether they should be investing or not. To conclude, the theory
underpinning the statement that aggregate investment is independent of economic
growth, is far less credible or realistic than the theories that include
economic growth as one of the determinants of investment decisions. Despite
these realistic theories about what drives investment, it is still very
unpredictable and volatile. Issues such as credit constraints are difficult to
forecast and data has shown that investment tends to be lumpy, rather than
smoothly increasing or decreasing as most models would predict. Lastly, the
role of uncertainty and an investors risk aversion is not explored in these
models, despite being a likely factor that also affects investment decisions.







Reference List:


Carlin, W and Soskice, D. (2006). Macroeconomics: Imperfections, institutions and policies. Oxford:
Oxford University Press


Caballero, Ricardo J (1999). Handbook of macroeconomics. Amsterdam: Elsevier