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.

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.

(Annual

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