Instability of investment: the accelerator
One of the major factors contributing to the ups and downs of the business cycle is the instability of investment.
When an economy begins to recover from a recession, investment can rise very rapidly. When the growth of the economy slows down, however, investment can fall dra- matically, and during a recession it can all but disappear.
Since investment is an injection into the circular flow of income, these changes in investment will cause multiplied changes in income and thus heighten a boom or deepen a recession.
The theory that relates investment to changesin national income is called the accelerator theory. The term ‘accelerator’
is used because a relatively modest rise in national income can cause a much larger percentage rise in investment.
When there is no change in income and hence no change in consumption, the only investment needed is a relatively small amount of replacement investment for machines that are wearing out or have become obsolete.
When income and consumption increase, however, there will have to be newinvestment in order to increase produc- tion capacity. This is called induced investment(Ii). Once this has taken place, investment will fall back to mere replacement investment (Ir) unless there is a further rise in income and consumption.
Thus induced investment depends on changes in national income (ΔY):
Ii= αΔY
where α is the amount by which induced investment depends on changes in national income, and is known as the accelerator coefficient. Thus if a £1 million risein
national income caused the levelof induced investment to be £2 million, the accelerator coefficient would be 2.
The size of αdepends on the economy’s marginal cap- ital/output ratio(ΔK/ΔY). If an increase in the country’s capital stock of £2 million (i.e. an investment of £2 million) is required to produce £1 million extra national output, the marginal capital/output ratio would be 2. Other things being equal, the accelerator coefficient and the marginal capital/output ratio will therefore be the same.
How is it that the cost of an investment to a firm will exceed the value of the output that the investment will yield?
Surely that would make the investment unprofitable?
(Clue: the increase in output refers to output over a specific time period, usually a year.)
The following example (see Table 17.5) illustrates some important features of the accelerator. It looks at the invest- ment decisions made by a firm in response to changes in the demand for its product. The firm is taken as representat- ive of firms throughout the economy. The example is based on various assumptions:
• The firm’s machines last exactly ten years and then need replacing.
• At the start of the example, the firm has ten machines in place, one 10 years old, one 9 years old, one 8 years old, one 7, one 6 and so on. Thus one machine needs replac- ing each year.
• Machines produce exactly 100 units of output per year.
This figure cannot be varied.
• The firm always adjusts its output and its stock of machinery to match consumer demand.
?
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Accelerator theory The level of investment depends on the rate of change of national income, and as a result tends to be subject to substantial fluctuations.
Induced investmentInvestment that firms make to enable them to meet extra consumer demand.
Accelerator coefficient The level of induced investment as a proportion of a rise in national income: α =Ii/ΔY.
Marginal capital/output ratio The amount of extra capital (in money terms) required to produce a £1 increase in national output. Since Ii= ΔK, the marginal apital/output ratio ΔK/ΔYequals the accelerator coefficient (α).
Definitions
Table 17.5 The accelerator effect
Year
0 1 2 3 4 5 6
Quantity demanded by consumers (sales) 1000 1000 2000 3000 3500 3500 3400
Number of machines required 10 10 20 30 35 35 34
Induced investment (Ii) (extra machines) 0 10 10 5 0 0
Replacement investment (Ir) 1 1 1 1 1 0
Total investment (Ii+Ir) 1 11 11 6 1 0
The example shows what happens to the firm’s invest- ment over a six-year period when there is first a substantial rise in consumer demand, then a levelling off and then a slight fall. It illustrates the following features of the accelerator.
• Investment will rise when the growth of national income (and hence consumer demand) is rising (ΔYt+1> ΔYt). Years 1 to 2 illustrate this (see Table 17.5). The rise in consumer demand is zero in year 1 and 1000 units in year 2.
Investment rises from one to eleven machines. The growth in investment may be considerably greater than the growth in consumer demand, giving a large acceler- ator effect. Between years 1 and 2, consumer demand doubles but investment goes up by a massive eleven times!
• Investment will be constant even when national income is growing, if the increase in income this year is the same as last year(ΔYt+1= ΔYt). In years 2 to 3, consumer demand con- tinues to rise by 1000 units, but investment is constant at eleven machines.
• Investment will fall even if national income is still growing, if the rate of growth is slowing down(ΔYt+1> ΔYt). In years 3 to 4, consumer demand rises by 500 units (rather than 1000 units as in the previous year). Investment falls from eleven to six machines.
• If national income is constant, investment will be confined to replacement investment only. In years 4 to 5, investment falls to the one machine requiring replacement.
• If national income falls, even if only slightly, investment can be wiped out altogether. In years 5 to 6, even though demand has fallen by only 1/35, investment will fall to zero. Not even the machine that is wearing out will be replaced.
In practice, the accelerator will not be as dramatic and clear cut as this. The effect will be extremely difficult to pre- dict for the following reasons:
• Many firms may have spare capacity and/or carry stocks.
This will enable them to meet extra demand without having to invest.
• The willingness of firms to invest will depend on their confidence in futuredemand (see Box 17.3). Firms are not going to rush out and spend large amounts of money on machines that will last many years if it is quite likely that demand will fall back again the follow- ing year.
• Firms may make their investment plans a long time in advance and may be unable to change them quickly.
• Even if firms do decide to invest more, the producer goods industries may not have the capacity to meet a sudden surge in demand for machines.
• Machines do not as a rule suddenly wear out. A firm could thus delay replacing machines and keep the old ones for a bit longer if it was uncertain about its future level of demand.
All these points tend to reduce the magnitude of the accelerator and to make it very difficult to predict. Neverthe- less the effect still exists. Firms still take note of changes in consumer demand when deciding how much to invest.
Box 17.6 shows how, from 1975 to 2008, fluctuations in investment were far more severe than fluctuations in national income. This tends to suggest that there was a sub- stantial accelerator effect operating during the period.
The multiplier/accelerator interaction
If there is an initial change in injections or withdrawals, then theoretically this will set off a chain reaction between the multiplier and the accelerator. For example, if there is a rise in government expenditure, this will lead to a mul- tiplied rise in national income. But this rise in national income will set off an accelerator effect: firms will respond to the rise in income and the resulting rise in consumer demand by investing more. But this rise in investment con- stitutes a further rise in injections and thus will lead to a second multiplied rise in income. If this rise in income is larger than the first, there will then be a second rise in investment (the accelerator), which in turn will cause a third rise in income (the multiplier). And so the process continues indefinitely.
But does this lead to an exploding rise in national income? Will a single rise in injections cause national income to go on rising for ever? The answer is no, for two reasons. The first is that national income, in real terms, cannot go on rising faster than the growth in potential output. It will bump up against the ceiling of full employ- ment, whether of labour or of other resources.
A second reason is that, if investment is to go on rising, it is not enough that national income should merely go on rising: instead, national income must rise faster and faster.
Once the growth in national income slows down, invest- ment will begin to fall, and then the whole process will be reversed. A fall in investment will lead to a fall in national income, which will lead to a massive fall in investment.
The multiplier/accelerator interaction is shown more form- ally in Table 17.6. A numerical example is given in Case Study 17.3 in MyEconLab.
Fluctuations in stocks
Firms hold stocks (inventories) of finished goods. These stocks tend to fluctuate with the course of the business cycle, and these fluctuations in stocks themselves con- tribute to fluctuations in output.
Imagine an economy that is recovering from a recession.
At first, firms may be cautious about increasing production.
Doing so may involve taking on more labour or making additional investment. Firms may not want to make these commitments if the recovery could soon peter out. They may, therefore, run down their stocks rather than increase output. Initially the recovery from recession will be slow.
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