EFA (9): The accelerator

As with cars, acceleration plays a key role in economics. The concept of the accelerator is the subject of the ninth item in our Economics for Amateurs (EFA) series. You can find this series here every Monday.

Let's assume that there is a fixed relation between production and the necessary capital stock. If demand and production are expected to stay the same, the only investment needed would be to replace capital that is wearing out. Investment to increase the capital stock ("net investment") will take place only if production is expected to increase.

Let's take a simple example. Imagine that a firm has sales of $50 million a year and a capital stock of twice that amount, $100 million, ten per cent of which wears out each year and needs to be replaced.

If sales stay at $50 million, gross investment will be $10 million (to replace the worn out capital) but net investment will be zero. If in the next year, however, sales rise by $10 million (or 20 per cent) to $60 million, the new desired capital stock would be twice that amount ($120 million).

This means that gross investment would now have to be $30 million — $10 million to replace worn out equipment and £20 million of net investment to increase the capital stock.

In other words, a 20 per cent increase in sales has led to a 200 per cent increase in investment (from $10 million to $30 million). This is the accelerator at work — the accelerated effect of a change in sales on investment.

But for investment to continue at this higher level, sales and production have to increase further. If sales stagnate at $60 million, the desired capital stock remains at $120 million. This means that the only investment needed each year is $12 million (ten per cent of $120 million) to replace capital that wears out.

In fact, sales have to keep rising at the same rate just for investment to stay at the same level. If sales just stop rising as fast, let alone fall, investment will be reduced, which can cause a recession.

The acceleration principle also applies to firms' investments in inventories. Indeed, inventories respond more quickly to the business cycle than investment in fixed assets. This makes the accelerator a key source of volatility in economies.