# Accelerator effect

The accelerator effect in economics refers to a positive effect on private fixed investment of the growth of the market economy (measured e.g. by Gross Domestic Product). Rising G.D.P. (an economic boom or prosperity) implies that businesses in general see rising profits, increased sales and cash flow, and greater use of existing capacity. This usually implies that profit expectations and business confidence rise, encouraging businesses to build more factories and other buildings and to install more machinery. (This expenditure is called fixed investment.) This may lead to further growth of the economy through the stimulation of consumer incomes and purchases, i.e., via the multiplier effect.

The accelerator effect also goes the other way: falling G.D.P. (a recession) hurts business profits, sales, cash flow, use of capacity, and expectations. This in turn discourages fixed investment, making a recession worse (especially when the multiplier effect is remembered).

The accelerator effect fits the behavior of an economy best when either the economy is moving away from full employment or when it is already below that level of production. This is because high levels of aggregate demand hit against the limits set by the existing labor force, the existing stock of capital goods, the availability of natural resources, and our technical ability to convert these inputs into products. Note also that this principle, like many others in economics, only works ceteris paribus or "all else equal." In plain prose, the accelerator effect may be cancelled out by other economic forces.

## Accelerator models

The accelerator effect is shown in the simple accelerator model. This model assumes that the stock of capital goods (K) is proportional to the level of production (Y):

K = k*Y

This implies that if k (the capital-output ratio) is constant, an increase in Y requires an increase in K. That is, net investment, In equals:

In = kY

Suppose that k = 2. This equation implices that if Y rises by 10, then net investment will equal 10/2 = 5, as suggested by the accelerator effect. If Y then rises by only 5, the equation implies that the level of investment will be 5/2 = 2.5. This means that the simple accelerator model implies that fixed investment will fall if the growth of production slows. An actual fall in production is not needed to cause investment to fall. However, such a fall in output will result if slowing growth of production causes investment to fall, since that reduces aggregate demand. Thus, the simple accelerator model implies an endogenous explanation of the business-cycle downturn, the transition to a recession.

Modern economists have described the accelerator effect in terms of the more sophisticated flexible accelerator model of investment. Businesses are described as engaging in net investment in fixed capital goods in order to close the gap between the desired stock of capital goods (Kd) and the existing stock of capital goods left over from the past (K-1):

In = x*(Kd - K-1)

where x is a coefficient representing the speed of adjustment (1 ≥ x ≥ 0).

The desired stock of capital goods is determined by such variables as the expected profit rate, the expected level of output, the interest rate (the cost of finance), and technology. Because the expected level of output plays a role, this model exhibits behavior described by the accelerator effect but less extreme than that of the simple accelerator. Because the existing capital stock grows over time due to past net investment, a slowing of the growth of output (G.D.P.) can cause the gap between the desired K and the existing K to narrow, close, or even become negative, causing current net investment to fall.

Obviously, ceteris paribus, a actual fall in output depresses the desired stock of capital goods and thus net investment. Similarly, a rise in output causes a rise in investment. Finally, if the desired capital stock is less than the actual stock, then net investment may be depressed for a long time.

In the Neoclassical accelerator model of Dale Jorgenson, the desired capital stock is derived from the aggregate production function assuming profit maximization and perfect competition.

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