The multiplier–accelerator model (also known as Hansen–Samuelson model) is a macroeconomic model which analyzes the business cycle. This model was developed by Paul Samuelson, and is based on the Keynesian multiplier, which is a consequence of assuming that consumption intentions depend on the level of economic activity, and the accelerator theory of investment, which assumes that investment intentions depend on the pace of growth in economic activity.
The accelerator model can be combined with Keynes’s theory of the consumption multiplier to produce a simple model of cyclical behavior. The multiplier, which Keynes actually borrowed from R.F. Kahn, was among the clearest concepts in The General Theory. Assuming that output is determined by aggregate demand, which includes consumption and investment, the multiplier shows that changes in consumption will amplify the effect of any change in investment on total output and income. Suppose that investment increases for some exogenous reason. This will raise aggregate spending and cause output to rise. Since output equals income in the economy, aggregate income rises as the producers of the new investment goods enjoy higher sales and incomes. According to Keynes’s fundamental psychological law, these people will spend part but not all of the increase in their incomes. This leads to a secondary (but smaller) increase in aggregate demand, which raises the incomes of those who produce the products that the first wave of new consumers buys. As their incomes go up, they will in turn increase consumption spending, but by less than their incomes rose. Thus, an increase in investment sets off a never-ending sequence of ever-smaller increases in consumption demand that augment or “multiply” the effect of investment on income. By simple algebra, the sum of these effects, or the Keynesian multiplier, can be shown to converge in the limit to 1/(1 - MPC). Keynesian economists generally reckoned the MPC to be well in excess of one-half, so the multiplier was thought to more than double the effect of investment on output.
When the multiplier is combined with the accelerator, the resulting model is capable of interesting dynamics. This is particularly true if either the consumption function or the investment function has a lagged response to changes in income. The multiplier-accelerator model is no longer used much as a theory of business cycles, though the accelerator occasionally crops up in analyses of particular regions or industries. There are several reasons for this. The first is that macroeconomists have become very skeptical of the aggregate-demand-based theory of output determination embodied in the model. As you know, modern approaches to business cycles emphasize the joint determination of output by demand and supply factors, with interest rates and prices playing an important role. Moreover, the great variation in lengths and severity of business cycles over time and across countries argues against an “endogenous” explanation of the cycle such as that provided by the multiplier-accelerator model. In such a model, each business cycle should be the same length and, depending on the formulation, perhaps of the same magnitude as well. Modern macroeconomic theory usually assumes that the business cycle results from repeated random disturbances to the economy by positive or negative shocks, together with a stable convergence mechanism. Depending on the timing and magnitude of shocks, it is possible to have both short and long business cycles and both severe and mild ones in such a model.