The accelerator model of investment, one of the first to attempt to understand why firms invest, expresses a simple notion: investment in plant and equipment will increase if demand for the product increases. It is a common sense idea that is easily taken as truth, at least until one looks at the model more carefully. The interesting result of the model is that investment, even if it is actually stimulated by a change in demand, will increase only if demand increases at an increasing rate. If the rate of growth in demand slows, investment will fall. One needs demand to grow at an accelerating rate for investment to grow, and hence the name of the model.
We have, in the accelerator model, the terms that are used commonly in current economics discussions: investment, demand (read consumption), income and output. It would seem to be an easy juxtaposition to put the original ideas into a consumption (C) + investment (I) (or 45 degree line) diagram or a saving (S) - I diagram and modernize the model.
In this paper we use both diagrams to show that the model is a very optimistic one at first glance. If one starts at equilibrium income, where C + I = income (Y) or where S = I, then an increase in the consumption function (the increase in demand) will push up investment (the idea). This has the effect of raising income, and if one goes a step further, the rise in income will push up consumption along the shifted consumption function and again stimulate income. The makings are there for an upward explosion. Of course in reality output does not rise forever, and so the model must be examined more carefully.
To further explore the model we look at the assumptions behind the model and present a table which shows the important result that consumption must rise at a certain rate in order for investment to rise, the basic important idea of the model. The Keynesian geometry seems to fail in properly understanding the accelerator principle.