Accelerator vs. investment multipliers in a production possibility curve framework

The objective of this paper is to introduce a new way to look at and teach two critical macroeconomic theories, the accelerator and the investment multiplier.  The accelerator presumes that additional demand stimulates investment.  In a two sector model we would translate this statement to read, additional consumption stimulates investment.  The investment multiplier argues that additional investment stimulates income which in turn stimulates consumption (via the marginal propensity to consume.)  Both have consumption and investment going up.  The accelerator has consumption driving the system while the multiplier has investment as the driving force. 

Despite the ground breaking article by Samuelson (1939) in which both operate at the same time to create economic cycles, it is true that the accelerator would operate strongly if full employment exists and the multiplier works if unemployment exists. But if we take liberties with the full employment issue, students can obtain insight into comparing the two models using a production possibility curve framework.  If the PPC has consumption on one axis and investment on the other, we can easily compare the two theories.  And while both have consumption and investment rising, it is not clear that both will lead to the same end point using this approach.

The paper starts with a point inside the production possibility curve.  Then, following the accelerator theory, consumption increases and we shift the point upwards.  This upward shift propels investment and so the raised point moves to the right.  If we began at point A inside the PPC, we would end at point B somewhat diagonally above A and closer to the frontier.  Following the multiplier logic, also starting at point A, the movement is first towards more investment.  Then through the linkage of income and using the mpc, the point moves up to another point, point B’, again somewhat diagonally above A and closer to the frontier. 

Are points B and B’ coincident?  It depends, of course, on the mpc.  And this is the beauty of this approach for students...it makes a comparison of the two models clear and indicates their differences in a simple manner.