A Reformulation of the Keynesian System

Abstract

The Keynesian faith in the effectiveness of fiscal policy consists in the belief that there is a positive rate of change of national income with respect to autonomous expenditure. This in turn stems from the belief that the marginal efficiency schedule is downward-sloping. This dependence can be seen from a simple formulation of the Keynesian system. Letting Y be national income, E1 investment expenditure, E2 autonomous expenditure, r the marginal efficiency of capital, i the interest rate, and M the stock of money:The dependent variables are Y, E1, r, and i. The derivative dY/dE2, evaluated from (1)–(4),is the expression:The addition of dE1/dt to the right side of (3) yields a differential-equation system whose solution is stable only if the denominator of this expression is positive. It follows that dY/dE2, the rate of change of national income with respect to autonomous expenditure, is opposite in sign to ∂η/∂E1, the slope of the marginal efficiency schedule.

Taxation and the “Fisher Effect”

“…7 7For a formal discussion of the requirements for a downward sloping investment function see Steigmann [7].…”