ABSTRACT
In a growing economy the problem of effective demand is best introduced in a formal way, by allowing for the possibility of disequilibrium between the growth rates of investment and of saving. To capture this formally, suppose initially the economy is in a state of equilibrium growth. This implies that the commodity market is cleared, and the equilibrium ratio of investment (I) to saving (S) remains at unity, ( / )I S∗ ∗ =1 This equilibrium ratio defi nes the locus of all possible commodity market clearing positions, and the equilibrium is maintained so long as the rate of growth is the same for investment and for saving. To develop the analysis farther along these lines, we postulate a power function,
Y A I S A Y= > = >[ / ] , , .*α α 0 0 (32)
Note that for all equilibrium values of the ratio I S Y
A( ) = ( ) =1 1, . Thus, A represents the locus of all the commodity market clearing equilibrium values. Writing g gA y= ∗ , for commodity market clearing growth rate of Y, logarithmic differentiation of (32) yields ( ) ( ).g g g gy y I s− = −∗ α
As the formulation above shows, the deviation in the growth rate of output g
between the growth rates in I and S, which in turn triggers off an adjustment in Y. Assuming savings as an increasing function of income, this would raise g
Approximating over continuous time, we write
dg
dt g gY I S= −α( ) (33)
where α is some arbitrary positive speed of adjustment. An investment (demand) function different from the saving function
has to be introduced to capture the possibility of a divergence between
their respective rates of growth. For neither the investment nor the saving function, a commonly accepted formulation exists. However, for simplicity of exposition it would suffi ce to consider a regime of static expectations, in which investment depends positively both on the current level of output as a predictor of the future state of demand as well as on labour productivity as a predictor of expected profi tability. Note expected profi t margin increases through higher labour productivity, only if productivity increases without a compensating increase in the real wage rate. Consequently, productivity (X) could be treated as an indicator of profi tability, if business takes the real wage as a given datum beyond its control. On these assumptions, the
investment function is specifi ed as, I I Y X= + +
( , ), with the sign of the partial derivative with respect to the relevant variable shown above it. Simple manipulation converts it into the growth rate of investment as
g g gI y y x x= +η η (34)
where, g j = the growth rate of variable j, Y = output level, X = labour
productivity level, and, η ηy x and are positive partial elasticities of investment with respect to output and investment respectively. In its simplest specifi cation, saving is treated as an increasing function only of income,8 so that
g gs y y= ε , (35)
Where ε y is the positive elasticity of saving with respect to income.
