Prosperity and Depression.pdf

Chap. 13 The Multiplier, Rigidities and Public Spending 475The following numerical assumption will illustrate the possible implicationsof these assumptions. ClWe assume governmental deficit spendingof one dollar per unit period, beginning at sQme initial time andcontinuing thereafter. The marginal propensity to· consume, c 1 is takento be one-half. This is taken to mean that the consumption of anyperiod is equal to one-half [of the increment in] the nati~nal incomeof the previous period. Our last assumption is that indyced privateinvestment is proportional to the increase in consumption betwee~ theprevious and the current period. This factor of proportionality or relation,{3, is taken to be equal to unity; i.e., a time increase in consumptionof one dollar will result in one dollar's worth of induced private investment.ClIn the initial period when the government spends a dollar for thefirst time, there will be no consumption induced from previous periods,and hence the addition to the national income will equal the one doUarspent. This will yield fifty centsQf consumption expenditure in thesecond period, an increase of fifty cents over the consumption of thefirst period, and so according to the relation we will have fifty centsworth of induced private investment. Finally, we must add the newdollar of expenditure by the government. .The national income of thesecond period must therefore total two dollars. ,Similarly, in the thirdperiod the national income would be the sum of one dollar of· consumption,fifty cents induced private investment, and one dollar currentgovernmental expenditure. It is dear that, given the values of themarginal propensity to .consume, c, ind the relation, {3, all succeedingnational income levels can be easily computed in succession.· This isdone in detail in Table II. It will be noted that the introduction ofthe acceleration principle causes our series to reach a.peak'" at the 3rdyear, a trough at the 7th, a peak at the I I th, etc." 2From a pure multiplier sequence no such oscillatory movem~nts couldbe obtained. It will be noted that in this particular case the oscillationsare damped, that is to say, the violence of the fluctuations (amplitude)decreases rapidly as they go on in spite of the fact that the force whichbrings them about-government spending-continues at a constant rate.Professor SAMUELSON then shows that by merely changing the as-1 Professor Samuelson calls it a.2 Loc. cit., pages 75-6.