Econ 154a Problem Set 8 Solution

# Econ 154a Problem Set 8 Solution - Economics 154a Fall 2005...

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Economics 154a Fall 2005 Bj¨orn Br¨ugemann Problem Set 8 Solution Problem 1 (Myopic Consumer and the Multiplier Efect o± Government Expenditures) 1. Private saving is given by S pvt = ( Y - T ) - C = ( Y - T ) - m ( Y - T ) = (1 - m )( Y - T ) . 2. Government saving is T - G , so adding private and government saving gives the saving curve S d IS - LM ( r | Y,T,G ) = (1 - m ) Y + mT - G. (1) Notice that in contrast to the saving curve obtained ±rom a utility maximizing consumer (and rederived below), now the timing o± taxation matters. It would not be innocuous to assume budget balance, which would imply that national saving is (1 - m )( Y - G ). Thus an increase in G that leaves T unchanged now has a diferent efect on national saving than an increase in G that is accompanied by an increase in taxes T . 3. In class, we derived the IS-LM desired national saving curve using the microeco- nomic saving ±unction S ( r,X - T,X f - T f ). We ±ound that due to Ricardian equivalence, national saving did not depend on the timing o± taxation. Thus the easiest way to obtain national saving is to use the trick to assume budget balance. ( Remark: As discussed above this trick does not work ±or a myopic consumer, since Ricardian equivalence does not apply. With a myopic consumer, the tim- ing o± taxes does matter ±or the consumption behavior o± the consumer.) This implies zero government saving, so national saving is just given by private saving S ( r,X - G,X f - G f ). Substituting X = Y and X f ( r | A f ,K ), we obtained S d IS - LM ( r | Y,A f ,K,G,G f ) = S ( r,Y - G,X f ( r | A f ,K ) - G f ) . Now we can compare this saving curve with the saving curve obtained ±or myopic consumers. (a) With a utility maximizing consumer, saving depends on the real interest rate ±or two reasons. First, there is a direct efect: because we assumed that the substitution efect is dominant, the consumer wants to save more i± saving pays a higher return. Second, there is an indirect efect through ±uture wages and pro²ts received ±rom the ²rm: a high interest rate makes it more costly

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Figure 1: T in S d IS - LM - I d diagram S d IS - LM ,I d r I d S d IS - LM, 1 E 1 S d IS - LM, 2 E 2 for the Frm to borrow, reducing the wages and proFts it is able to pay out to the consumer in the second period. With a myopic consumer, both e±ects are absent. The consumer just consumes a Fxed fraction of his disposable income. Thus there is no direct e±ect of the real interest rate. And since the consumer does not consider future income when determining consumption, the indirect e±ect through future income is absent as well. (b) Suppose current taxes increase. As long as government expenditures remain unchanged in both periods, a utility maximizing consumer realizes that he is not actually poorer, and that taxes will be lower in the future, so he just reduces saving exactly by the amount of the tax increase, and national saving remains unchanged. The myopic consumer ignores that future taxes will be lower and behaves as if he is poorer, so he both saves less and consumes less.
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Econ 154a Problem Set 8 Solution - Economics 154a Fall 2005...

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