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ans4154a

# ans4154a - Economics 154a Spring 2005 Intermediate...

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Economics 154a, Spring 2005 Intermediate Macroeconomics Problem Set 4: Answer Key 1. Consider an economy that consists of a single consumer who lives for two time periods. The consumers income in the current period is Y and the consumers income in the future period is Y f ... (a) Let Y = 2100, Y f = 1050, G = T = 0 . 3 Y , G f = T f = 0 . 3 Y f , and r = 0 . 1. Find C and C f . What is national saving in the current period, i.e., what is S = Y - C - G ? ANSWER: We can ﬁnd consumption and saving by solving: C + C f 1 + r = Y - T + Y f - T f 1 + r (1 + r ) C + C f = (1 + r )( Y - T ) + ( Y f - T f ) (1) which, after plugging in C = C F and the values above, is: (2 . 1) C = (1 . 1)(0 . 7)( Y ) + (0 . 7)( Y f ) (2 . 1) C = . 77(2100) + 0 . 7(1050) C = 1120 . Therefore: S = Y - C - G = 2100 - 1120 - 630 = 350 also, note that Y f - C f - G f = 1050 - 1120 - 315 = - 385 = (1 . 1)350 = (1 + r ) S (2) (b) Suppose that T increases by 50 (but government expenditures in the two time periods remain unchanged). By how much must T f decrease so that the govern- ments budget constraint is satisﬁed? How does the increase in T (and accompa- nying decrease in T f ) aﬀect C, C f , and S? 1

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ANSWER: The rate at which money can be passed on from one period to the next is 1+r. From the government’s inter-temporal budget constraint in particular we can see that Δ T + Δ T f 1 . 1 = 0 which implies that Δ T f = - 1 . T = 55. The agent’s budget constraint doesn’t change at all, since the changes in taxes cancel out: C + C f 1 + r = Y + Y f 1 + r - ˆ T + Δ T + T f + Δ T f 1 + r ! = Y + Y f 1 + r - ˆ T + T f 1 + r ! Therefore consumption does not change, and since government consumption doesn’t change either, savings are also unchanged. (c) Suppose instead that there is a temporary increase in government spending: G increases by 50 but G f remains unchanged. At the same time, T increases by 50, so that the governments budget constraint is still satisﬁed. How does the increase in G (and accompanying increase in T) aﬀect C, C f , and S? ANSWER:Intuitively, with the change from T = 630 to ˆ T = 680 the consumer will be \$50 poorer the ﬁrst period than he used to be, but he still wants to equalize consumption in both periods, so he’ll spread the loss across periods. Since private consumption does not fall as much as government spending increases, national saving decreases in the ﬁrst period. Since consumption decreases in the second period, then savings increases. Analytically:
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ans4154a - Economics 154a Spring 2005 Intermediate...

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