Questions for Review. By buying bonds This period you save s, next period you get s(1+r)

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1 MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume s lifetime budget constaint? -() 3. What ae the thee popeties of a consume s pefeences? Moe is pefeed to less, The consume likes divesity, Both cuent and futue consumption ae nomal goods. 4. How is the consume s motive to smooth consumption captued by the shape of an indiffeence cuve? Consumption smoothing Diminishing MRS convex indiffeence cuves 5. Give two easons that consumption is moe vaiable in the data as theoy seems to pedict. (note the change in question) Cedit maket impefections Movements in the equilibium eal inteest ate pevent all consumes fom simultaneously tying to smooth consumption. 6. What does theoy tell us about how the value of stocks held by consumes should be elated to consumption behaviou? Does the data suppot this? Some pat of the wealth is held as stocks The maket value of stocks is a poxy fo expected pesent value of lifetime wealth Stock pices ae matingales (andom walk). Any changes in stock pices is a supise and expected to be pemanent. Pemanent changes in wealth has highe effect on consumption than do the tempoay changes. An incease in stock pices is likely to incease consumption In the data, stock pices and aggegate consumption ae positively coelated. 7. State the Ricadian equivalence theoem. 1

2 Holding cuent and futue govenment spending fixed, a change in the timing of taxation has no effect on the equilibium inteest ate, and no effect on any consume s choice of cuent and futue consumption. Poblems 1. A consume s income in the cuent peiod is y = 100, and income in the futue peiod is y = 120. He o she pays lump-sum taxes t = 20 in the cuent peiod and t = 10 in the futue peiod. The eal inteest ate is 0.1, o 10% pe peiod. a. Detemine the consume s lifetime wealth. Lifetime budget constaint (y - t ) w=y-t+ = (120-10)/1.1=180 b. Suppose that cuent and futue consumption ae pefect complements fo the consume and that he o she always wants to have equal consumption in the cuent and futue peiods. Daw the consume s indiffeence cuves. c I 1 I 2 Pefect complements Consume in fixed popotions c. Detemine what the consume s optimal fist- and second-peiod consumption ae, and what optimal saving is, and show this in a diagam with the consume s budget constaint and indiffeence cuves. Is the consume a lende o a boowe? 110 c I 1 I 2 c c+ = c+0.91c = 180 =94.2 s=y-t-c = = c consume is a boowe 2

3 2. Assume a consume who has cuent-peiod income y = 200, futue-peiod income y = 150, cuent and futue taxes t = 40 and t = 50, espectively, and faces a maket eal inteest ate of = 0.05, o 5% pe peiod. The consume would like to consume equal amounts in both peiods; that is, he o she would like to set c 1 = c 2, if possible. Howeve, this consume is faced with a cedit maket impefection, in that he o she cannot boow at all that is, s 0. a. Show the consume s lifetime budget constaint and indiffeence cuves in a diagam. c + = c c = E 1 = (160,100) initial endowment point BE 1 D initial budget constaint a kink at E 1 because the consume cannot boow, and theefoe cannot consume moe than 160 (which is y-t) in the fist peiod. b. Calculate his o he optimal cuent-peiod and futue-peiod consumption, and optimal saving, and show this in you diagam., c c = =130.7 and s=y-t-c s= =29.3 In this case, the fact that the consume cannot boow does not matte fo the consume s choice, as the consume decides to be a lende. c. Suppose that eveything emains unchanged, except that now t = 20, and t = 71. Calculate the effects on cuent and futue consumption and optimal saving, and show this in you diagam. c + = c c =

4 Consume s lifetime wealth emains unchanged at Howeve, the budget constaint shifts to BE 2 F, The new endowment point is E 2 = (180,79). This change does not matte fo the consume again becau he chooses to be a lende. Consumption is still, c c = =130.7 But now savings is s=y-t-c= = 49.3 d. Now, suppose altenatively that y = 100. Repeat pats (a)-(c), and explain any diffeences. c + = c c = New the budget constaint is AE 1 D When the consume chooses the point on he budget constaint which is on the highest indiffeence cuve, any point on the line segment BE1 will do. Let he choose the endowment point E1 whee c =60 and c = 100. s = 0 The consume is cedit-constained( she would like to boow, but she cannot) When taxes change The budget constaint shifts to AE2G, The endowment point is E 2 = (80,79). Now the consume can choose c = c on the new budget constaint: c c = and =79.5 s=y-t-c= =0.5 Note that the ise in c is =19.5 is vey close to the tax cut (40-20=20) But thee is no change in lifetime wealth, The budget constaint fo the consume is elaxed. Fo tax cuts that leave lifetime wealth unchanged, the cuent consumption will Remain unchanged fo lendes Incease fo cedit constained consumes 3. Suppose in ou two-peiod model of the economy that the govenment, instead of boowing in the cuent peiod, uns a govenment loan pogam. That is, loans ae made to consumes at the maket eal inteest ate, with the aggegate quantity of loans made in peiod 1 denoted by L. Govenment loans ae financed by lump-sum taxes on consumes in the cuent peiod, and we will assume that govenment spending is zeo in the cuent and futue peiods. In the 4

5 futue peiod, when the govenment loans ae epaid by consumes, the govenment ebates this amount as lump-sum tansfes (negative taxes) to consumes. a. Wite down the govenment s cuent-peiod budget constaint and its futue-peiod budget constaint. No govenment spending in eithe peiod. In the fist peiod, the govenment must collect lump-sum taxes so that T = L. In the second-peiod, a lump-sum ebate is given: T =-(1 + )L b. Detemine the pesent-value budget constaint of the govenment. T + T' = 0 c. Wite down the lifetime budget constaint of a consume. s=y+l-t-c c =()(s+y -t -l) whee l epesents the size of the loan that the individual consume takes fom the loan pogam. c+ = y + y' - t - t' = y + y' - 1 n T ' T n=population d. Show that the size of the govenment loan pogam (i.e. the quantity L) has no effect on cuent consumption o futue consumption fo each individual consume, and that thee is no effect on the equilibium eal inteest ate. Explain this esult. The size, L, of the loan pogam, does not change the fact that the pesent value of tax collections must equal zeo. 5