Problem Set 5 Answers

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1 conomcs 302 Menze D. Chnn Sprng 2012 Socal Scences 7418 Unversty of Wsconsn-Madson Problem Set 5 Answers Due n lecture on Wednesday, May 9th. Be sure to put your name on your problem set. Put boxes around your answers to the algebrac questons. Chapter 17, Problem 3 a. The IS curve shfts rght. b. The LM curve shfts rght. c. There are three effects. Frst, an ncrease n expected future taxes tends to reduce expected future after-tax ncome (for any gven level of ncome), and therefore to reduce consumpton. Ths effect tends to shft the IS curve to the left. Second, the ncrease n future taxes (a defct reducton program) tends to reduce real nterest rates n the future. The fall n the expected future nterest rate tends to shft the IS curve to the rght. Thrd, the fall n future real nterest rates leads to an ncrease n nvestment n the medum run and to an ncrease n output n the long run. The ncrease n expected future output tends to shft the IS curve to the rght. The net effect on the IS curve s ambguous. Note that the model of the text has lump sum taxes. If taxes are not lump sum, the tax ncrease may ncrease dstortons n the economy. These effects tend to reduce output (or the growth rate). d. The IS curve shfts to the left. Chapter 19, Problem 7 a. Y = C + I + G + X IM Y=c 0 +c 1 (Y-T)+d 0 +d 1 Y+G+x 1 Y*-m 1 Y Y=[1/(1-c 1 -d 1 +m 1 )][c 0 -c 1 T+d 0 +G+x 1 Y*] b. Output ncreases by the multpler, whch equals 1/(1-c 1 -d 1 +m 1 ). The condton 0< m 1 < c 1 +d 1 <1 ensures that the multpler s defned, postve, and greater than one. As compared to the orgnal multpler, 1/(1+c 1 ), there are two addtonal parameters: d 1, whch captures the effect of an addtonal unt of ncome on nvestment, and m 1, whch captures the effect of an addtonal unt of ncome on mports. The nvestment effect tends to ncrease the multpler; the mport effect tends to reduce the multpler. c. When government purchases ncrease by one unt, net exports fall by m 1 ΔY= m 1 /(1-c 1 - d 1 +m 1 ). Note that the change n output s smply the multpler. d. The larger economy wll lkely have the smaller value of m 1. Larger economes tend to produce a wder varety of goods, and therefore to spend more of an addtonal unt of ncome on domestc goods than smaller economes do. e. ΔY ΔNX small economy (m 1 =0.5) large economy (m 1 =0.1) 2 0.2

2 f. Fscal polcy has a larger effect on output n the large economy, but a larger effect on net exports n the small economy. Queston We have two equatons for ncome determnaton: To solve for domestc demand, we plug n from the second equaton nto the frst, to get: Where Solvng for Y, we get: 1 When Δ,Δ ncrease by 1, then ncreases by / If the foregn government decreases spendng by 1 unt, but the domestc government ncreases spendng by 1 unt, then the multpler s /1. Notce that ths multpler s postve f 1. In other words, f the margnal propensty to export s suffcently small, then ths condton holds! 3.3 Bascally, what I was thnkng about s that one naton s consumpton can drve another country s ncome. Queston The equatons are: 1 1 Whch, after pluggng n numbers, we get / Ths s just two equatons, and two unknowns, so solvng ths, we get Y=5/2,Y*= The Marshall-Lerner condtons tell us when deprecatng the currency ncreases net exports. In ths case, net exports s just / and ths s ncreasng when decreases, so t does satsfy the Marshall-Lerner condtons. 4.3 The new equatons are: / The prevous domestc trade surplus was -1/6 (whch means that the foregn trade surplus s 1/6). Solvng for the above two equatons, Y=8/3, Y*=7/2. The new trade surplus s -1/9, so that the trade defct has decreased!

3 4.4 You want to plot Z=Y, Z=Y/3+10/6, Z=Y/3+16/9 for ncome determnaton, and NX=-Y/3+4/6, NX=-Y/3+7/ Notce that f the domestc country runs a defct, then the foregn country must run a surplus of the exact same sze (though opposte sgn!). Foregn GDP goes from 4 to 3.5 when the currency deprecates! 4.6 When the currency deprecates, domestc ncome ncreases and the domestc trade defct decreases. On the other hand, when the currency deprecates, foregn ncome and the foregn trade surplus falls. Clearly, there s an ncentve for countres to deprecate ther currency! 5. Consder an economy on a flexble exchange rate, and descrbed by the IS-LM-UIP framework n Chapter 20 of the textbook. 5.1 Suppose autonomous nvestment collapses. Usng the IS-LM-UIP dagrams, show what happens to nterest rates, output, and the exchange rate.

4 LM M 0, P 0 IRP relaton 0 1 IS b 0 IS b 0 Y 1 Y 0 LM 1 0 The reducton n autonomous nvestment (b 0 declnes to b 0 ) shfts the IS curve nward (gray arrow). The nterest rate declnes, so wth the foregn nterest rate * and the future expected exchange rate constant, the exchange rate deprecates. 5.2 What could monetary polcy do to restore output to pre-shock levels? LM M 0, P 0 LM M 1, P 0 IRP relaton 0 2 IS b 0 IS b 0 Y 0 LM If the monetary authorty ncreases the money supply to M 1, then the LM curve wll shft out (black arrow), drvng down the nterest rate to 2, drvng down the exchange rate to 2. As the nterest rate drops, nvestment rses; and as the exchange rate drops, net exports rse. 6. Consder the same economy as n problem 5, but assume that t s a small economy relatve to the other economy n the world (wth nterest rate *). 6.1 Suppose the foregn economy s nterest rate rses. What happens to the home economy? Show usng the IS-LM-UIP framework.

5 Recall the IRP relatonshp s gven by: (1 + ) = (20.4) t e t t * + 1 (1 + t ) Rearrangng: (1 + (1 + t ) = * t ) e t+ 1 t So when the foregn nterest rate * rses, then IRP relatonshp rses by the fgure below. t e t+1. Ths s shown n LM M 0, P 0 IRP relaton * IRP relaton * 1 0 IS * IS * Y 0 Y 1 LM 1 0 The shft up n the IRP relaton (gray arrow) nduces a deprecaton of the exchange rate, 0 to 1 ; wth prce levels fxed, the real rate deprecates, nducng a shft outward n the IS curve (gray arrows). Output rses from Y 0 to Y Suppose the home economy s government s commtted to keepng the exchange rate,, constant aganst the foregn country s. What does the home country have to do n order to acheve that objectve?

6 LM M 1, P 0 LM M 0, P 0 IRP relaton * 1 IRP relaton * 0 IS * Y 1 Y 0 LM 0 The same upward shft n the IRP relaton occurs (gray vertcal arrow). The central bank s e commtted to keepng the exchange rate at 0 (and t + 1 remans constant), and can only do that by rasng the nterest rate to 1. And that requres the central bank shrnk the money supply to M 1 thereby shftng the LM curve back (gray horzontal arrow). 7. Suppose the economy s gven by AD and AS equatons 21.1 and 21.2 n the textbook, assumng the economy s on a fxed exchange rate. You can assume the current perod s expected prce level equals the prevous perod s prce level. 7.1 Draw the AD AS dagram. 7.2 Suppose autonomous nvestment collapses. What happens, both n the short run, and over the long run? P AS AS AS fnal P 0 P 1 P 2 P Fnal AD b 0 AD b 0 Y 1 Y 2 Y n Y

7 The answer to 7.1 s the orgnal sold lnes, wth output at Y n and prce level at P 0. The answer to 7.2 s shown by the nward shft of the AD curve (gray arrow), n the short run. The prce level falls to P 1. In perod 2, the AS curve shfts down to ntersect the Y n lne at P 1, and the output level rses to Y 2. Over tme, the prce level keeps on fallng, and the AS curve shfts out, untl output returns to Y n. 7.3 What happens to nvestment n the medum run? As the prce level falls, the real money supply ncreases, and so the nterest rate falls. Hence, nvestment rses. 7.4 What happens to the real exchange rate n the medum run? The real exchange rate s P/P*, so as P falls, the real exchange rate falls. 7.5 What s an alternatve approach to restorng full employment? P AS P 0 P 1 AD b 0 = AD G, b 0 AD b 0 Y 1 Y n Y As the AD curve shfts n, expansonary fscal polcy can be mplemented, so the AD shfts back to where t started from, so output s restored. Chapter 12, Problem 6 a.. People have asked questons about ths one. We talked prmarly about captal and steady-states when populaton was not growng. To thnk about a model where there s populaton and technology growth, we have to have I=δK+(g A +g N ) K. Ths s because deprecaton lowers the stock of captal, whle ncreasng populaton and technology requres

8 that you ncrease the captal stock to match the new populaton. Hence, solvng for the balance equaton s(y/n)=[δ+(g A +g N )]( K/(AN)), we get K/(AN) = (s/(δ+g A +g N )) 2 = 1. Y/(AN)= (K/AN) 1/2 =1. g Y/(AN) = 0 v. g Y/N = g A =4% v. g Y = g A +g N =6% b.. K/(AN) = (s/(δ+g A +g N )) 2 = Y/(AN)= (K/AN) 1/2 =0.8. g Y/(AN) = 0 v. g Y/N = g A =8% v. g Y = g A +g N =10% An ncrease n the rate of technologcal progress reduces the steady-state levels of captal and output per effectve worker, but ncreases the rate of growth of output per worker. c.. K/(AN) = (s/(δ+g A +g N )) 2 = Y/(AN)= (K/AN) 1/2 =0.8. g Y/(AN) = 0 v. g Y/N = g A =4% v. g Y = g A +g N =10% People are better off n case a. Gven any set of ntal values, the level of technology s the same n cases (a) and (c), but the level of captal per effectve worker s hgher at every pont n tme n case (a). Thus, snce Y/N=AY/(AN)=A(K/(AN)) 1/2 =A 1/2 (K/N) 1/2, output per worker s always hgher n case (a). e302ps5a_s12.doc