Fall 2017 Social Sciences 7418 University of Wisconsin-Madison Problem Set 3 Answers

Transcription

1 ublc Affars 854 enze D. Chnn Fall 07 Socal Scences 748 Unversty of Wsconsn-adson roblem Set 3 Answers Due n Lecture on Wednesday, November st. " Box n" your answers to the algebrac questons.. Fscal polcy n an IS-L model Suppose the real sde of the economy s gven by: (.) = AD (.) AD = C + I + G + X I (.3) C = C + c( T ) T = T (.) I = I b Investment depends on nterest rate (.4 ) I = I + m nq Real exchange rate fxed (.) X = X + vq G = G and the monetary sector s gven by: Eq.No. Equaton Descrpton (.3) (.4) (.5) d s d s = Equlbrum condton = oney supply = k h oney demand For now, we gnore the external balance condton.. Solve for the IS curve, wth on the left hand sde. Show your work. Substtute n all the equatons nto equaton (.) = AD = C + c( T ) + I b + G + ( X + vq) ( I nq + m ) Solve for : = α [ A + X I + ( n + v) q b] where α = c + m, A C ct + I + G

2 . Solve for the L curve, wth on the left hand sde. Show your work. Substtute (.4) and (.5) nto (.3): k h h = = = h k k + h <L curve>.3 Graph the IS and L curves on a sngle graph. Show the vertcal ntercepts, the slopes, and the ntersecton of the two curves. L Slope = k/h.4 Solve for equlbrum ncome. Show your work. = αα [AA + XX IIII + (nn + vv)qq bb h + kk h ]

3 ( cc + mm) = [AA + XX IIII + (nn + vv)qq bb h + kk ] h ( cc + mm + bbbb/h) = [AA + XX IIII + (nn + vv)qq + bb h ] = αα [AA + XX IIII + (nn + vv)qq + bb h ] where αα cc+mm+ bbbb h.5 Calculate the change n ncome resultng from a gven change n government spendng on goods and servces, ΔG. Take the total dfferental of your answer to queston.3: b = α A + X + I + ( n + v) q + h Set all the other changes to zero, and set : A = G = αˆ G.6 Show graphcally what happens when government spendng s ncreased. Clearly ndcate the dstance of the curve shfts, and the amount of the ncome change. L 3

4 .7 Is the effect of government spendng on ncome greater or less n ths model, as compared to the smple Keynesan model? Explan why the dfference occurs, n words. The effect s less, because of crowdng out. As ncome rses, demand for money rses. Snce the money supply s fxed, the equlbratng nterest rate n the money market must rse. As a consequence, nvestment falls, and ths decreases aggregate demand and output relatve to what t would have been f nterest rates reman unchanged. As a consequence, output rses by only = αˆ G, rather than = α G..8 Answer.7 agan, f the nterest senstvty of money demand were zero. Explan why ths s true. When the nterest senstvty of money demand s zero, ncreases n ncome lead to ncreases n money demand that cannot be reduced by hgher nterest rates (hence, the L curve s vertcal). Only when nvestment declnes suffcently to offset the ncrease n ncome s money demand equal to the orgnal money supply, so that there s complete crowdng out of nvestment, and crowdng out of ncome. L.9 Answer.7 agan, f the nterest senstvty of nvestment were zero. Explan why ths s true. 4

5 L When the nterest senstvty of nvestment s zero, then the IS slope s nfnty (the IS curve s vertcal). A zero b mples that the lnk between nterest rates and the real sde of the economy s cut, so there s zero crowdng out of nvestment due to the hgher nterest rate resultng from hgher transactons demand for money, that s n turn assocated wth hgher ncome. Ths s shown n the fgure below.. onetary polcy n an IS-L model Usng the model lad out n Queston, Take the total dfferental of your answer to queston.3: b = α A + X + I + ( n + v) q + h Set all the changes to zero wth the excepton of the real money supply: b = h α. Show graphcally what happens when the real money stock s ncreased. Clearly ndcate the dstance of the curve shfts and the amount of the ncome change. 5

6 L L.3 Suppose nstead that the nterest senstvty of nvestment were very low. Show graphcally the effect upon output and nterest rates that results from an ncrease of the real money stock. Clearly ndcate the dstance of the curve shfts and the amount of the ncome change. L L 6

7 .4 Suppose the nterest senstvty of money demand were nfnte. Show graphcally the effect upon output and nterest rates that results from an ncrease of the real money stock. Clearly ndcate the dstance of the curve shfts and the amount of the ncome change. L L IS The L curve shfts sdeways..5 Assume non-zero values for the nterest senstvty of nvestment and money demand. Show graphcally how the Fed could keep the nterest rate constant as the government pursued an expansonary fscal polcy. Clearly ndcate the dstance of the curve shfts and the amount of the ncome change. What s the effect on output? The monetary authortes could shft around the L curve always keepng the nterest rate constant. Ths s accommodatve monetary polcy. In ths case, fscal polcy would be as effectve as t would be n the smple Keynesan model. In the graph below, a shft out n the IS curve s matched by an ncrease n the L curve suffcent to keep the nterest rate constant. 7

8 L L 3. olcy under Fxed Exchange Rates n the IS-L-B=0 model Suppose the economy s gven by the followng set of equatons. (.) = α [ A + X I + ( n + v) q b <IS curve> where α = c + m, A C ct + I + G (.6) k = + h h (.) m [( X I FA) ( n v) q * = ] κ κ <L curve> <B=0 curve> 3. Draw a graph of ntal equlbrum, where the goods and money markets are n equlbrum, as s the balance of payments. Assume that m/κ > k/h. 8

9 B=0 L m/ κ 3. Show what happens f the government decreases government spendng by ΔG, both mmedately, and over tme n the absence of central bank sterlzaton. Note, the money base changes by an amount equal to the change n foregn exchange reserves, B = FXRes = B = -ORT And the change n the money stock s a multple of the change n the money base, = constant B B=0 L L 9

10 B = Res = B = -ORT The decrease n government spendng shfts the IS curve n by α G (ths s ndcated by arrow []). At the new level of ncome and nterest rates, there s a balance of payments surplus, so that foregn exchange reserves ncrease, and n the absence of sterlzaton the money base ncreases, thereby ncreasng the money supply. Hence the L shfts out (as ndcated by arrow []), yeldng,. 3.3 Answer 3., assumng the central bank sterlzes changes n offcal reserves. At the new equlbrum, what s true about () the level of output; () the level of nvestment; () the real exchange rate; and (v) the trade balance? B=0 L The decrease n government spendng shfts the IS curve n by α G (ths s ndcated by arrow []). At the new level of ncome and nterest rates, there s a balance of payments surplus, so that foregn exchange reserves ncrease. Snce the central bank s sterlzng, the money base s unchanged, so the money supply s also unchanged. Hence the L stays n place, yeldng,. Income s lower, nvestment s hgher, real exchange rate s constant, and the trade balance s larger. 3.4 Redraw 3., and show the mpact of a monetary contracton, both mmedately and over tme. Assume over tme, captal flows are sterlzed. 0

11 B=0 L 3 L Explan why the process you lay out n 3.4 occurs. A decrease n to decreases the real money stock, shftng the L to the left (arrow []). Interest rates rse above that consstent wth external equlbrum; there s a balance of payments surplus so that foregn exchange reserves ncrease. Snce nflows are sterlzed, the money supply stays fxed at, so output and nterest rates stablze at 3 and Answer 3.4 f captal flows are not sterlzed. B=0 L 3 L 3 In ths case, the L shfts back to where t started, so that the orgnal ncome level and nterest rate are restored at 0 and 0. As captal flows n, foregn exchange reserves ncrease, ncreasng the money base, n the absence of sterlzaton. Consequently, the money supply ncreases, and the L shfts back out (arrow []).

12 4. olcy under Floatng Exchange Rates n the IS-L-B=0 model Suppose the exchange rate s floatng. I assume m/κ > k/h (m/κ < k/h s covered n the textbook; just reverse the example gven n the textbook). 4. Assume the economy descrbed above s under a floatng exchange rate regme. Show graphcally what happens f the government decreases government spendng. B=0 B=0 L B=0 4. Explan your answer to 4.. The IS curve ntally shfts n by α G (arrow []). The nterest rate () s above that requred to obtan balance of payments equlbrum (B=0 ) leads to a apprecaton of the real exchange rate to q. Ths n turn shfts nward the IS curve, and the B=0 curve upward (as denoted by arrow shfts []). Fnal ncome and nterest rate s and. 4.3 Now examne a monetary contracton from ntal equlbrum, carefully dstngushng between ntal mpact, and the effect over tme. The L shfts n frst (arrow []). In ths ntal equlbrum wth lower ncome, the resultng nterest rate () s greater than requred for external equlbrum (B=0 ). As a consequence, there s an ncpent balance of payments surplus and the exchange rate apprecates. The resultng decrease n net exports means that the requred nterest rate for external equlbrum rses (the B=0 curve shfts upward arrow []). The decrease n net exports means that domestc aggregate demand falls, and the IS curve shfts n (arrow []). The equlbrum settles at ncome level and nterest rate.

13 B=0 q B=0 L L B=0 4.4 Explan why monetary polcy has a larger effect n ths open economy as opposed to that n a closed economy. Wth floatng exchange rates, monetary polcy can affect aggregate demand through two channels (nvestment, and the trade balance va the exchange rate), rather than only nvestment, whch s the only channel n closed economes 4.5 Answer 4., assumng κ =. L B=0 a854ps3a_f7.doc..07 The decrease n government spendng shfts n the IS curve (arrow ). The resultng nterest rate s below the nterest rate consstent wth external balance (0). The balance of payments defct of nfnte magntude nduces an mmedate currency deprecaton that shfts out the IS curve (arrow ). Only when the IS curve returns to ts prevous poston wll equlbrum be restored. 3