2) In the medium-run/long-run, a decrease in the budget deficit will produce:

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1 4.02 Quz 2 Solutons Fall 2004 Multple-Choce Questons ) Consder the wage-settng and prce-settng equatons we studed n class. Suppose the markup, µ, equals 0.25, and F(u,z) = -u. What s the natural rate of unemployment n ths economy? A) 0.2 ) 0 C) 0.25 D) 0. ) 0.5 Answer: A). The wage determnaton equaton s W=P e F(u,z) or W=P e (-u). Snce we are n medum-run/long-run equlbrum, P= P e W=P(-u). The prce settng equaton s P=W(+µ). Therefore, W/P=/(+0.25)=0.8. From the wage determnaton equaton, we get that W/P=0.8=-u n. Therefore, u n = ) In the medum-run/long-run, a decrease n the budget defct wll produce: A) No effect ) An ncrease n nvestment C) An ncrease n consumpton D) A decrease n output ) No effect on the prce level Answer: ). A decrease n the budget defct produces a shft of the AD curve to the left. So, n the medum-run/long-run, we wll get a decrease n the prce level, P, whle output wll reman unchanged. (Agents are expectng lower prces n the future. Nomnal wages fall, and therefore the actual prce level decreases. So, the AS curve shfts down, keepng output constant.) From the IS-LM equlbrum, we wll have that the nterest rate wll decrease. Thus, nvestment wll ncrease, consumpton s ambguous (f the decrease n the budget defct s acheved usng an ncrease n taxes, consumpton wll decrease, f not, t wll reman constant). Thus, the correct answer s ).

2 3) Suppose that workers n the Republc of Communa are hghly unonzed, whle workers n the Republc of Indvduela are not. In all other respects, the two countres are exactly the same. Whch statement s true? A) Communa s lkely to have a hgher natural level of output than Indvduela. ) Communa s lkely to have a hgher natural rate of unemployment than Indvduela. C) Wages are probably lower n Communa than n Indvduela. D) In the short-run, the prce level s always lower n Communa than n Indvduela. ) In the short-run, output s always hgher n Communa than n Indvduela. Answer: ). In our model of the labor market, the level of unonzaton s captured by the varable z, whch affects wages postvely (the hgher unonzaton, the more collectve barganng power workers have, whch most lkely leads to hgher wages). Recall that the natural level of unemployment s defned by assumng that P = P e and by fndng the ntersecton of the wage settng relaton W = P e F(u,z) and the prce settng relaton P = (+µ)w. Thus, F(u n,z) = /(+µ). Hgher unonzaton means that z s hgher, whch shfts up the wage settng relaton and leads to a hgher natural rate of unemployment. W/P /(+µ) u n Prce-settng relaton Wage-settng relaton Wage-settng relaton u n u e e 4) Suppose the Phllps curve s gven by π t = π t u t whereπ t = θπ t Assume that only for the frst two perods (t= and t=2) people form ther expectatons usng θ=0. From t=3 on, they start usng θ= forever. Assume that the government stll wants to keep unemployment at 2%. What s the expected rate of nflaton for t=4? A) 2% ) 4% C) 8% D) 2% ) 6% Answer: C). π t π t- =0. 3(0.02)=0.04 (Inflaton goes up every perod by 4%.) π 2 =0.04 π 3 = 0.08 π 3 e =0.04 π 4 =0.2 π 4 e =0.08

3 5) ou observe that the domestc nterest rate ncreases from 5% to 5%, and you are n a fxed exchange rate system, then ths mples that A) The level of the nternatonal nterest rate ncreased by 5% ) Agents are expectng a nomnal apprecaton of 5% C) Agents are expectng a nomnal deprecaton of 5% D) oth A) and ) ) oth A) and C) e * t+ t Answer: ). Consder the UIP: t = t +. So f the nterest rate ncreases by t 0%, the rght-hand sde of the equaton should also ncrease by 0%. Thus, A) and C) are not enough by themselves. Opton ) produces the opposte effect. Thus, ) s the correct answer.

4 Long Queston I (40/00 ponts) Open conomy IS-LM Assume that the economy s descrbed by the followng model: C = c 0 + c ( T), where C s consumpton; s ncome; T represents taxes; and c 0 and c are postve constants I = b b 2, where I s nvestment; s the nterest rate; and b and b 2 are postve constants G = G, where G s a postve constant IM = m, where IM s mports; and m s a postve constant X = x *, where X s exports; * s foregn ncome (exogenous); and x s a postve constant The LM equaton n ths economy s = m (m M s ), where M s s money 2 supply (M s >); and m and m 2 are postve constants Let P*=P= Assume that the Marshall-Lerner condton s satsfed (that s, followng a deprecaton of the exchange rate, the trade balance mproves). Note, gven that IM = m and X = x * the Marshall-Lerner condton actually does not hold. NX are actually equaton to x * -- ε(m ), and therefore only the only effect of a deprecaton s a prce effect. As the currency deprecates, ε ncreases and NX decrease (not ncrease!). Whether you used the supposton that the Marshall-Lerner condton holds here or f you used the expressons gven to you, we gave you full credt. Part I. Fxed xchange Rate. Assume for now that the real exchange rate s fxed at one (ε = ). Assume that the nterest rate party condton holds, and the nterest rate n the foregn country s *.. Fnd the expresson for equlbrum ncome. (2 ponts) = C + I + G + X - εim = c 0 + c ( T) + b b 2 * + G + x * ()( m ) = (c 0 c T b 2 * + G+ x *) c b + m 2. Calculate the change n output (), net exports (NX), the domestc nterest rate (), and the real exchange rate f taxes ncrease by T. Also draw a dagram. (5 ponts) If there s an ncrease n taxes, the resultng change n ncome would be

5 = T (output decreases by T). + m + m NX = X εim = x * m NX = m m m NX = T (net exports ncrease by ; the effect on net + m + m exports comes through the mport sde). The domestc nterest rate and the real exchange rate do not change, because of the fxed exchange rate regme. So, =* and ε= (Note that snce ε=p*/p and P=P*=, ε==.) Money supply must decrease to accommodate the fscal contracton (monetary polcy s endogenous). If t doesn t, the nterest rate,, wll decrease to (whch mples a large deprecaton of the exchange rate). ut that would break the peg. To brng the nterest rate back up to the level *, the LM curve must shft up. LM LM 0 =* IS 0 UIP IS 0 3. Calculate the effect of a change n foregn output (*) on domestc output (), net exports (NX), the domestc nterest rate (), and the real exchange rate. (Assume that c + b <.) (4 ponts) x = > 0 f c * + b < + m, whch s true because we are gven + m that c + b <. In general, there are two opposng effects: on one hand, an ncrease n foregn output, *, ncreases foregn demand, and thus ncreases domestc exports, whch ncreases. On the other hand, hgher domestc GDP leads to hgher mports. However, we assume that the export effect domnates (because the Marshall-Lerner condton holds).

6 To answer the part about net exports, we need to solve for NX n terms of only foregn output. m NX = x * m = x * (c 0 c T b 2 * + G+ x *) + m NX m = x( ) > 0 f c * + b < whch s gven. (Alternatvely, we can + m m wrte ths as NX= x ( ) * + m.) Agan, there are two opposng effects: on one hand, an ncrease n foregn output, *, ncreases exports. On the other hand, hgher exports result n hgher domestc GDP, whch leads to hgher mports. However, agan, the frst effect domnates (because the Marshall-Lerner condton s satsfed). The domestc nterest rate and the real exchange rate do not change, because of the fxed exchange rate regme. So, =* and ε= 4. Suppose the Central ank mplements expansonary monetary polcy. What effect wll ths have on output (), net exports (NX), the domestc nterest rate (), and the real exchange rate. Also draw a dagram. (4 ponts) xpansonary monetary polcy has no effect on any of the four varables mentoned n the queston, because monetary polcy s endogenous n a fxed exchange rate regme. LM LM =* IS = Interest party condton

7 Part II. Flexble xchange Rate. Assume that the exchange rate s allowed to float, the nterest rate party condton holds, and that e =. 5. What s the effect on output (), net exports (NX), the domestc nterest rate (), and the real exchange rate f taxes ncrease? Use ntuton and draw a dagram (no calculatons requred). (5 ponts) If taxes ncrease, the IS curve shfts to the left. Therefore, an ncrease n taxes wll lead to a decrease n output), a decrease n the nterest rate, and a deprecaton of the exchange rate. What happens to net exports? If you assumed that the Marshall- Lerner condton holds, then net exports ncrease followng ths deprecaton, because (NX=NX(,*,) as output decreases, net exports ncrease, and as the exchange, +, + rate ncreases (a deprecaton), net exports ncrease,.e. the two effects go n the same drecton. On the other hand, f you used the expressons gven to you, the effect on net exports s ambguous. Output ncreases and the exchange rate ncreases. In the expresson x * -- ε(m ), decreases, whle ε ncreases, makng the effect ambguous. So, we gave credt f you sad that the effect on NX s postve or ambguous. IS IS LM Interest rate party condton 6. What s the effect of an ncrease n foregn output on domestc output (), net exports (NX), the domestc nterest rate (), and the real exchange rate? Use ntuton and draw a dagram (no calculatons requred). (4 ponts) If foregn output ncreases, the IS curve shfts to the rght, because foregn demand rses and they buy more of domestc exports. Therefore, an ncrease n foregn output wll lead to an ncrease n domestc output, an ncrease n the nterest rate, and an apprecaton of the exchange rate. What happens to net exports? NX=NX(,*,), +, + the drect channel s that as foregn output ncreases, net exports ncrease. ut note that there s also an ncrease n domestc output and a decrease n the exchange rate (an apprecaton). So, theoretcally, the net effect on net exports s ambguous

8 (whether or not you used the fact that the Marshall-Lerner condton holds). However, emprcally the effect s unambguously postve (NX ncrease as * ncreases). So, we gave credt f you sad that the effect on NX s postve or ambguous. IS IS LM Interest rate party condton 7. What s the effect of an ncrease n the money supply on output (), net exports (NX), the domestc nterest rate (), and the real exchange rate? Use ntuton and draw a dagram (no calculatons requred). (4 ponts) If money supply ncreases, the LM curve shfts down and to the rght. Therefore, output ncreases, nterest rate decreases, and the exchange rate deprecates. What happened to net exports? If you use the assumpton that the Marshall-Lerner condton holds, the effect s ambguous. Agan, remember that NX=NX(,*,). In, +, + ths case, output ncreases, whch decreases net exports, but on the other hand, the exchange rate ncreases (a deprecaton), whch ncreases net exports. What f you used the math? NX= x * -- ε(m ). We have that ncreases, and ε ncreases. Ths means that NX decreases unambguously. So, we gave credt f you sad that the effect on NX s negatve or ambguous. LM LM IS Interest party condton

9 8. Suppose that nvestors expectatons of the future exchange rate ncrease ( e ncreases). However, the Central ank does not want the exchange rate to deprecate today. What effect wll ths have on the economy (no calculatons requred)? Draw a dagram. (5 ponts) The fact that nvestors expect an ncrease n e n the future wll shft the nterestrate-party-condton (UIP) curve up and to the rght. In order to keep the exchange rate from deprecatng today, the Central ank wll have to enact a monetary contracton (decrease money supply). Ths wll shft the LM curve up and to the left, brngng the nterest rate up to the level ( ) at whch the exchange rate s at ts orgnal level ( ). LM LM 0 =* UIP IS UIP 0 0 Note that we also gave credt to those of you who sad that the IS curve would shft f response to the changng expectaton. Ths s a possble secondary effect that we dd not focus on.

10 Long Queston II (40/00 ponts) Closed conomy AS-AD Prce Settng Relaton: Wage Settng Relaton: Goods Market: Fnancal Market: W = P e F (u,z) P = ( + µ ) W = C(, T) + I(, ) + G M s = M d (, ) P. Fnd the aggregate supply relaton. Descrbe the channel through whch the AS curve slopes up/down. (5 ponts) Puttng together the prce settng relaton and the wage settng relaton, AS: P = P e ( + µ ) F (u,z) The AS curve slopes up. (There s a postve relatonshp between P and.) Why? Let us start at a pont on the AS curve. Now, f we were to ncrease, then u decreases snce u = -/L. A decrease n u would ncrease W. Ths s because wth a lower unemployment rate, people demand hgher wages. When W ncreases, P ncreases snce W s part of the nput cost for frms. Therefore, there s a postve relatonshp between and P. 2. Assume that the economy s at a pont such that the unemployment rate s equal to the natural rate of unemployment. What does ths mply about the prce level and output? xplan. (5 ponts) When P = P e, we can set the prce settng and wage settng relaton to each other. Ths gves us u N (natural rate of unemployment). In other words, f u = u N, then P = P e. If = N, then u = (/L). (See pages 36-38) Therefore, f u = u N, then = N. The three condtons (u = u N, = N, and P = P e ) gve us the same nformaton; the economy s at the medum-run/long-run equlbrum.

11 3. If the Fed carres out a monetary contracton, what happens n the short-run and the medum-run/long-run? Start from pont A where P = P e. Label the followng: all curves ncludng (IS 0, IS SR, IS MR, LM 0, LM SR, LM MR, AD SR, AD MR, AS SR, AS MR ), the short-run equlbrum as pont, the medum-run/long-run equlbrum as pont C, and output assocated wth natural rate of unemployment. (0 ponts) short-run medum - run LM LM SR LM 0 LM LM SR LM 0 = LM MR A A = C IS 0 IS 0 SR N SR N P AS 0 P AS 0 AS MR A A AD 0 AD 0 AD SR C AD MR = AD SR SR N MR = N

12 4. What does neutralty of money mply about the effectveness of contractonary monetary polcy n affectng output n the short- and medum-run/long-run? Defne neutralty of money. (4 ponts) In the short-run, a monetary contracton leads to a decrease n output, an ncrease n the nterest rate, and a decrease n the prce level. However, over tme, the prce level decreases further as the changes n expected prce affect the actual prce level n the economy. In the medum-run/long-run, the decrease n nomnal money has no effect on output or on the nterest rate because the decrease n nomnal money s matched by a proportonal decrease n prces. Ths phenomenon s called the neutralty of money. Therefore, the neutralty of money holds only n the medumrun/long-run.

13 5. If the prce of ol ncreases sharply, what happens n the short-run and the medumrun/long-run? Start from pont A where P = P e. Label the followng: all curves ncludng (IS 0, IS SR, IS MR, LM 0, LM SR, LM MR, AD SR, AD MR, AS SR, AS MR ), the short-run equlbrum as pont, the medum-run/long-run equlbrum as pont C, and output assocated wth natural rate of unemployment. (0 ponts) short-run medum - run LM SR LM 0 LM MR LM SR LM 0 C A A IS 0 IS 0 N new SR N old N new SR N old AS MR P AS SR AS 0 P AS SR AS 0 C A A AD 0 AD 0 N new SR N N new SR N

14 5. 6. Indcate whether these varables ncrease, decrease or reman the same when the prce of ol rses sharply. (ou may use arrows.) (6 ponts) n P I P e short-run decreases decreases ncreases ncreases decreases no change medumrun/long-run decreases no change ncreases ncreases decreases ncreases

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