Quz 2 nswers PRT I 1) False, captal ccumulaton alone wll not sustan growth n output per worker n the long run due to dmnshng margnal returns to captal as more and more captal s added to a gven number of workers, the ncrements to output become smaller and smaller and ultmately level off. In the long run, techncal progress wll be needed to sustan growth. 2) Part a) False. The company s value added s $700 - $200 n wages and $500 n profts. It s contrbuton to US GNP s therefore only $200. I gave 3 ponts for It contrbutes only $200 to US GNP or It contrbutes value added to GDP rather than GNP or Its contrbuton to US GNP s not equal to ts value added snce profts are subtracted from GDP when calculatng GNP. 0 ponts for anythng along the lnes of The company contrbutes nothng to US GNP snce t s foregn owned. Part b) True. The company s value added does not contrbute anythng to the GDP of the country whch the busnessman hals from, snce the value s not added wthn that country s domestc borders. 3) If nether consumpton nor nvestment are affected by the nterest rate, the equlbrum n the goods market s gven by = I() + () + G, ndependent of the nterest rate level. Monetary polces can only affect the equlbrum output n the short run through changng the nterest rate level. The nterest lnk s not present n ths case, so the monetary polcy s completely neffectve. 4) n ol shock affects the markup level (µ) and then the natural unemployment rate (u n ) and the natural output level ( n ). Te output level s affected both n the short run and n the long run. If tax revenues are proportonal to output (T=t), the revenues are gong to be affected and therefore the udget Defct (D=G-T).
PRT II 1) u t -u t-1 =β(g y -g yt ) : Okun s law Ths equaton recognzes the fact that productvty of labor () and labor tself (L) are growng at the combne rate of g y (normal growth rate). So unemployment rate decreases every tme output growth rate s above the normal rate. The relaton s derved from the producton functon =N so u = 1-/L. g yt =g mt -π t : D-relaton Ths equaton s derved from the - model. Increasng the real amount of money ncreases the level of output n equlbrum. The above equaton s descrbng that relaton n rate of growth terms, assumng the relaton between the equlbrum output level and the real amount of money s lnear (=ϑm/p). π t -π t-1 =-α(u t -u n ) : Phllps curve The Phllps curve s the equvalent of the S-curve n growth rate terms. It s descrbng the fact a decrease n unemployment leads to hgher wages and then prces. 2) The medum run equlbrum s attaned when u t =u t-1, unemployment rate s constant n the medum run. u t =u t-1 Æ g yt =g y Æ π t =g m -g y Æ π t =π t-1 =π e t Æ u t =u n If the normal growth rate ncreases (g y >g y ), the new medum run equlbrum s g yt =g y Æ π t =g m -g y < g m -g y. gan, π t =π t-1 =π e t Æ u t =u n Graphcally π g m -g y g m -g y u n u The causes of nflaton n the medum run are purely monetary. Inflaton s equal to the excess of nomnal money supply. Intutvely, money demand and output are proportonal so an ncrease n the normal output growth rate s an ncrease n the real money demand. Keepng the growth rate of nomnal money constant, the equlbrum s attaned wth a lower growth rate of prces.
3) lower money growth rate s only affectng nflaton n the medum run. From the prevous answer, the ntal and medum run equlbrum are as follow. Intal MR equlbrum (pont n the graph): u =u n, g y =g y, π Α =g m -g y New MR equlbrum (pont n the graph): u = u =u n, g y =g y =g y, π Β =g m -g y < π Α In the transton, gven that adaptatve expectatons prevent the ndvduals to adjust nflaton rght away to the new medum run equlbrum, the nomnal money growth decreases more than the nflaton rate and the output growth rate decreases. That leads to a hgher unemployment rate, whch n turns nduces a decrease n nflaton. We can see that graphcally (pont 2 n the graph): t tme 1 (before the change n g m ), the economy s n ts MR equlbrum and the P and OL+D curves are as follow: P: π t =-π t-1 - α(u t -u n ), wth π t-1= π t OL + D: π t = g m -g y + (u t -u t-1 ) /β, wth u t = u t-1. t tme 2 (when gm changes to ts new level), the P and OL+D curves are as follow P: π t =-π t-1 - α(u t -u n ), wth π t-1= π t OL + D: π t = g m -g y + (u t -u t-1 ) /β, wth u t = u t-1. π OL+D 1 2 OL+D 2 P 1 =P 2 u n u The nomnal money growth changes once and for all from g m to g m. The real money s growth rate s endogenous, equal to g m - π t (notce that the real money growth s equal to the output growth g yt snce the money demand s growng at the same rate as output). In the very short run (pont 2) the nflaton decreases less than the drop n nomnal money growth, so the real money supply decreases. Then, t oscllates around ts steady state tll t gets to ts medum run equlbrum were the real money growth s equal to g y. g m/p g y t 2 t
4) Sacrfce rato accounts for the cost of a desnflatonary polcy n terms of unemployment. It s the number of pont years of excess unemployment that an economy has to suffer n order to acheve a one-percentage pont decrease n nflaton. If ndvduals form expectatons about future nflaton based on prevous year s nflaton rate, ths rato s equvalent to the nverse of the slope of the Phllp urve (1/α). In ths case, the sacrfce rato s not affected by the degree of gradualsm of the desnflatonary polcy, snce the number of pont years of excess of unemployment s not affected. So, polcy makers can choose between a gradual desnflatonary polcy that nvolves a lower excess unemployment rates for a long tme or a hgh excess of unemployment for a short perod of tme. 5) If the Fed has a hgh degree of credblty, the announcement of a desnflatonary polcy may nduce lower expected nflaton rate. In the extreme case where ndvduals form ther expectatons accordng to the Fed s nflaton target, the transton towards the new medum run equlbrum s nstantaneous (n queston 3, the economy jumps from equlbrum to ) wthout sufferng from excess of unemployment. In ths extreme case, the sacrfce rato s zero. PRT III. 1) = Intal medum run equlbrum Short run equlbrum Fnal medum run equlbrum P e P S D vs vs vs < > = < > = I I <I I >I I =I P P <P P <P P <P > < = M/P M/P <M/P M/P >M/P M/P =M/P n
decrease n the nomnal supply of money leads to an ncrease n the nterest rate level n order to nduce a decrease n the demand of money and equlbrate the money market. That reduces prvate nvestment, whch n turn leads to a decrease n the equlbrum output and therefore consumpton (frst movement n the curve and shftng the D curve). decrease n output s followed by a drop n prces so, even n the very short run, the moves back a lttle. In the short run (pont ), the output s below ts natural level (so consumpton s also below ts orgnal level) and the nterest s hgher than n pont, so the prvate nvestment s also lower. In the short run equlbrum (pont ) prces are below the expected prce level, so wage setters wll revse ther expectatons down tll they get to the actual prce level (consecutve shfts n the S curve). The pont were the expected prce level s equal to the actual prce level concdes wth the pont were output s back to ts natural level (pont ). In ths fnal medum run equlbrum, the overall reducton n the prce level completely offset the monetary contracton and the real amount of money s back to ts orgnal level, so s output, consumpton, nvestment and nterest rate. 2) Intal medum run equlbrum Short run equlbrum Fnal medum run equlbrum P e P S D vs vs vs > < = > < = I I?I I <I I <I P P >P P >P P >P > > > M/P M/P <M/P M/P <M/P M/P <M/P n
In the short run (pont ), the ncrease n government expendture results n an output expanson (shft and D curves), whch leads to an ncrease n prces (frst shft n the curve). The nterest rate has to go up n order to restore the equlbrum n the money market.e., frst, an ncrease n the nterest rate s needed to compensate the effects of the output expanson on the money demand, and second, to reduce the demand of money even further and equalze t to the smaller amount of real money-. The evoluton of total nvestment n the short run s ambguous: the fscal expanson s partly on publc nvestment but hgher nterest rate reduces the prvate nvestment. In pont, the expected prce level s below the actual prce so wage setters are revsng ther expectatons tll they match wth actual prce level (consecutve shfts n the S curve). t that pont (pont ), output goes back to ts natural level (also consumpton does), but the prce level ncreases even more resultng n further real money contractons (consecutve shfts n the curve). The effect on nvestment s not ambguous any more: =+I+G, so f and are n ther ntal values and G s hgher than t was n pont, t has to be that I went down. In effect, the nterest rate keeps on ncreasng tll the drop n prvate nvestment s such that total nvestment decreases n the same amount that the government expendture n wages ncreased. 3) W/P PS WS P e P n 2 n 1 S D 1 2 u n u n u Intal medum run equlbrum Short run equlbrum Fnal medum run equlbrum vs vs vs < < < < < < I I <I I <I I <I P P >P P >P P >P > > > M/P M/P <M/P M/P <M/P M/P <M/P
n ncrease n ol prces shfts the PS curve down, snce prces are gong to be hgher for any level of wages (decrease n real wages). Therefore, the natural unemployment rate ncreases from u n 1 to u n 2 and the correspondng natural output level gos down from n 1 to n 2. That s, the S curve moves to the left resultng n hgher prces and lower output n the short run. That ncrease n prces reduced the real amount of money (frst shft n the curve) ncreasng the nterest rate and therefore, reducng prvate nvestment. t pont then, output, consumpton and nvestment are lower. In pont prces are above the expected prce level. So wage setters revse ther expectatons up tll they match the actual prce level (consecutve shfts n S and the consequent shfts n ). t that pont (pont ), output concdes wth ts new natural level. oncludng, a permanent ncrease n ol prces wll nduce an ncrease n prces and a decrease n nvestment both n the short run and n the medum run.