1 4 .02 — Fa ll 2 0 01 — QUIZ 3 A nswer sPA RT 1: True, False or Uncertain. (30 points)a. TRUE. The natural level of output is defined as the level of output con-sisten t with equilibrium in the labor market when the actual price levelis equal to the expected price level. The Aggregate Supply relation is thelevel of output consistent with equilibrium in the labor market given eachlevel of prices. Therefore, Ynis simply a point on the AS curve (the onethat corresponds to Pe).b. FALSE. Changes in fiscal policy will shift Aggregate Demand. As result,prices will c hange in the short run and the AS will shift over time untilit intersects AD at the natural level of output again. In the medium runequilibrium, output is back to the same initial level (Yn), but the interestrate is now different. Therefore, investment will necessarily have changed.(A fiscal expansion increases the int erest rate in the medium run and re-duces investment; a fiscal contraction raises investment).c. FALSE. An increase in unemplo yment benefits (z,intermsoftheAS-AD model we have seen) will reduce the natural level of output. In themedium run, output will go down to its new natural level —so the increasein z will indeed have permanent effects on output in the medium run.d. FALSE. The expectations-augmented Phillips Curve implies that main-taining a rate of unemplo yment below the natural rate requires increasing(not simply high) inflation. This is because inflation expectations continueto adjust to actual inflation.e. UNCERTAIN. An increase in the rate of money growth (a monetary ex-pansion) is likely to lead to a decrease in the nominal interest rate in theshort run, but to an increase in the nominal in terest rate in the mediumrun. (For the curious: Initially, an increase in money growth leads toan increase in the real money stock, which in turn causes an increase inoutput and a decrease in both the nominal and the real in terest rate. Aslong as the real interest rate is below its natural level and output is aboveits natural level (and hence unemployment is below its natural rate), weknow from the Phillips Curve relation that inflation must be increasing.As inflation increases, eventually it becomes higher than nominal moneygrowth, leading to negative real money growth. When real money growthturns negative, the nominal interest rate starts increasing —and given ex-pected inflation, so does the real interest rate. In the medium run, the1real interest rate increases back to its initial value, output is back to itsnatural level, unemployment is back to its natural rate, and inflation isno longer changing. As the real interest rate converges back to its initialvalue, the nominal interest rate converges to a new higher value, equal tothe real interest rate plus the new higher rate of nominal money growth.See Figure 14.6 in page 281 in the textbook.)(5points)f. FALSE. Capital accumulation by itself cannot sustain growth. Because ofdecreasing returns to capital, sustaining a steady increase in output percapita would require larger and larger increases in the level of capital percapita —in other words, a steady increase in capital per capita will producesmaller and smaller increases in output per capita (increases which, in thelong run, will converge to zero). Hence, long-run output per capita growthcan only be sustained by steady technological progress.2PART 2: In vestment and Monetary P olicy(40 Poin ts)a. The natural level of output is Yn.Assuming that the economy is initially at its medium run equilibrium, sothat output starts at its natural level, at t =0we will have Y = Yn,M = M0,so:Yn= c(M0− P0) and hence P0= M0−1cYn.(8points).b. Assuming that price expectations are formed by looking at the level ofprices in the previous period (Pet= Pt−1), then Pe1= P0and we have:Y1= c (2M0− P1)P1= P0+ d (Y1− Yn)→ Y1= c [2M0− P0− d (Y1− Yn)]→ Y1=c1+cd(2M0− P0+ dYn)Using P0= M0−1cYnfrom (a), we get:→ Y1=c1+cd·M0+µ1c+ d¶Yn¸=c1+cdM0+ Yn(8 points)c. The monetary expansion reduces the interest rate and raises output (it isstraightforward to show this in the IS-LM framewo rk, whic h is one of thebuilding blocks of the AD-AS). Hence, investment goes up as the interestrate is lower and output is higher (this is, as we move along the IS to theinteraction with the new LM). (8 points)d. In the medium run, Y = Yn.(8points)e. In the medium run, investment returns to its initial level, because outputand the interest rate return to their original levels (Turn to Figure 1 ifyou prefer to see this argument graphically). (8 points)3i Y Y P IS IS’ LM1 LM0 = LMmr AD0 AD1 AS ASmr Y n Y1 imr = i0 i1 P 0 Pmr P1 n Y Y1 Figure 1:4PART 3: Indexation of Wages (30 poin ts)a. π2001= π2000+0.1 − 2u2001=0.00 + 0.1 − 0.08 = 0.02 = 2%π2002= π2001+0.1 − 2u2002=0.02 + 0.1 − 0.08 = 0.04 = 4%π2003= π2002+0.1 − 2u2003=0.04 + 0.1 − 0.08 = 0.06 = 6%π2004= π2003+0.1 − 2u2004=0.06 + 0.1 − 0.08 = 0.08 = 8%It is even easier to derive these by using the fact that the Phillips Curvecan be simplified as: πt= πt−1+0.1 − 2ut= πt−1+0.02 = πt−1+2%,since ut=0.04 for all t here. (10 points)b. The PC becomes:πt=0.5πt−1+0.5πt+0.1 − 2utand henceπt− πt−1=0.2 − 4utIf ut=0.04 for all t, then:πt= πt−1+0.04 = πt−1+4%(5 points)c. π2001= π2000+0.04 = 0.04 = 4%π2002= π2001+0.04 = 0.08 = 8%π2003= π2002+0.04 = 0.12 = 12%π2004= π2003+0.04 = 0.16 = 16%(5 points)d. As indexation increases (this is, as more workers have indexed labor con-tracts), low unemployment leads to a larger increase in inflation over time.In other words, the impact of u on π becomes stronger. (10
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