14.02 Problem Set 3Dennis V. Perepelitsa20 March 2006Ruben Segura-CayuelaPart I - T/F/U1. False - If wages fall below the reservation rate, then all workers would prefer to be unemployedthan to be employed. More likely, wages in Europe are probably very close the reservation rate.Because of the high unemployment, firms have more bargaining power and can set wages this low,knowing that some workers will accept them.2. True - Powerful labor unions increase the bargaining power of workers significantly. Workersin a better bargaining position can typically ask for higher wages.3. Uncertain - The AS curve is upward sloping because an increase in output correspondswith an increase in the price level. This takes place because an increase in output leads to anincrease in employment, w hich leads to a decrease in the unemployment rate and therefore anincrease in the nominal wage. Firms then increase their prices to keep up with the nominal wageincrease.4. False - The US unemployment rate will not increase as long as the output growth is higherthan the natural output growth. By Okun’s law, ut− ut−1= −β(gyt−gy). So the change inunemployment rate will not be negative, as long as gyt> gy.5. True - According to Lucas and Sargent, inflation depends partially on expected futureinflation. That is, πt= πeτ− α(ut− tn), and πtwill eventually change to πτ. Thus, if you canabsolutely convince the participants in the e conomy that the inflation will be a certain value, theinflation rate will actually tend towards that value.6. True - John Taylor’s argument regarding nominal rigidities, and favoring the staggeringof wage decisions, showed that it is possible to lower the inflation rate slowly over time without asignificant increase in unemployment. The traditional Phillips curve is at odds with this, because itimplies that a negative change in inflattion corresponds with a positive increase in unemployment.Part II - Short QuestionsProblem 1A. Traditionally, investment depends on interest because if interest is high, people and firmsmay want to invest, as opposed to when interest is low, at which point people and firms may decideto spend their income instead of investing it. A situation in which interest has no effect on invest-ment is when banks and the government do not sell bonds or other interest-bearing investments.1B. The traditional IS relation is Y = C(Y − T ) + I(Y, i) + G, which must now be mo di-fied to Y = C(Y − T ) + I(Y ) + G. For any i, this has the same solution Y . That is, the IS curveis a vertical line.C. The LM relation,MP= Y $L(i) does not contain investment as one of its variables, andthus is unchanged. The slope of the line,didY, is positive, because an increase in output will lead toan increase in the interest rate, and so on.D. Well, since every intersection of the IS and LM curves is at the same Y , but with a variable i,the AD curve looks like a vertical line, intersecting the x-axis at Y . This means that if the interestrate has no effect on investment, then the price level has no effect on output.E. As the AS curve shifts upward, prices increase but not output. In the short run, thereare many small effects on the AD curve (the higher price of oil may lower firms’ investment plans,but it may also redistribute wealth from oil buyers to oil producers), and we will assume that theycancel out. The economy moves upward along the (vertical) AD curve. Price increases, but outputstays the same.F. In the medium run, when the price level increases, wage setters revise their expectationof what the price level will be, so expected wage level increases, which shifts the AS curve up. Butsince Y still exceeds natural production Yn, the price level is still higher than the expected pricelevel. So the process repeats. Since the AD curve is vertical, there is only one price level, and itwould seem that the price level increases forever towards infinity.Problem 2A. A drop in consumer confidence that decreases investment will shift the IS curve to the left,leading to a lower interest rate and a lower output. On the AS-AD graph, the AD curve will moveto the left, leading to a lower price level and, as we have stated, lower output. In the medium run,the lower price level would cause wage setters to revise their expectations, moving the AS curve tothe right, until the price level is at the new natural price level. The output is, however, permanentlylower. So in the short run, output and price level both decrease slightly. In the medium run, theprice level decrease significantly.B. Since u = 1 −YL, a decrease in output raises unemployment slightly in the short run,and s ignificantly in the medium run.C. If the Fed wants to keep unemployment constant, then it must offset the dec rease in produc-tion by moving the LM curve to the right with a monetary expansion. In the short run, this will2cause the desired increase in output level, along with a decrease in the interest rate, and a smallincrease in the price level, as the output moves above natural output. In the medium run, as wagesetters revise their estimates of the expected price level, the AS curve moves upward. This has theeffect of increasing the price level without altering the level of output.D. The loss in business investment is countered by the monetary expansion in the short termand the long term. Since the IS relation involving Y has re mained constant while the I(Y, i) termdecreased, the interest rate must have decreased to make up for this.E. The unemployment rate, which depends on Y , returns to normal since Y returns to normal.Part III - Long Question1. If it takes a nominal wage and a unit of oil to produce a unit of ouput, then the nominalcost of this is W + P x.2. If firms determine the price by multiplying the markup by the nominal cost of produc-ing another unit, then P = (1 + µ)(W + P x). If µ = 0, then P = W + P x, which leads to P =W1−xas a function of W and x. As x increases, P increases.3. If we rederive this in terms of wage setting, we getWP= (1 − x). This means that ifthe price of oil increases, real wage will necessarily decrease.4. Plugging this into the wage se tting equation W = PeF (1 −YL, z), we end up with theagreggate supply equation, P =11−xPeF (1 −YL, z). The natural level of output Ynis equal to Ywhen P = Pe.5. The aggregate demand curve implies that the output decreases as the price level increases,and thus is downward sloping. The aggregate supply curve implies
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