Managment Engineering - Macroeconomics of finance

Exercises of Block 1

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Macroeconomics of Finance Exercises on AS/AD model and Phillips Curve 1 AS/AD model Ex 1 Consider the following economy: C= 110 + 0:8Y d T= 0:4Y I= 100100i G= 640 Md = 0:25Y200i Md = real money demand Ms = 2BM BM= 1365BM= nominal base money w= 25w= nominal wage Y =N= 5Y =N= labour productivity Prices are set using a 50% markup over unit costs. Solve for the equilibrium levels of prices, output, interest rates, and employment. SolutionP= 7:5,Y= 1600,i= 18%,N= 320. Ex 2 Take an economy where the following relations hold: C= 200 + 0:8Y dY d= disposable income T= 0:2Y T R= 45 I= 100160i G= 400 Ld = 0:25Y160i Ld = real money demand BM N= 7260BM N= base money in nominal terms c= 0:8 (currency-to-deposits ratio)r= 0:1 (reserves-to-deposits ratio) Average and marginal labour productivity are equal to 2, while prices are initially expected to bePe = 30. a) Find the analytical expressions for the AD and AS curves, and the equilibrium level of output and pricesunder the hypothesis that price setters apply a 50% markup over marginal costs and nominal wages are set following the equation w=Pe 43 0:5 1YY n ; whereY n= 2000 is the natural level of output. b) Use a graph to discuss how the initial equilibrium changes if the central bank decides to raise base moneyby 10%. Discuss both the short and medium run outcomes. SolutionInitial equilibrium:P= 30,Y= 2000 (i.e., it is a medium run equilibrium). After the monetary expansion prices and output will immediately increase toP0 = 30:38 andY0 = 2068:3> Y n. In the long run, real balances will revert to the initial level thanks to the adjustment in prices (P MR= 33 , Y MR= Y n= 2000). Does the monetary expansion aect the natural rate of interest? 1 Ex 3 Consider the following economy: C= 0:8Y d T= 0:25Y I= 10035i G= 250 L= 0:25Y35i L= real demand for money M= 5400M= nominal supply of money Assume that labour productivity is equal to 10 and that nominal wages depend on the number of employed workersNaccording to w= 100 + 0:2N : Producers want to obtain a markup of 50% over labour costs. The existing production capacity allows to produce 1000 units at full utilization. Compute the equilibrium level of production and of the price index. SolutionP= 18,Y= 1000. Ex 4 Consider the economy: L= 0:125Y L= real demand for money M= 4:375M= nominal supply of money a) Obtain the analytical expression for the aggregate demand relation. b) Suppose prices and wages are sticky and that aggregate supply is given by Pt+1= Pe t+1 1" 1Y t+1Y  : Knowing thatY = 7,Pe t+1= P t= 5 and "= 14=15, compute prices and output at equilibrium. c) What happens in the short and medium run if the nominal stock of money is increased to 9? SolutionInitial equilibrium:P t+1= 5, Y t+1= 7. The monetary expansion leads to P0 t+1= 7 :1 andY0 t+1= 10:15> Y nin the short run, while real balances return to the starting level in the medium run after the adjustment in prices (P MR= 10 :28,Y LP= Y n= 7). 2 Ex 5 Consider the economy: C= 400 + 0:8Y d I= 400400i T R= 240 G= 680 L= 0:2Y200i M= 2BM N M= nominal money supply BM N= 3860BM N= nominal base money a= 1a= labour productivity  N= 4400 N= labour force = 1= markup t= 0:25t= tax rate (all incomes are taxed, including transfers) All amounts are in real terms, unless stated otherwise. Nominal wages are set according to the relation w=w 1 1 + 2 YY P 1 whereY Pis potential output and w 1= 6 :25 in the current period. a) Find the aggregate demand and supply curves for the initial period. Find the equilibrium levels of output,interest rates, prices. b) Find the equilibrium levels of output and prices in thenextperiod and the level of wages in the medium run. SolutionInitial equilibrium:P 0= 10, Y 0= 3960 (below natural output), i 0= 10%. The AS curve shifts down in the next period and the equilibrium moves toP 1= 8 :99,Y 1= 4177 :33 (still below natural output). In the medium runP MR= 8 :14,Y MR= Y n= 4400, w MR= 4 :07. Ex 6 Take an economy with the following relations (all amounts in real terms, unless stated otherwise): C= 250 + 0:8Y DT = 0:25Y I= 460960i G= 922 Ld = 0:1Y100i Ld = money demand BM N= 3400BM N= nominal monetary base Ms = 2BM N Ms = nominal money supply FL= 1320 F L= labour force Average and marginal labour productivity are equal to 3 and nominal wages are set followingW=Pe 0:5 +N800  ; whereNstands for employment andPe is the the level of expected prices (suppose expectations are adaptive). Firms set prices by applying a 50% markup over production costs. a) Find the analytical expressions for the AS and AD curves. 3 b) Suppose the economy is on a medium-run equilibrium. Determine the equilibrium level of output, prices and interest rates. c) Using an adequate graph, discuss the change in the short- and medium-run equilibrium that occurs afterrms adopt new IT equipment that raises labour productivity by 5%. Solutiona) (IS)Y=10 :4(1632 960i), (AD)P=9 :6(6800)1 :36Y1632, (AS) P=Pe 0:25 +Y4800
. b)Y= 3600,P= 20,i= 20%. c) AS shifts down and in the medium run the equilibrium moves toN= 1280,Y= 4032,P= 16:95. 4 2 Phillips Curve 1. Reserves = 50, currency = 250, deposits = 500. What should the central bank do in order to raise moneysupply by 100? 2. Consider the \original" Phillips curve and suppose that policymakers want to reduce unemployment. Howdoes in ation vary? Discuss with a graph. 3. Consider the Phillips curvet= e t+ 0 :12u t; e t=  t1: a) Assume= 0:25 and computeu n. b) Assume= 0:1 and computeu n. c) How does a change inaectu n? 4. Assume thate t=  t1and that the the Phillips curve is t  t1= 1:5 (u t u n) : Supposeu t= 0 :07,u n= 0 :08 and t1= 0 :04. How will tbe with respect to  t1? 5. Suppose that a country is experiencing an acceleration in in ation. What should we infer about theunemployment rateu? 6. Wage indexation has become less and less common in the US in past three decades. Will a reduction inunemployment have a stronger or weaker eect on in ation? 7. Considert e t= 0 :183u t; e t=  t1: a) Computeu n. b) Rewrite the Phillips curve for= 0 and for= 1. c) Now assume thatu t1= u nand  t1= 0. Starting from pediod t, policymakers act to take unemployment down to 5%. What happens to in ation intand in the next periods if= 0? And if = 1? 5