Managment Engineering - Macroeconomics of finance

IS-LM Model Exercise and Solution

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Macroeconomics of Finance Exercises on IS/LM model Ex1 Consider the following economy: C= 0:75Y dC =consumptionY d= disposable income T= 0:2Y T=tax revenue I= 8001500i I=investmenti=interest rate G= 760G=government spending Ld = 0:1Y500i Ld =demand for money Central Bank Balance SheetAssets Liabilities Gold 55Currency 60 Loans to commercial banks35Commercial bank reserves 100 Government bonds70Banking System Balance Sheet Assets Liabilities Reserves 100Checkable deposits 260 Loans195Loans from the central bank 35All amounts above are expressed in real terms. a) Determine the equilibrium levels of output and of the interest rate. In addition, determine the governmentbudget decit under the assumption that the government nances its decit spending by selling bonds to private investors. b) How do previous results change if we assume that the government forces the central bank to buy the newlyissued bonds in order to nance the decit spending? (Assume that households and rms do not alter their preferences about holding cash and deposits.) Ex2 To protect the domestic producers from international competition, the government of the Republic of Maradagàl decided to cease all economic relationships with the rest of the world. However, current national output is 8% below its potential and the government wants to increase spending in order to bring the economy to full employment. Consider that: a) The central bank has the following balance sheet (in real terms):Assets Liabilities Gold 20Currency 400/3 Bonds160Required reserves 200/3 Credit20b) The required reserve ratio is 0.1, while the amount of free reserves is negligible. c) The real demand for money isLd = 0:25Y500i. d) The labour force is 7000 and average labour productivity is 0.5.e) The income multiplier is equal to 2 while investments increase by 2 units if the interest rate falls by 1%. Determine:1) The interest rate associated with the initial equilibrium. 2) The variation in government spending that is required to reach full employment. 1 Solution 1 a) At equilibrium income is 3600, the interest rate is 8%, the budget decit is 40. b) In this case the central bank cannot manage the money supply independently. At the new equilibriumincome is 3726.31, the interest rate is 4.63%, the budget decit is 14.73. Solution 21) The initial interest rate is 0.01%. 2)
G= 168. 2