PS 3 with answers - 1/7 METU Department of Economics Econ...

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Unformatted text preview: 1/7 METU Department of Economics Econ 202 Macroeconomic Theory Spring 2010 Answers of Problem Set 3 Q.1 Assume the following IS-LM model: C = 80 + 2/3Y d ; M d = 1/2Y + 400 – 20i; T = 1/4Y + 20; I = 250 – 5i; TR = 80 P = 1; G = 130; M s = 500 a) Derive the IS curve. Y = 80 + 2/3(Y - 1/4Y – 20 + 80) + 250 – 5i + 130 = 500 + 1/2Y – 5i Y = 500 + 1/2Y – 5i Y = 2(500 – 5i) = 1000 – 10i b) Derive the LM curve. 500 = 1/2Y + 400 – 20i Y = 200 + 40i c) Calculate the equilibrium value of income. 1000 – 10i = 200 + 40i i eq = 16 and Y eq = 840 d) What is the value of the government spending multiplier when interest rates are assumed to be constant? Multiplier = [1/1-c(1-t)] = 1/[-2/3(1-3/4)] = 2 e) Calculate the equilibrium values of investment, tax revenues, and real money demand. I = 250 – 5*16 = 170; T = (1/4)*840 – 20 = 190; ࡹ ࢊ = 500 f) How much of I will be crowded out if the government increases its expenditure by ∆G = 100? ∆IS = 2*100 = 200 then, 1200 – 10i = 200 + 40i → ࢏ ࢋࢗ = 20 and ࢅ ࢋࢗ = 1000 Since ∆i = 4, ∆I = -4*5 = -20 Check: I = 250 – 5*20 = 150 g) What is the value of the government spending multiplier when interest rates are allowed to vary? Multiplier = ∆Y/∆G = 160/100 = 1.6 (the multiplier is reduced) Q.2 ܥ = ܥ ଴ + ܿ ଵ ሺܻ − ܶሻ ; ܫ = ܾ ଴ − ܾ ଵ ݅ ; ሺܯ/ܲሻ ௗ = ݉ ଵ ܻ − ݉ ଶ ݅ ; ܩ ܽ݊݀ ܶ ܽݎ݁ ܿ݋݊ݏݐܽ݊ݐ. a) How should the parameters b1, m1, and m2 be interpreted? ࢈ ૚ is the sensitivity of investment to changes in the interest rate. ࢓ ૚ is the sensitivity of real money demand to changes in income, and ࢓ ૛ is the sensitivity of real money demand to changes in the interest rate. b) Use the IS-LM model to graphically determine the effectiveness of fiscal versus monetary policy when investment is very sensitive to changes in i, and money demand is very insensitive to changes in i. 2/7 IS relation is: ࢅ = ૚ ૚ − ࢉ ૚ ሾ࡯ ૙ + ࡵ + ࡳ − ࢉ ૚ ࢀሿ = ૚ ૚ − ࢉ ૚ ሾ࡯ ૙ + ࢈ ૙ − ࢈ ૚ ࢏ + ࡳ − ࢉ ૚ ࢀሿ Notice that when ࢈ ૚ is larger (investment more sensitive to changes in i, the IS curve is flatter. LM relation is : ࡹ/ࡼ = ࢓ ૚ ࢅ − ࢓ ૛ ࢏ . When ࢓ ૛ is smaller (real money demand less sensitive to changes in i, the LM curve is steeper. c) Now suppose that the government imposes a tax, ݐ ଵ , on income, so that the following is true: ܶ = ݐ ଴ + ݐ ଵ ܻ ǡ Ͳ ൏ ݐ ଵ ൏ ͳ . If money demand is very insensitive to changes in the interest rate, is a decrease in the income tax rate an effective way to stimulate the economy? Q.3 Suppose the goods market is described as follows: Goods Market: ܥ = ܽ + ܾሺܻ − ܶሻǡ ܽ ൐ Ͳǡ Ͳ ൏ ܾ ൏ ͳ ....
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This note was uploaded on 03/22/2012 for the course ECON 202 taught by Professor Tunc during the Spring '10 term at Middle East Technical University.

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PS 3 with answers - 1/7 METU Department of Economics Econ...

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