Econ 318_F2014_Assignment 1_Answers

Econ 318_F2014_Assignment 1_Answers - 1 Concordia...

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Concordia University Department of Economics ECON 318/2 – Section BB Instructor: G. Tsoublekas Fall 2014 ASSIGNMENT 1 Answers Due at noon on Tuesday, October 7, 2014 Name: I.D. Section: Question 1: The IS-LM Model [45 points] Consider the following numerical version of mixed open economy: The Money Market Ms = 21200 where Ms = Supply of Money Md = 20000 – 16000 r + 2 Y Md = Demand for Money The Goods & Services Market C = 110 + 0.8 Yd – 200 r C = Private Consumption I = 150 – 600 r I = Gross Private Investment G = 200 G = Autonomous Government Spending T = – 50 + 0.2 Y T = Taxes X = 150 – 500 r X = Exports Z = 26 + 0.04 Y + 300 r Z = Imports S = Y – T – C r = Interest Rate Yd = Y – T S = Private Saving Yd = Disposable Income Determination of Equilibrium in the Economy a. Set the money market at equilibrium and derive the equation of the level of output as a function of the interest rate ( the LM curve ). (3 points) Ms = Md 21200 = 20000 – 16000 r + 2 Y 2 Y = 1200 + 16000 r Y = 600 + 8000 r b. Set the goods market at equilibrium and derive the relationship for the level of output as a function of the interest rate ( the IS curve ). (4 points) AE = Y = C + I + G + X – Z Y = {110 + 0.8[Y – (– 50 + 0.2 Y)] – 200 r} + {150 – 600 r} + 200 + {150 – 500 r} – {26 + 0.04 Y + 300 r} Y = 110 + 0.8 Y + 40 – 0.16 Y – 200 r + 150 – 600 r + 200 + 150 – 500 r – 26 – 0.04 Y – 300 r (1 – 0.8 + 0.16 + 0.04) Y = 110 + 40 + 150 + 200 + 150 – 26 – (200 + 600 + 500 + 300) r 0.4 Y = 624 – 1600 r Y = 1560 – 4000 r 1
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c. Solve for the levels of output and interest rate that equilibrate both the money market and the market for goods and services. (3 points) Combining the two equations (one from the Money Market and the other from the Goods Market) that show the level of output as a function of interest rate, we get 600 + 8000 r = 1560 – 4000 r 12000 r = 960 r = 960 / 12000 and r = 0.08 or 8% Y = 1560 – 4000 * 0.08 = 1240 or Y = 600 + 8000 * 0.08 = 1240 d. Solve for the equilibrium levels of all components of Aggregate Expenditure, Taxes, and Private Saving. (4 points) T = – 50 + 0.2 * 1240 = – 50 + 248 = 198 I = 150 – 600 * 0.08 = 150 – 48 = 102 X = 150 – 500 * 0. 08 = 150 – 40 = 110 Z = 26 + 0.04 * 1240 + 300 * 0.08 = 26 + 49.6 + 24 = 99.6 C = 110 + 0.8 (1240 – 198) – 200 r = 110 + 0.8 * 1042 – 200*0.8 = 110 + 833.6 – 16 = 927.6 S = 1240 – 198 – 927.6 = 114.4 AE = Y = C + I + G + X – Z = 927.6 + 102 + 200 + 110 – 99.6 = 1240 Expansionary Fiscal Policy e. Assume that the government, through its Department of Finance, pursues an expansionary fiscal policy through an increase in its spending by 72. Compute the impact of this policy on output and the interest rate (derive the new IS curve that comes from the equilibrium in the goods and services market and combine it with the original LM curve). (4 points) The new equilibrium in the Goods Market AE = Y = C + I + G + X – Z Y = {110 + 0.8[Y – (– 50 + 0.2 Y)] – 200 r} + {150 – 600 r} + 272 + {150 – 500 r} – {26 + 0.04 Y + 300 r} Y = 110 + 0.8 Y + 40 – 0.16 Y – 200 r + 150 – 600 r + 272 + 150 – 500 r – 26 – 0.04 Y – 300 r (1 – 0.8 + 0.16 + 0.04) Y = 110 + 40 + 150 + 272 + 150 – 26 – (200 + 600 + 500 + 300) r 0.4 Y = 696 – 1600 r Y = 1740 – 4000 r Equilibrium in both markets For the equilibrium in both markets (to determine output and interest rate) we proceed as before: 600 + 8000 r = 1740 – 4000 r or 12000 r = 1140 and r = 1140 / 12000 = 0.095 or 9.5% Replacing for r in any of the two equations we get the equilibrium output for both markets Y = 600 + 8000 r = 600 + 8000*0.095 = 1360 or Y = 1740 – 4000 r = 1740 – 4000*0.095 = 1360 2
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f. Solve for the equilibrium levels of all components of Aggregate Expenditure, Taxes, and Private Saving. (5 points) T = – 50 + 0.2 * 1360 = – 50 + 272 = 222 I = 150 – 600 * 0.095 = 150 – 57 = 93
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