Ps 4 with answers economics

METU Department of Economics ECON 102 Sections 01, 02, 03 Spring 2009 PROBLEM SET # 4 (CHAPTERS 24&25&26 CF and 25&26 from Lipsey) (with answers) PART A: PROBLEMS Q1. Money Demand: H Money Supply: H % I{ . { Nominal Income: I

(All units are billions of TL)

where is the interest rate. a) Find H If If H H JJ { { IJ . . { { H { I{; IJ H have a negative relationship

b) What is therelationship between IJ H ? H is function of interest rate and income: H whereas I IJ H have a positive relationship. High interest rate makes the opportunity cost of

holding money high. So, people start to hold less money to keep the value of money that they have. c) Graph H IJ H and calculate the equilibrium . In money market, equilibrium occurs at a level of interest rate where money supply and moneydemand are equal to each other. H 2 H 2 I{ . { % Interest Rate (%) Ms

10

M Money

480

d) The Central Bank of the Republic of Turkey decreases H by 60 TL. What happens to money market equilibrium? Solve the problem again and show the new equilibrium on a separate graph. If the money supply changes, we can find the equilibrium in money market by solving supply and Ms’ Ms demand functionsagain. Interest Rate (%) H 2 H


2

I{

. {

12.5 10 Md Money 1 / 15

420 480

Q2. The following system of equations describes the economy of Gotham where C is private consumption expenditures; I is investment; r is real interest rate; G is government purchases on goods and services; Tr transfer payments from government to households; T is taxes; X is export demand; M is importdemand; π is rate of expected annual inflation rate; H is money demand and is nominal interest rate. All figures are in billions of Bat (currency of Gotham). C = 450 + 0.8Yd; X = 240;

I = 350 – 2,000r; M = 0.2Y;

G = 200; π = 10%;

Tr = 50;

T = 125 + 0.25Y;

H = 225 + 0.75Y – 1,500

a) Assume that the Central Bank of Gotham sets the nominal interest rate at 15% and keeps it at thatlevel. Find equilibrium levels of national income, consumption, investment, budget balance of the government and net exports. Y = C + I + G + X – M = 450 + 0.8(Y – T + Tr) + 350 – 2,000(‹ – π) + 200 + 240 – 0.2Y Y = 1,240 + 0.8(Y – 125 – 0.25Y + 50) – 2,000 (0.05) – 0.2Y 0.6Y = 1,080 Y = 1,800 C = 1,470

C = 450 + 0.8(Y – T + Tr) = 450 + 0.8(Y – 125 – 0.25Y + 50) I = 350 – 2,000(‹ – π) = 350 – 2,000(0.05) I = 250

Budget Deficit = G + Tr – T = 200 + 50 – 125 – 0.25 (1,800) Net Exports = X – M = 240 – 0.2 (1,800) NX = – 120

BD = – 325

b) How could the Central Bank of Gotham guarantee that the nominal interest rate is 15%? In order to determine the money supply that is consistent with an interest rate of 15%, money market should be in equilibrium:  G =  > . Ms = 225 + 0.75 (1,800) –1,500 (0.15) = 1,350 To keep nominal interest rate at 15%, The Central Bank of Gotham should maintain the money supply at the level of Bat 1,350 billion. c) Show that the equilibrium condition holds for this economy. Since this economy is an open economy with government, the equilibrium condition is as follows: S + T + M = I + G + Tr + X Leakages must be offset by injections. Y = 1,800 – 450 +0.2Yd + 125 + 0.25Y + 0.2Y = 250 + 200 + 50 + 240

d) If the Central Bank of Gotham prints just Bat 270 billion worth of money; what is the required reserve ratio? (assume that there is no cash drain, banks don’t keep excess reserves and the Central Bank don’t keep cash) According to money creation process; amount of created money in a banking system (under the given assumptions above) is equal toprinted money multiplied by money multiplier. Since money supply is 1,350 billion and printed money is 270 billion; money multiplier is 5. Since it is reciprocal of required reserve ratio; it is 20%. 2 / 15

e) The Central Bank of Gotham decides to set money supply equal to Bat 1,500 billion. Plot H and H in appropriate graph for Y = 1,800 and Y = 2,200. What are the corresponding levels of...