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Principles of Macroeconomics (with Xtra!)

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Page 1 of 6 Π M M Y Y = + T HE U NIVERSITY OF T ORONTO AT S CARBOROUGH Division of Management ECM B06H – Macroeconomic Theory and Policy: A Mathematical Approach TUTORIAL #2 - SOLUTIONS Q1. Consider an economy is such that real output is growing at 5% each year, the real interest rate is constant at 4%, and the money supply is growing at 5% each year. The demand for money is given by: ( M d /P ) = k @ Y ( Suppose ( =1, and k = 1/V = a constant (where V is the income velocity of money). a) Calculate the rate of inflation and the nominal interest rate. We have the following information: Y Y M M r V V = = = = 5% 5% 4%, 0% , , M S = M, M d = k @ P @ Y ( , ( =1, and k = (1/V) Money Market Equilibrium implies: M S = M d M = k @ P @ Y M @ (1/k) = M @ V = P @ Y So money market equilibrium here yields the Standard/Basic Quantity Equation Clearly, the following relationship holds with respect to changes in the terms of the quantity equation: M M V V P P Y Y + = + Π = - M M Y Y A = 5% - 5% = 0%
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Page 2 of 6 The Fisher Equation implies: i = r + A Here i = r + 0% i = r = 4% b) Calculate the effect on the price level and the rate of inflation if the rate of growth of the money supply changes to 10% each year. Represent your answer in a graph (with horizontal axis=time). Π = - M M Y Y A = 10% - 5% = 5% The rate of inflation rises one-for-one with the increase in the rate of growth of the money supply (i.e. the M s growth rate rose 5 percentage points as did A ). Here we have assumed that the policy change occurs at time t 1 and at that time the money supply rises by a full 5 percent (this is why the P curve jumps from 1 to 1.05 immediately - if the money supply did not rise by the full 5% initially then the P curve would still jump upwards, be discontinuous, but would rise to a value less than 1.05 at time t
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