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**Unformatted text preview: **Page 1 of 8 THE UNIVERSITY OF TORONTO AT SCARBOROUGH Division of Management ECM B06H – Macroeconomic Theory and Policy: A Mathematical Approach TUTORIAL #3 - SOLUTIONS Q1. Suppose that a small open economy with perfect capital mobility and no risk premium is described by the following set of equations: Y = F(K bar ,L bar ) = 2400, C = 250 + 0.75(Y - T), I = 400 - 10r, G = 300, T = 200, r* = 5 (i.e. 5 percent), and NX = 500 - 100 , a) Compute the real exchange rate. The equilibrium real exchange rate ( , *) solves, NX( , *) = S - I . S = S NAT = Y - C - G = 2,400 - ( 250 + (3/4)(2,400 - 200) ) - 300 = 200 I = I(r*=5) = 400 - 10(5) = 350 S - I = -150 = NX( , *) =500 - 100( , *) 100( , *) = 650 so the Real Exchange Rate = , * = 6.5 b) Compute net exports and the three kinds of saving (private, government or public, and international or rest of world). Net Exports = NX( , *) = S - I = 200 - 350 = -150 Private Saving = S PVT = Y - T - C = 2,400 - 200 - 1,900 = 300 Government Saving = S GOVT = S PUBLIC = T - G = 200 - 300 = - 100 Rest of World Saving (in the domestic economy) = S ROW = S INTERNATIONAL = - NX = 150 Page 2 of 8 Check (for errors), I = S PVT + S GOVT + S ROW 350 = 300 - 100 + 150 (okay) c) Suppose that the set of equations given above is not altered from 2002 to 2006 and that PPP holds. Compute the rate of appreciation (or depreciation) of the domestic currency during these five years if domestic inflation is 2 percent and foreign inflation is 5 percent. Same equations means that the real exchange rate ( , *) is equal to 6.5 and constant ( ), =0) for all of these years. We know that the nominal exchange rate (e) can be written as the following function of the real exchange rate ( , ) and the domestic and foreign price levels (P and P f respectively): e = , @ P f /P This expression implies the following relationship holds for rates of change: ∆ ∆ ∆ Π Π e e P P P P f f f = - =- In this case, the nominal exchange rate (e) should rise (appreciate) by 3 per cent per year since the foreign inflation rate exceeds the domestic rate of inflation by 3 percentage points (i.e. B f = 5% and B = 2% per year). After five years the total (compounded) appreciation of the domestic currency against the foreign currency is approximately equal to 15.92 per cent (i.e. ( (1.03) 5 - 1) – 1.1592 - 1). Q2. Suppose a small open economy with perfect capital mobility and no risk premium is characterized by the following set of equations: Y = F(K bar ,L bar ) = 832, C = 10 + 0.75(Y - T), I = 70 - 1000r, G = 100, T = 100, r* = 0.05 (i.e. 5 percent), and NX = 195 - 40 , a) Compute the real exchange rate ( , ). Page 3 of 8 The equilibrium real exchange rate ( , *) solves, NX( , *) = S - I ....

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