Master EPP - Sciences Po & Ecole polytechnique Eco 572 : International Economics - Final Test December 3, 2014 Answer both international trade and international macro questions. Both parts have equal weights in the final grade.

International Macro : Two Exchange-Rate Crisis Models 1 Consider the following two-period model (t = 1, 2) of a small, open economy : mt − pt = φy − βit

φ > 0, β > 0

(1)

pt = p∗ − st

(2)

i1 = i∗ + s1 − se2

(3)

∗

i2 = i

(4)

where all variables except it and i∗ are expressed in logarithms. mt denotes (the log of) money supply, pt corresponds to the price level, y corresponds to output, it and i∗ denote the domestic and foreign nominal interest rates, respectively. We define (log) exchange rates in foreign currency units, so that an increase in s represents an appreciation. st represent (log) exchange rates, with se2 the expected value of s2 at time t = 1. We investigate the feasibility of a fixed exchange rate agreement s1 = s2 = s¯. Assume p1 = p∗ − s¯. 1. Speculative Attack Model 1.1. Denote m ¯ = φy + p∗ − βi∗ − s¯. What is the economic interpretation of m ¯ ? Express i1 as a simple function of ∗ m1 , i , m ¯ and parameters. Using that relationship, show that in theory floating exchange rates would equal s1 = s¯ + m ¯ − me2 −

1 (m1 − m) ¯ β

(5)

s2 = s¯ + m ¯ − m2

(6)

Comment briefly on the impact of money supply shocks at t = 1 and t = 2 on exchange rates. 1.2. We consider that the Central Bank’s assets consist in foreign exchange reserves rt and loans to the private sector dt (again, all variables are in logs), and we treat credit growth as exogenous. Specifically we assume : mt = θrt + (1 − θ)dt d2 = d1 + µ,

1>θ>0

(7)

µ>0

(8)

Show that there will be a speculative attack if 1 ((1 − θ)d1 − m) ¯ + ((1 − θ)de2 − m) ¯ >0 β

(9)

Explain why a speculative attack would occur at time t = 1. 1.3. Discuss briefly which economic variables should be monitored to assess the risk of a speculative attack against a currency. 1. Adapted from Olivier Jeanne (1996), ”Les mod` eles de crise de change : un essai de synth` ese”, Economie et pr´ evision, no 123-124, pages 147-162.

2. Escape Clause Model Consider another model where the Central Bank is less passive. Assume the Bank always defends the peg at t = 1, but may devalue the currency at t = 2. For simplicity assume that if a devaluation occurs, s2 = s1 − ∆ where ∆ > 0 is a parameter. Assume the Central Bank’s minimizes the following loss function at time 2 : 2

L2 = [U2 (s2 )] + C1s2 −s1 =∆ ,

C>0

where U2 denotes the unemployment rate at date 2, 1s2 −s1 =∆ is an indicator function that takes value one if s2 − s1 = ∆ and zero otherwise, and C is a political cost of devaluation. Assume that unemployment has some persistence (0 < ρ < 1) and depends on surprise inflation π − π e (e.g. if wages are set in advance, surprise inflation reduces the real wage and stimulates employment) : U2 = ρU1 − λ(π2 − π2e ) with 0 < ρ < 1, 0 < λ < 1 Expectations are assumed to be rational. Note that Ut , πt , πte , C are not in logs. 2.1. Suppose the exchange rate is expected to remain constant. Under which condition will the Bank defend the c − 2ρU1 ] peg at t = 2 ? [Hint : define Ψ(U1 ) = λ∆ 2.2 Suppose now that agents expect a devaluation. Under which condition will the Bank devalue at t = 2 ? 2.3. In which parameter region are there multiple equilibria ? Comment. 2.4. Relative to question 1.3., which additional economic variables should be monitored to assess the risk of an exchange-rate crisis ?

International Trade : Factor Proportions, Productivity Differences and Comparative Advantage In the Home economy, goods 1 and 2 are produced out of 2 factors, L and S, according to the following production functions : Y1 = F1 (L1 , S1 ) ≡ AL1 , 1 2

Y2 = F2 (L2 , S2 ) ≡ (L2 ) (S2 )

A>0 1 2

where Lj , Sj denotes factor use by sector j. Total factor endowments are denoted by L and S. Consumers have utility 1−α U (Q1 , Q2 ) = Qα 1 Q2 with 0 < α < 1. Qj denotes consumption of good j. Product and factor markets are perfectly competitive. Goods and factor prices are denoted by p1 , p2 , wL , wS . 1. Show that profit maximization and the S factor market clearing condition imply L2 wS = S wL and comment briefly. Express both sectors’ unit costs as functions of wL , wS and parameters, and plot both sectors’ zero-profit conditions in {wL , wS } space. 2

2. Write down Marshallian demand functions for goods 1 and 2. Using these functions and product market clearing conditions, show that p2 1 − α AL1 = p1 α (L2 ) 21 S 21 3. Show that in autarky equilibrium p2 = κA p1

  21 L S

where κ is a positive constant term that you should determine. 4. Consider a Foreign economy that is identical to the Home economy, except for its endowment in S. Denoting with stars all Foreign variables, the difference between the two countries is that S ∗ = 4S. wS Which good will Home export under free trade ? How does the relative price of the S factor w vary after L opening to trade ? Why ? 5. Suppose now there is technological progress in the Foreign country and A∗ = 3A. Which good will Home export under free trade ? Will factor prices be equalized across countries ? [Hint : you might want to refer to your answer to question 1] 6. Suppose now that Home has caught up with skill accumulation (S = S ∗ ) and technological progress (A∗ = A), but there is a demand shock such that α > α∗ . Which good will Home export under free trade ? Conclude.

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