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Long-Run Equilibrium Output, Wages, Prices and the Exchange Rate in the Long Run Aggregate Demand & Aggregate Supply LRAS AS AS” P” AD” AS’ P P’ AD’ o AD Q Q Money Stock and the Economy • Money and the real output in the long run The quantity theory of money: (The equation of exchange) P.Q* = M .V • Money and the price level M/P = L ( Q , i) • Money and the interest rate Money, Price, and the Interest Rate i Mo/Po = M1/P1 D M/P =L (Q,i) o Real Money Money and the X Rate • The X rate is simply the price of foreign currency in terms of the domestic currency; it is a price. P = e . P* • The doubling of M leading to a doubling of the P in the long run (the equation of exchange) would cause the expected future spot rate to increase (expected depreciation of the home currency), shifting the demand for FX to the right. The FX Market e SFX e1 eo DFX (i,i*,ee1) DFX (i,i*,eeo) 0 FX Purchasing Power Parity and the Law of One Price • Arbitrage and the law of one price Ph = e . P f • Why doesn’t it hold? • Transaction/transportation costs • Trade barriers • Perceived quality differentials • The PPP theory of foreign exchange e = P /P* %Δ e = %Δ P – %Δ P* %Δ P = %Δ e + %Δ P* or P = e + P* Why PPP May Not Hold (A Second Look) • Transportation/transaction costs • CPI measurement problems • • • • • Tradables vs. nontradables Different consumer baskets Changing relative prices within each country Trade barriers Absolute vs. relative PPP PPP and Inflation Let us recall: %Δ P = %Δ e + %Δ P* This equation can be rearranged as: %Δ e = %Δ P - %Δ P* e = P – P* Are inflation rates really important in determining the X rate? The Big Mac Index: http://www.oanda.com/ The Monetary Approach to the Exchange Rate • David Hume’s Specie-Flow Mechanism Adjustments to full-employment output Price adjustments Mercantilists’ accumulation of gold will result in increases in the price level (lower gold prices), thus, reducing exports and increasing imports A Simple Model • Recall that the equilibrium in the money market requires that real money stick be equal to the demand for money: M/P = L ( Q, i), where Q is constant. We can then write: M – P = L or P = M- L That simply means that inflation rate is equal to the difference between the growth rate of money stock and the growth rate of the demand for money. We can write the same equation for the foreign country(*): P* = M*- L* Subtracting one form the other: P – P* = (M - L) – (M*- L*) Or, P – P = (M - M*) – ( L - L*) Now recalling e = P – P* (relative PPP) e = (M – M*) – ( L – L*) Assuming no changes in the demand for money (L and L*), a difference in the money stock growth rates would result in a change in the exchange rate; e = 0 PPP and Inflation Let us now recall what we learned earlier in the semester about the relationship between the exchange rate and the interest rate: i – i* = (ee – e)/e = ee (Expected rate of change in X rate) From e = P – P* we write: ee = Pe – Pe* Thus we write: ee = Pe – Pe* = i – i* Now think about how an increase in the money stock at home (ceteris paribus) could affect the exchange rate. An alternative approach to the same concept: Real interest rate = r = i – p or re = i – pe Or, pe = i – re For the foreign country: p*e = i* – r*e Subtracting one from the other: (pe– p*e) = (i – i*) – ( re –re*) Assuming the real interest rates at home and abroad are equal (under free capital flows), (i – i*) = (pe– pe*) = ee The Real Exchange Rate Now recall: R = P/ (e P*) We write the equation in terms of % changes: R = P – e – p* = (P – P* ) – e Or, e = (P – P*) – R Note that here R is in fact the real “exchange rate”. If PPP holds R will not change; R = 0 When PPP does not hole R = 0 R = e - (P – P*) The Real Exchange Rate and the Real Interest Rate We had: (i – i*) = ( pe – p*e) = ee From the previous analysis we can write: ee = (pe – p*e) – Re Substituting (i – i*) for ee, (i – i*) = ( pe – p*e) - Re Now from the real interest rate equations we write: (re – re*) = (i –i*) – ( pe – p*e) Now substituting ( pe – p*e) – Re for (i –i*), the equation will simplify to: (re – re*) = - R e , linking the real interest rate to the real exchange rate .