# Price Levels and the Exchange Rate in the Long Run

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Price Levels and the Exchange Rate in the Long Run
Chapter 16 International Economics Udayan Roy

Overview Long-run analysis Flexible exchange rates Real variables
Nominal variables Flexible exchange rates We will study fixed exchange rates in Chapter 18

The Real Exchange Rate We discussed exchange rates in Chapter 14
Example: €1 = \$1.50 Those exchange rates are nominal exchange rates Now we’ll discuss real exchange rates

The Real Exchange Rate Let us consider the price of an iPhone in US and Europe: In US, it is PUS = \$200 In Europe, it is PE = €150 The value of the euro is E = 2 dollars per euro So, Europe’s price in dollars is E × PE = \$300 So, each iPhone in Europe costs as much as 1.5 iPhones in US E × PE / PUS = 1.5 This is the real dollar/euro Exchange Rate for iPhones

The Real Exchange Rate In general, the real exchange rate is a broad summary measure of the prices of one country’s goods and services relative to another’s. The real dollar/euro exchange rate is the number of US reference commodity baskets—not just iPhones—that one European reference commodity basket is worth Equation (16-6) in KOM9e E\$/€ is the nominal exchange rate, the price of one euro in dollars PE is the overall price level in Europe, such as the consumer price index PUS is the overall price level in the United States

Depreciation and Appreciation
Euro Dollar Europe’s exports America’s exports q\$/€↑ Real Appreciation Real Depreciation More expensive Less expensive q\$/€↓

The Real Exchange Rate Example: If the European reference commodity basket costs €100, the U.S. basket costs \$120, and the nominal exchange rate is \$1.20 per euro, then the real dollar/euro exchange rate (q\$/€) is 1 U.S. basket per European basket.

Real Depreciation and Appreciation
Real depreciation of the dollar against the euro A rise in the real dollar/euro exchange rate (q\$/€↑) is a fall in the purchasing power of a dollar within Europe’s borders relative to its purchasing power within the United States Or alternatively, a fall in the purchasing power of America’s products in general over Europe’s. Real appreciation of the dollar against the euro is the opposite of a real depreciation: a fall in q\$/€.

Absolute PPP A very simple theory of the real exchange rate is called Absolute Purchasing Power Parity It says that: q = 1 Why?

Law of One Price Going back for a second to the iPhone example, one can argue that PUS, the dollar price in the US, ought to be equal to E × PE, the dollar price in Europe. That is, E × PE = PUS. In general, E\$/€ x PE = PUS. Therefore, q\$/€ = (E\$/€ x PE)/PUS = 1. This is the Law of One Price or Absolute Purchasing Power Parity. Immediately after this slide, I should skip to the empirical relevance of APPP. And immediately after that, I should develop the Y = D(q) equation of chapter 16, and then derive the long run value q by imposing Y = Yf. The long run effect of Ms on E and Ee can then be derived. This will also allow the discussion of the long run effects of fiscal policy.

Absolute and Relative PPP
Chapter 16 of the textbook (KOM9e) uses Absolute PPP in the first part of the chapter and Relative PPP in the second part Absolute PPP: q = 1 Relative PPP: q = a constant, not necessarily 1 Although the results in the following slides have been proved for APPP, they are also true under RPPP

Prices and the Exchange Rate
Absolute PPP says: 𝑞= 𝐸∙ 𝑃 ∗ 𝑃 =1 Therefore, 𝐸= 𝑃 𝑃 ∗ Therefore, the faster domestic prices (P) grow, the faster the foreign currency’s exchange value (E) will grow And, the faster foreign prices (P*) grow, the slower the foreign currency’s exchange value (E) will grow

Prices and the Exchange Rate
Equation (16-2) of the textbook, KOM9e In general, 𝐸 𝑔 =𝜋− 𝜋 ∗ where Eg is the growth rate of E. This is the appreciation rate of the foreign currency π* is the foreign inflation rate, and π is the domestic inflation rate Example: If US inflation is 3% a year and Canadian inflation is 1% a year, then the exchange value of the Canadian dollar, measured in US dollars, will increase 2% a year

The Interest Rate We have seen in Chapter 15 that the interest parity equation is 𝑅= 𝑅 ∗ + 𝐸 𝑒 −𝐸 𝐸 The second term on the right-hand side is the expected appreciation rate of the foreign currency Assumption: The expected appreciation rate is assumed to be equal to the actual appreciation rate (Eg), in the long run

Equation (16-5) of the textbook, KOM9e
The Interest Rate Therefore, 𝑅= 𝑅 ∗ + 𝐸 𝑒 −𝐸 𝐸 = 𝑅 ∗ + 𝐸 𝑔 We saw two slides earlier that 𝐸 𝑔 =𝜋− 𝜋 ∗ Therefore, 𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗ Assumption: The foreign interest rate (R*) and the foreign inflation rate (π*) will be assumed to be exogenous constants Equation (16-5) of the textbook, KOM9e

The Interest Rate: Fisher Effect
𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗ As the foreign interest rate (R*) and the foreign inflation rate (π*) are assumed to be exogenous constants, any change in the domestic inflation rate will cause an equal change (both in magnitude and direction) in the domestic nominal interest rate This is called the Fisher Effect

The Interest Rate 𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗ implies 𝑅−𝜋= 𝑅 ∗ − 𝜋 ∗
R is the nominal interest rate. It tells you how fast the dollar value of your wealth is increasing R – π is the real (or, inflation-adjusted) interest rate. It tells you how fast the purchasing power of your wealth is increasing We now see that in the long run equilibrium, real interest rates must be equal in all countries

The Interest Rate Assumption: The domestic inflation rate (π) is constant in the long run equilibrium Then 𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗ must also be constant in the long run equilibrium We will now use this constancy of R to get a theory of long run inflation

Output The real GNP produced when all resources are fully utilized is known by various names: Long-run GNP Natural GNP Full-employment GNP Potential GNP(Yp) Assumption: In the long run, the economy makes full use of all its resources Therefore, in long-run equilibrium, Y = Yp.

Inflation We have seen in Chapter 15 that equilibrium in the money market implies 𝑀 𝑠 = 𝑀 𝑑 Moreover, 𝑀 𝑑 =𝑃∙𝐿(𝑅,𝑌) Simplifying a bit, 𝑀 𝑑 = 𝑃∙ 𝐿 0 ∙𝑌 𝑅 Therefore, in equilibrium, 𝑀 𝑠 = 𝑃∙ 𝐿 0 ∙𝑌 𝑅 Therefore, 𝑃= 𝑀 𝑠 ∙𝑅 𝐿 0 ∙𝑌

Inflation Therefore, in the long-run, 𝑃= 𝑀 𝑠 ∙𝑅 𝐿 0 ∙𝑌 = 𝑀 𝑠 ∙𝑅 𝐿 0 ∙ 𝑌 𝑝 We saw three slides back that R is constant in the long run equilibrium. Moreover, L0 is an exogenous constant Therefore, the faster the money supply (Ms) grows, the faster the price level (P) will grow And, the faster potential GDP (Yp) grows, the slower the price level (P) will grow

Inflation In general, 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔
For example, if the Federal Reserve expands US money supply at the rate of 5% a year and if the US economy’s potential GDP increases at the rate of 3% a year, then, in the long run, the US inflation rate will be 2% a year.

The Interest Rate, again
So far, we have 𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗ and 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 Therefore, the domestic nominal interest rate in the long run is 𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ , a constant

The Price Level A few slides back, we saw that in the long run the domestic price level is 𝑃= 𝑀 𝑠 ∙𝑅 𝐿 0 ∙ 𝑌 𝑝 Moreover, we just saw that 𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ Therefore, in the long run, the domestic price level is 𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝

Appreciation Rate of the Foreign Currency
We saw earlier that the foreign currency appreciates at the rate 𝐸 𝑔 =𝜋− 𝜋 ∗ As the inflation rate is 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 , we can now write 𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗

The Exchange Rate: APPP version
Recall that under absolute purchasing power parity, we have 𝑞= 𝐸∙ 𝑃 ∗ 𝑃 =1, which implies 𝐸= 𝑞∙𝑃 𝑃 ∗ = 𝑃 𝑃 ∗ We have also seen two slides back that 𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 Therefore, 𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗

Summary: Long-Run, Flexible Exchange Rates
q = 1, absolute PPP Y = Yp 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗ The crucial point to note about these expressions is that the variables on the right-hand sides of these equations are all exogenous. As exogenous variables are ‘mystery variables’ about which our theory has nothing to say, the equations on this slide say all that our theory can say about the endogenous variables on the left-hand sides of these equations.

Summary: Long-Run, Flexible Exchange Rates
q = 1, absolute PPP Y = Yp 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗ Keep in mind that we are talking about the long run here. So, these equations show us the long run effects of permanent changes in the exogenous variables on the equations’ right-hand sides.

Summary: Long-Run, Flexible Exchange Rates
q = 1, absolute PPP Y = Yp 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗ The first two variables are real variables: they can be measured even in barter (or, non-monetary) economies. The remaining variables are nominal variables: they make sense only on monetary economies. Note that the money supply (Ms) has no effect on real variables. This is an instance of monetary neutrality in the long run.

Summary: Long-Run, Flexible Exchange Rates
q = 1, absolute PPP Y = Yp 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗ Flashback to Ch. 15 of the textbook (KOM9e): “A change in the supply of money has no effect on the long-run values of the interest rate or real output.” (p. 369) “A permanent increase in the money supply causes a proportional increase in the price level’s long-run value. In particular, if the economy is initially at full employment, a permanent increase in the money supply eventually will be followed by a proportional increase in the price level.” (p. 370)

Absolute PPP: logical but not factual
Despite the logical appeal of Absolute Purchasing Power Parity, available data suggests that it is not true We need to look for another theory of the real exchange rate, q.

Law of One Price for Hamburgers?

Bonus Topic: The Current Account
We will return to this after discussing Chapter 17 The balance on a country’s current account (CA) is roughly its net exports What does CA depend on in the long run? Bonus Topic: The Current Account

The Current Account Recall the goods market equilibrium equation: 𝑌=𝐶 𝑌−𝑇 +𝐼+𝐺+𝐶𝐴 Therefore, 𝐶𝐴=𝑌−𝐶 𝑌−𝑇 −𝐼−𝐺 Recall that 𝑌= 𝑌 𝑝 in the long run Therefore, 𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺

The Current Account 𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺
𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺 If Yp increases by, say, \$100, then, in the long run, income (Y) will increase by \$100 and consumption (C) will increase, but by less than \$100 Therefore, CA will increase Therefore, in the long run, Yp and CA move in the same direction

The Current Account 𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺
Y CA Yp + T I, G 𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺 It is also straightforward to check that When taxes (T) change, CA moves in the same direction, and When I and G change, CA moves in the opposite direction Fiscal austerity (T↑ or G↓) is a way to raise CA A fall in consumer wealth—caused by, say, a real estate crash or a stock market crash—has the same effect as a tax increase. So, CA will increase!

The Long Run The macroeconomic analysis of the long run is characterized by the concept of monetary neutrality That is, monetary arrangements and monetary policy have no effect on the behavior of real variables Therefore, the predictions summarized by the table on this and the previous slide are true for both the flexible exchange rate system of this chapter and the fixed exchange rate system of Chapter 18 Y CA Yp + T I, G

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