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Chapter 15. Supplementary Notes. Law of One Price. The law of one price: the same good in different competitive markets must sell for the same price, when transportation costs and barriers between markets are not important. Law of One Price (cont.).

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Chapter 15 l.jpg

Chapter 15

Supplementary Notes


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Law of One Price

  • The law of one price: the same good in different competitive markets must sell for the same price, when transportation costs and barriers between markets are not important.


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Law of One Price (cont.)

  • Consider pizzas in Seattle and Vancouver.

  • The law of one price says that

    PpizzaUS= (EUS$/Canada$) x (PpizzaCanada)

    PpizzaUS = price of pizza in Seattle

    PpizzaCanada = price of pizza in Vancouver

    EUS$/Canada$ = US dollar/Canadian dollar exchange rate


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Purchasing Power Parity

  • Purchasing power parity is the application of the law of one price across countries for all goods and services, or for representative groups (“baskets”) of goods and services.

    PUS= (EUS$/Canada$) x (PCanada)

    PUS = price level of goods and services in the US

    PCanada = price level of goods and services in Canada


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PPP (cont.)

  • Purchasing power parity implies that

    EUS$/Canada$ = PUS/PCanada

    • The exchange rate is determined by the ratio of the domestic to foreign price levels.

    • If the price level in the US is US$200 per basket, while the price level in Canada is C$400 per basket, PPP implies that the US$/C$ exchange rate should be 200/400 = ½. 1 CAD is worth ½ USD.


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Alternative Derivation of PPP

The exchange value of a currency in terms of another is related to the relative purchasing power of the two currencies.

PPP rate of C$ in terms of US$ (US$/C$)

= (PP of C$)/(PP of US$)

= (1/ PCanada)/(1/PUS)

= PUS/PCanada


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PPP (cont.)

Purchasing power parity comes in 2 forms:

  • Absolute PPP: Exchange rates equate price levels across countries.

    E$/€ = PUS/PEU

  • Relative PPP: changes in exchange rates equal changes in prices (inflation) between two periods:

    (E$/€,t - E$/€, t –1)/E$/€, t –1 = US, t - EU, t

    where t = inflation rate from period t-1 to t


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Monetary Approach to Exchange Rates

  • Monetary approach to the exchange rate: uses monetary factors to predict how exchange rates adjust in the long run.

  • Ingredients

    • PPP

    • Prices are flexible (in the long run)

    • Price levels adjust to equate real (aggregate) money supply with real (aggregate) money demand.

      PUS = MsUS/L (R$, YUS)  P = M/L(R,Y)

      PEU = MsEU/L (R€, YEU)  P* = M*/L(R*,Y*)


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MAER (cont.)

  • Money supply E  : a permanent rise in the domestic money supply causes a proportional depreciation in the domestic currency

  • Interest rates  E  : a rise in the domestic interest rate causes a depreciation of the domestic currency

  • Output level  E  : a rise in the domestic output level causing an appreciation of the domestic currency

  • All 3 changes affect money supply or money demand, thereby causing prices to adjust to maintain equilibrium in the money market. The exchange rate moves to maintain PPP.


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MAER (cont.)

  • A change in the level of the money supply results in a change in the price level.

  • A change in the money supply growth rate results in a change in the growth rate of prices (inflation).

    • Other things equal, a constant growth rate in the money supply results in a persistent growth rate in prices (persistent inflation) at the same constant rate.

    • Inflation does not affect the productive capacity of the economy and real income from production in the long run.

    • Inflation, however, does affect nominal interest rates.


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The Fisher Effect

  • The Fisher effect (named after Irving Fisher) describes the relationship between the nominal interest rate and inflation.

    R$= r$ + eUS

    R€ = r€+eEU

  • A rise in the domestic inflation rate causes an equal rise in the domestic interest rate, with other things (including the real interest rate, r$ and r€ ) constant.

  • Assuming real interest rates are equal, the Fisher effect implies that interest rate differential equals difference in the expected rates of inflation.

    R$- R€ = eUS- eEU


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The Fisher Effect (cont.)

  • We can derive the Fisher effect from the interest parity condition:R$- R€ = (Ee- E)/E

  • PPP implies that the expected rate of DC depreciation will equal difference in expected inflation between countries (Relative PPP in expectations):

    (Ee- E)/E= eUS- eEU

  • Combine the above two to obtain

    R$- R€ = eUS- eEU


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Increase in Money Supply Growth

  • Assume

    • the Federal Reserve unexpectedly increases the money supply growth rate at time t0.

    • The inflation rate is π in the US before t0 and rises to π + π after this time (due to flexible prices).

    • Inflation remains at 0% in Europe.

    • The interest rate adjusts according to the Fisher effect to reflect this higher inflation rate in the US.


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Increase in Money Supply Growth

  • Effects on the price and the exchange rate

    • The increase in nominal interest rates decreases real money demand.

    • To maintain equilibrium in the money market, prices must jump so that P= Ms/L (R, Y).

    • To maintain PPP, the exchange rate will then jump (the dollar will depreciate): E = P/P*

    • Thereafter, the money supply and prices grow at rate π +  π and the domestic currency depreciates at the same rate.





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Empirical Evidence on PPP

  • There is little empirical support for purchasing power parity.

    • The prices of identical commodity baskets, when converted to a single currency, differ substantially across countries.

  • Relative PPP is more consistent with data, but it also performs poorly to predict exchange rates.



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Empirical Evidence on PPP (cont.)

Reasons why PPP may not be a good theory:

  • Trade barriers and non-tradable goods and services

  • Imperfect competition

  • Differences in price level measures


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Empirical Evidence on PPP (cont.)

  • Trade barriers and non-tradables

    • Transport costs and governmental trade restrictions make trade expensive and in some cases create non-tradable goods or services.

    • Services are often not tradable: services are generally offered within a limited geographic region (e.g., haircuts).

    • One price need not hold in two markets.


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Empirical Evidence on PPP (cont.)

  • Imperfect competition may result in price discrimination: “pricing to market”.

    • A firm sells the same product for different prices in different markets to maximize profits, based on expectations about what consumers are willing to pay.

  • Differences in price level measures

    • Price levels differ across countries because of the way representative groups (“baskets”) of goods and services are measured.

    • Because measures of goods and services are different, the measure of their prices need not be the same.


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The Real Exchange Rate

  • The real exchange rate: qUS/EU = (E$/€ x PEU)/PUS

  • The real exchange rate is the rate of exchange for real goods and services across countries.

    (E$/€ x PEU)/PUS

    =($/€)(€/EU goods) / ($/US goods)

    =US goods/EU goods

  • In other words, it is the relative value/price/cost of goods and services across countries.


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The Real Exchange Rate (cont.)

qUS/EU = (E$/€ x PEU)/PUS

  • If the EU basket costs €200, the US basket costs $120 and the nominal exchange rate is $1.20 per euro, then the real exchange rate is 2 US basket per EU basket. (EU goods are twice as expensive as US goods.)

  • An increase in qUS/EU is called a real depreciation of the US dollar. It means a fall in the price of US goods relative to EU goods. (US goods become less expensive relative to EU goods.)

  • A decrease in qUS/EU is called a real appreciation of the US dollar. It means US goods become more expensive and more valuable relative to EU goods.


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The Real Exchange Rate (cont.)

  • According to PPP, exchange rates are determined by relative price ratios:

    E$/€ = PUS/PEU

  • According to the real exchange rate approach, exchange rates may also be influenced by the real exchange rate:

    E$/€ = qUS/EU x PUS/PEU

  • (PPP assumes that the real exchange rate is constant and therefore ignores it.)

  • What influences the real exchange rate?


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The Real Exchange Rate (cont.)

  • A change in world relative demand for US products

    • An increase in relative demand for US output causes the price of US goods relative to foreign goods to rise.

    • Examples

      • Shifts in demand in favor of US goods

      • An increase in government spending in the US

    • This is a real appreciation of the value of US goods = a decrease in q

    • Conversely, a decrease in relative demand for US output leads to a real depreciation of the dollar.


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The Real Exchange Rate (cont.)

  • A change in world relative supply of US products

    • An increase in relative supply for US output (caused by an increase in US productivity) causes the price of US goods relative to foreign goods to fall.

    • This is a real depreciation of the value of US goods = an increase in q

    • Conversely, a decrease in relative supply for US output leads to a real appreciation of the dollar.


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Determining the Long Run Real Exchange Rate

In the long run, the supply

of goods and services in

each country depends on

factors of production like

labor, capital and

technology—not prices or

exchange rates.


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Determining the Long Run Real Exchange Rate (cont.)

The demand for

US products relative

to the demand for EU

products depends on

the relative price of

these products, or the

real exchange rate.

When the real

exchange rate,

qUS/EU= (E$/€PEU)/PUS

is high, the relative

demand for US

products is high.


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The Real Exchange Rate Approach to Exchange Rates

  • The real exchange rate is a more general approach to explain exchange rates. Both monetary factors and real factors influence nominal exchange rates:

    1a. Changes in monetary levels, leading to temporary inflation and changes in expectations about inflation.

    1b. Changes in monetary growth rates, leading to persistent inflation and changes in expectations about inflation.

    2a. Changes in relative demand: increase in relative demand for domestic products leads to a real appreciation.

    2b. Changes in relative supply: increase in relative supply for domestic products leads to a real depreciation.


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The Real Exchange Rate Approach to Exchange Rates (cont.)

  • What are the effects on the nominal exchange rate?

    E$/€ = qUS/EU x PUS/PEU

  • When only monetary factors change and PPP holds, we have the same predictions as before with no changes in the real exchange rate.

  • When factors influencing real output change, the real exchange rate changes.

    • With an increase in relative demand for domestic products, the real exchange rate adjusts to determine nominal exchange rates. In this case, E and q move in the same direction.

    • With an increase in relative supply of domestic products, the situation is more complex…


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The Real Exchange Rate Approach to Exchange Rates (cont.)

  • With an increase in the relative supply of domestic products, the real exchange rate adjusts to make the relative price of domestic goods to decline, but also the relative amount of domestic output increases. (I.e., both q and Y change at the same time. Both increase.)

    • This second effect increases the real money demand in the domestic economy relative to that in the foreign economy:

      PUS = MsUS/L (R$, YUS)

    • The domestic price level decreases relative to the foreign price level.

    • The effect on the nominal exchange rate is ambiguous:

      E$/€ = qUS/EU x PUS/PEU

?


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Interest Rate Differences

  • A more general equation of differences in nominal interest rates across countries can be derived from:

    (qeUS/EU - qUS/EU)/qUS/EU = [(Ee$/€ - E$/€)/E$/€] – (eUS- eEU)

    R$- R€ = (Ee$/€- E$/€)/E$/€

    R$- R€ = (qeUS/EU - qUS/EU)/qUS/EU + (eUS- eEU)

  • The difference in nominal interest rates across two countries is now the sum of:

    • The expected rate of depreciation in the real exchange rate (the value of domestic goods relative to foreign goods)

    • The expected inflation difference between the domestic economy and the foreign economy


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Real Interest Rates

  • Real interest rates are inflation-adjusted interest rates:

    re = R – πe

    where πe represents expected inflation and R represents nominal interest rates.

  • Real interest rates are measured in terms of real output: what quantity of real goods and services can you earn in the future by saving real resources today?


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Real Interest Rates (cont.)

  • Real interest rate differentials are derived from

    reUS – reEU = (R$ - eUS) - (R € - eEU)

    R$- R€ = (qeUS/EU - qUS/EU)/qUS/EU + (eUS- eEU)

    reUS – reEU = (qeUS/EU - qUS/EU)/qUS/EU

  • The last equation is called real interest parity.

    • The differences in real interest rates (return on saving in terms of real resources earned) between countries is equal to the expected change in the value/price/cost of goods and services between countries.




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