In the terminolgy given in the question, predicted exchange rate is for the real exchange rate. In the question the actual exchange rate has been given This is also called the nominal exchange rate.
So, your predicted exchange rate is the Real exchange rate
= Nominal exchange rate * Domestic price / Foreign Price
=9,541 * (14,600 / 3) =
you can calculate now.
But I suspect thereis some problem with your textbook formula. The purchasing power parity ratio is $3= rupiah 14600, or $1 is equivalent to rupia 4866.67.
Thus , Domestic price / Foreign Price = 4866.67 Multiplying this with the nominal exchange rate of 9,541 is a huge sum which cannot be said to be the real exchange rate!!!
I think you check the text book again. The formula should have been (though strictly still not accurate):
Real exchange rate = Nominal exchange rate *Foreign price / Domestic Price.
With my formula above, the real exchange rate =
9,541 * (3 /14,600) = close to 1.9
This means that the real exchange rate of rupaih is 1.9 times the actual/ noimal exchange rate. In other words, the real exchange value of rupiah would be 9,541/ 2 or about 5026 rupiah per dollar.
It is easy to see why it is so. You can buy a big mac abroad at $3 which is equivalent to 3* 9541= 28,623 rupaih as against big mac oprice of 14,600 rupiah at home. So, the real value of rupiah is 28,623/ 14,600 = 1.9 times higher than the nominal exchange rate. So, you should be giving 1.9 times fewer rupaih per dollar than the nominal/ ctual/ official/ market exchange rate. The real worth of rupiah is 9,541/ 2 or about 5026 rupiah per dollar.
See notes below:
1. Nominal and real exchange rates
The nominal exchange rate e is the price in domestic currency of one unit of a foreign currency.
The real exchange rate (RER) is defined as
RER = e * (P*/P), where P is the domestic price level and P * the foreign price level. P and P * must have the same arbitrary value in some chosen base year. Hence in the base year, RER = e.
The RER is only a theoretical ideal. In practice, there are many foreign currencies and price level values to take into consideration. Correspondingly, the model calculations become increasingly more complex. Furthermore, the model is based on purchasing power parity (PPP), which implies a constant RER. The empirical determination of a constant RER value could never be realised, due to limitations on data collection. PPP would imply that the RER is the rate at which an organization can trade goods and services of one economy (e.g. country) for those of another. For example, if the price of a good increases 10% in the UK, and the Japanese currency simultaneously appreciates 10% against the UK currency, then the price of the good remains constant for someone in Japan. The people in the UK, however, would still have to deal with the 10% increase in domestic prices. It is also worth mentioning that government-enacted tariffs can affect the actual rate of exchange, helping to reduce price pressures. PPP appears to hold only in the long term (3–5 years) when prices eventually correct towards parity.
More recent approaches in modelling the RER employ a set of macroeconomic variables, such as relative productivity and the real interest rate differential.
Nominal exchange rate = (Real exchange rate+1)* (expected inflation +1) -1.
Next, Start with the domestic (U.S.) and foreign (German) prices of a good, say a gallon of gas:
P = price in $ of domestic good (say, one gallon of gas cost $1.20)
Pf = price in units of foreign currency of the same good in a foreign country (say, a gallon of gas in Germany cost DM 2.0)
Is gas more expensive in the U.S. or in Germany? Clearly, the answer depends on the exchange rate between $ and DM.
The price in dollars (P$f) of a unit of the foreign good (a gallon of gas in Germany) is equal to its price in the foreign currency (Pf = DM 2) divided by the exchange rate of the dollar relative to the foreign currency e (DM/$) = 1.5
P$f = Pf / e = 2 / 1.5 = 1.33
The relative price of the domestic good to the foreign good (price of gas in the U.S. to the price of gas in Germany expressed in $) is:
P / (Pf / e) = 1.20 / 1.33 = 0.90
where e is the (spot) exchange rate. Gasoline in the U.S. is about 10% cheaper than it is in Germany. We can call this the real exchange rate for gasoline. If all goods were the same in the U.S. and Germany and there were no barries or costs of trade, then we would expect the price of goods to be the same when expressed in the same currency. That is, if the price of gasoline in the U.S. rose to $1.33 while the nominal exchange rate and the price of gasoline remained unchanged, then the real exchange rate for gasoline would be 1.0. In fact, if the real exchange rate were less than one and trade could take place costlessly, buyers in Germany would only buy in the cheap country (US), driving up prices there until foreign and domestic prices were equal. If Germans could fill up their tanks in the U.S., the prices of gas, expressed in a common currency, should be the same, leading the real exchange rate of gasoline to stay around one. However, we do know that it is hard to drive across the ocean to fill one's tank of gasoline. Remember though, that if there were no tunnel tolls, we might be tempted to drive to New Jersey where gasoline is cheaper than in New York.
Often we use price indexes, like CPI or GDP deflators, representing baskets of goods to compare exchange rate adjusted prices in different countries.. In this case the ratio of domestic prices to foreign prices in domestic currency is referred to as the real exchange rate. A real exchange rate calculated with price indexes does not tell us anything about difference in the absolute price levels in the two countries. If both price indexes have a vaule of 100 in some base year, the real exchange rate is equal to the nominal exchange rate in that year. However, movements in the real exchange rate from year to year tell us about changes in the purchasing power of one currency compared to the other.
Real Exchange rate index = P / (Pf / e) = eP / Pf
Purchasing Power Parity
The theory of price equalization around the world can be applied to the baskets of goods underlying aggregate price indexes. We call this purchasing power parity, (or PPP) since the purchasing power of a dollar is predicted to be the same in both countries. The PPP condition is:
P = Pf /e (= P$f )
In the gasoline example we did not satisfy the PPP condition:
P =1.20 < Pf /e =1.33 (divergence from PPP)
So how, can we reach a PPP equilibrium when the relative price differs from unity ? There are three alternative ways the equilibrium can be restored:
1. German prices could fall from DM 2 to DM 1.8 so that:
P = 1.20 = Pf /e = 1.8 / 1.5
2. US prices may go up from $1.20 to $ 1.33 so that:
P = 1.33 = Pf /e = 2.0 / 1.5
3. The DM/$ exchange rate could appreciate from e = 1.5 to e = 1.67 so that:
P = 1.20 = Pf /e = 2.00 / 1.67
In practice, all of the three effects will be at work in reality.
What are the forces that might lead to convergence towards PPP?
What is the evidence on the PPP ? If the PPP holds, the real exchange rate should be equal to one and constant over time.
If the PPP holds:
e P / Pf = P / P = 1
However, we find, when we compute real exchange rate using consumer price indexes, that it varies a lot: prices of gasoline in particular, and goods in general, are often much different in Germany and the US, and between any two other countries, as well.
At least in the short-run, PPP is a poor description of reality.