Purchasing-power parity holds between the nations of Ectenia...

Purchasing-power parity holds between the nations of Ectenia and Wiknam, where the only commodity is Spam. a. In $2020,$ a can of Spam costs 4 dollars in Ectenia and 24 pesos in Wiknam. What is the exchange rate between Ectenian dollars and Wiknamian pesos? b. Over the next 20 years, inflation is expected to be 3.5 percent per year in Ectenia and 7 percent per year in Wiknam. If this inflation comes to pass, what will the price of Spam and the exchange rate be in $2040 ?$ (Hint: Recall the rule of 70 from Chapter $14 .$ ) c. Which of these two nations will likely have a higher nominal interest rate? Why? d. A friend of yours suggests a get-rich-quick scheme: Borrow from the nation with the lower nominal interest rate, invest in the nation with the higher nominal interest rate, and profit from the interest-rate differential. Do you see any potential problems with this idea? Explain.

Purchasing-power parity holds between the nations of Ectenia and Wiknam, where the only commodity is Spam.
a. In $2020,$ a can of Spam costs 4 dollars in Ectenia and 24 pesos in Wiknam. What is the exchange rate between Ectenian dollars and Wiknamian pesos?
b. Over the next 20 years, inflation is expected to be 3.5 percent per year in Ectenia and 7 percent per year in Wiknam. If this inflation comes to pass, what will the price of Spam and the exchange rate be in $2040 ?$ (Hint: Recall the rule of 70 from Chapter $14 .$ )
c. Which of these two nations will likely have a higher nominal interest rate? Why?
d. A friend of yours suggests a get-rich-quick scheme: Borrow from the nation with the lower nominal interest rate, invest in the nation with the higher nominal interest rate, and profit from the interest-rate differential. Do you see any potential problems with this idea? Explain.

Key Concepts

Purchasing Power Parity (PPP)

Purchasing Power Parity is an economic theory which posits that in the absence of transaction costs and other trade barriers, identical goods should have equal prices when expressed in a common currency across different countries. This theory is foundational for understanding how currencies should exchange to equalize the purchasing power of money in different economies.

Exchange Rate Determination

Exchange rate determination in the context of PPP involves setting the rate of conversion between two currencies so that a basket of goods has the same price across countries. This concept implies that differences in the prices of the same commodity in different countries are neutralized by adjusting the exchange rate, thus ensuring balanced purchasing power across economies.

Inflation and Its Impact on Relative Prices

Inflation refers to the rate at which the general level of prices for goods and services rises and subsequently erodes purchasing power. When two nations experience different inflation rates, the relative prices of goods will change over time, affecting the real value of their currencies. This concept is crucial for understanding how differential inflation rates lead to adjustments in the exchange rate, as a country with a higher inflation rate typically sees its currency depreciate in order to maintain PPP.

Rule of 70

The Rule of 70 is a simple formula used to estimate the number of years it will take for a variable, such as inflation or investment returns, to double given a constant annual growth rate. By dividing 70 by the annual percentage growth rate, one can quickly approximate the doubling time, making it a handy tool for forecasting long-term changes in economic variables.

Nominal vs. Real Interest Rates

Nominal interest rates are the stated rates on financial instruments without adjustment for inflation, while real interest rates are adjusted for the effects of inflation, representing the true cost of borrowing. This differentiation is important because it explains how countries with higher inflation tend to offer higher nominal interest rates to attract lenders, compensating for the expected loss in purchasing power.

Arbitrage and Exchange Rate Risk

Arbitrage involves exploiting price differences between markets to earn a profit, such as borrowing in a country with low nominal interest rates and investing in one with higher rates. However, such strategies are subject to exchange rate risk, as fluctuations in the value of currencies can offset expected gains. This concept underscores the challenges and potential pitfalls in attempting to profit solely from interest rate differentials without accounting for transaction costs and unforeseen currency movements.

Transcript

00:02 Okay, guys, this is chapter 31, section 1, 12, 9, and there are four parts to the towel.

00:11 This first part, we are given that purchasing power parity holds that there are two countries, actinia and wickham, that spam is $4 per can in actinia, and that spam is $20 per can in wickham, and we want to know what the exchange rate is.

00:33 So purchasing power parity is based on the law of one price.

00:38 Basically this means that the exchange rate between any two countries is that given the exchange rate, the price of a good will be the same in both countries.

00:48 We get this by simply dividing the cost of a can of spam in both countries.

00:58 So here we have 24 passive in wickham, divided by $4 .4 .5.

01:05 In ectenia, and that's going to give us $6 per peso.

01:13 Or it could be one six.

01:21 Sorry, this is peso per dollar.

01:28 Or one six dollar per peso.

01:33 In part two, in power b, we're given that inflation is 3 .5 % in ectenia, inflation is 7 % in wicnam.

01:48 And that this level of inflation will last for 20 years.

01:51 So giving this information, what is the price of spam in each country after 20 years? and then what is the exchange rate? so inflation is the rate by which prices increase over time.

02:05 And so while the term inflation is generally used to describe the overall or aggregate price level, it can be used to describe individual goods in this case like spam.

02:15 So recall the rule of 70.

02:17 The rule of 70 says that if a variable, in this case, spam, grows at a rate of x percent per year, so variable grows at x percent per year, then it's going to take 70 divided by x years to double.

02:47 So looking at this problem, we see that inflation in nectonia is 3 .5 % for year, right? so 3 .5 % inflation.

02:58 So if the price of stamp is increasing 3 .5 % per year, it's then going to take 70 divided by 3 .5, which equals 20 years to double in value.

03:12 And we're given in the question that this level of inflation will last for 20 years.

03:18 So then the price level is going to double.

03:21 So it was, remember the last question, it was $4.

03:26 So now it's going to be, you know, four times two equals $8.

03:34 Four times equals dollars.

03:41 So in wickham, the inflation is 7%...