Nov 25 2013

## A mathematical proof of the Marshall Lerner Condition

One of the toughest topics to teach in IB higher level Economics is the Marshall Lerner Condition, which is an International Economics concept which states the following:

If the combined price elasticities of demand of a nation’s imports and exports is greater than one (PEDx + PEDm > 1), then a depreciation or a devaluation of the nation’s currency will move its current account balance towards surplus.

This is a concept I have been teaching for eight years now, and I have even written about it in my textbook and produced a YouTube video lecture explaining it to students, but one thing I’ve never done is attempted a mathematical proof of the concept (needless to say, I avoid using math as much as possible, and the prospect of “proving” the MLC was always too daunting).

But this evening I received an email from an Economics teacher in Paris asking for just such a proof. So I buckled down and worked it out. In her email, the teacher said:

The Marshall Lerner Condition states that if the PEDx + PEDm > 1 then a depreciation in a country’s currency will reduce a current account deficit.

Suppose the PED for exports = .6 and the PED for imports = .5. The sum is greater than 1, therefore the MLC is met. A depreciation of this country’s currency should therefore improve its current account balance.

But based on my analysis, this country’s current account should be getting worse, not better.

For Exports: price is decreasing but the quantity demanded is increasing by proportionally  less (since PEDx = 0.6) so the country’s total export revenue is decreasing

For Imports: price is increasing and quantity demanded is decreasing by proportionally less (since PEDm = 0.5) so the country’s total spending on imports is increasing

The country’s revenues from exports are decreasing while the country’s spending on imports are increasing, so overall the trade balance is getting worse (moving deeper into deficit) not improving.

What am I doing wrong?

This teacher’s email really stumped me at first, because her logic is totally sound. I figured the only way I was going to be satisfied was if I worked it mathematically. So here’s the result and the reply I sent to the teacher:

Hello,

Your email really got me thinking about this. Your logic stumped me at first, but then inspired me to go work it out with numbers. So, hopefully my “proof” of the MLC below will clarify your confusion.

To simplify the analysis we will use easy numbers. I will use your values of PEDx = 0.6 and PEDm = 0.5

Assumptions:

• Current exchange rate: \$1 US = \$1 CA
• US exports 10 widgets at \$1 US apiece for a total export revenue of \$10 US
• US imports 10 wingdings at \$1 CA apiece for a total import expenditure of \$10 US
• US trade balance: \$10 – \$10 = 0
• PEDx = 0.6 and PEDm = 0.5

Next, assume the US \$ depreciates by 10% against the CA \$. Now,

• \$1 US = \$0.90 CA
• \$1 CA = \$1.11 US

Impact on imports:

• Price to Americans of Canadian wingdings rises to \$1.11 US
• Quantity demanded falls by 5.5% to 9.45
• Total expenditures on Canadian imports expressed in US \$: \$1.11 x 9.45 = \$10.49

In order for the US trade balance to improve US export revenues must increase by more than \$0.49 US.

Impact on exports:

• Price to Canadians of US widgets falls by 10% to \$0.90 CA
• Quantity demanded increases by 6% to 10.6
• Total revenue from exports to Canada expressed in CA \$: \$0.90 x 10.6 = \$9.54 CA.
• Since \$1 CA = \$1.11 US, the value of US exports to Canada expressed in US \$ is \$9.54 x \$1.11 = \$10.59

Expressed in US \$, exports increased by \$0.59 and imports increased by \$0.49.

Therefore, US net exports are now \$10.59 – \$10.49 = \$0.1. The MLC is met and the US trade balance moves into surplus.

I think the only mistake with the logic you applied in your email was that you were not considering that a country’s balance of trade is measured in its own home currency. As you can see, if we measured the value of US exports following the depreciation in Canadian dollars, the export revenues actually decreased following the depreciation of the US \$, moving the US into a current account deficit. But even though Canadians are spending less of their own dollars on US goods, the Canadian dollar has now appreciated by 11%, therefore the value of US exports expressed in US \$ actually increases (due to the now weaker US \$)!

I hope this all makes sense! Thanks for inspiring me to buckle down and tackle this analysis! I’ve been teaching this concept for eight years and have never actually taken the time to walk through a proof like this.

Best,
Jason

Feb 07 2013

## Lesson plan: Elasticity, exchange rates and the balance of payments – understanding the Marshall Lerner Condition

Related Unit: IB Economics Unit 4.7 – Balance of Payments (Unit 3.3 in the new IB Economics syllabus)

Topic: The Marshall Lerner Condition and the J-Curve

Learning Goals/Objectives:

Test of prior knowledge:

1. Define ‘price elasticity of demand’ and explain how it is measured.
2. With the use of examples, explain why some products have low price elasticity while others have a high elasticity. With the use of examples, explain why the price elasticity of demand for some goods changes over time
3. Explain how the depreciation of a country’s exchange rate might affect its current account balance. IS THIS ALWAYS THE CASE?
4. How might the PED for exports and imports influence the balance on the current account following a change in the value of a nation’s currency?

Part 1:

The exchange rate of Japanese Yen in the United States over the last two years:

Take a snapshot of your two-year exchange rate diagram in OneNote, then copy and paste the questions below into the page.

1. Write a brief description of the changes in your country’s exchange rate over the last two years. (2 marks)
2. Focus on two specific time periods from during the last two years: One in which your currency appreciated noticeably and one in which it depreciated noticeably. These could be periods of just a couple of days or longer periods of weeks or more. Highlight these in two different covers in your graph.
3. Describe what is happening to your currency during the two time periods you highlighted in your chart. (2 marks)
4. Explain TWO factors that may have caused the currency to change in value. (2 marks)
5. Given the changes to the exchange rate you identified above, what would you predict would happen to your country’s current account balance over the two periods identified? Explain. Following appreciation – in the short-run and in the long-runFollowing depreciation – in the short-run and in the long-run. (4 marks)
6. Why does the price elasticity of demand for imports and exports increase over time following a change in a country’s exchange rate? (2 marks)
7. Draw a J-Curve showing the likely change in your nation’s current account balance following the period of depreciation of its currency shown in your chart above and explain its shape, referring to your country’s currency. (2 marks)
8. For both the period of appreciation and the period of depreciation you identified above, explain the impact of the change in exchange rates on the following (4 marks)
• a firm that imports its raw materials from the other country
• a firm that exports its finished products to the other country
• consumers who buy imports from the other country
• a firm that produces good for the domestic market and competes with firms from the other country

Part 2:

Read the following article:  . Based on the extracts below, answer the questions that follow.

Some applaud the dollar’s fall because they believe it makes U.S. exports less expensive and that higher demand will cut the trade deficit. The downside of a low-value dollar is that it makes all the imports we consume more expensive, including raw material and parts used by U.S. businesses, and makes it costlier for U.S. dollar holders to travel or invest outside the U.S. A continued drop in the dollar’s value could destabilize the international economy, leading to a worldwide recession.

• Why might the weaker dollar worsen the US trade deficit? Under what conditions would the weaker dollar improve America’s trade deficit? (2 marks)

Some argue our large trade deficit (or current account deficit) is responsible for the fall in the dollar’s value. They have it backward. It is the flow of foreign investment dollars (the capital account) into the U.S. economy that drives the trade deficit.

The world now is actually on a two-currency standard — the dollar and the euro. China in effect has fixed its currency to the dollar for the last two decades, and the Japanese central bank only allows the yen to fluctuate within a limited range against the dollar.

• How do exchange rate controls by China and Japan reduce the likelihood that a weaker dollar will improve the United States’ current account balance? (2 marks)

So long as the U.S. continues to offer a higher return on capital than its foreign competitors, both foreign banks’ and private investors’ demand for dollars grow, and the current account deficit can be sustained.

• If investments in the United States began earning lower returns relative to investments in other countries’ financial and capital markets, what would ultimately happen to the US balance of payments in its current and financial accounts? Explain (2 marks)

The above lesson was inspired by the Biz-Ed activity “International Trade: The Falling Dollar or Rising Pound?”

Mar 06 2012

## Planet Money Podcast – “China’s Giant Pool of Money”

NPR’s Planet Money team did a great podcast last week about China’s accumulation of US dollars from its large trade surplus with the United States. This story offers a great illustration of the theories I introduced in my recent video lesson, The Relationship between the Current Account Balance and Exchange Rates

Listen to the podcast, watch the video lesson, and respond to the discussion questions that follow.

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Discussion Questions:

1. Why does the Chinese Central Bank possess over \$3 trillion of foreign exchange reserves?
2. What does the Chinese Central Bank do with the vast majority of the money it earns from the sale of its exports that it does NOT spend on US goods? Why not keep this money in cash?
3. Why does the Chinese Central Bank manage the value of its currency, the RMB? Why not let the exchange rate be determined by the free market?
4. As the RMB is slowly strengthened against the dollar, who are the winners and losers? What impact should a stronger RMB have on the balance of trade between China and the US?

Nov 23 2011

## Why the falling rupee makes Mr. Welker a happy man! (and may help the Indian economy in the long-run)

Indian Rupee hits all-time low against the dollar – CBS News

A couple of years ago I wrote what I would call a “fantasy” blog post about how the recent depreciation of the British pound would have made a ski trip to India a whole lot cheaper since the tour company I was planning to go with quoted its prices in the British currency. Well, at the time I wasn’t really planning to go skiing in the Himalayas, but this year, because of a fall in the value of another currency, I really AM going to ski in the Himalayas!

The chart below shows how the value of the Swiss franc has changed against the Indian rupee over the last year and a half.

The Value of the Swiss Franc in terms of India Rupees – last 18 months

As can be seen, the franc, which is the currency in which I get paid here in Switzerland, has risen from only 40 rupees 18 months ago to as high as 63 rupees in August this year, and is currently at 57 rupees per Swiss franc. We’ll explore the underlying causes of this appreciation of the franc in a moment, but first let’s examine its effect on my dream of skiing in the Himalayas.

So just yesterday morning I did, at last, after six years of dreaming of this adventure, book a six day guided ski trip in the Indian Kashmir town of Gulmarg, which sits at an elevation of 2800 meters and has lift-accessed skiing up to 4,000 meters, making Gulmarg the second highest ski resort in the world. Okay, enough facts. The strong franc made this trip a reality for me for the following reason:

• 18 months ago, the 40,000 rupee price tag of this ski trip would have meant a cost of 1,000 swiss francs.
• Today, due to the strong franc, the 40,000 rupee price tag means this trip is only costing me 700 swiss francs.
Due to the strengthening of the franc, and the weakening of the rupee, my Himalayan ski odyssey is now costing me 30% less than it would have 18 months ago… so… I’m doing it! YEAH!
-
The Swiss currency has appreciated by 42.5% in the last 18 months against the India rupee. WHY?! What could be going on in the world that accounts for this massive swing in exchange rates? There are a few causes worth mentioning here, which have to do with factors within Switzerland and India, but also external factors beyond the control of either country. Here are some of the major ones:
-
In Europe:
• The franc has risen against most world currencies, not just the rupee, due, ironically, to economic uncertainty in the rest of Europe. Since Switzerland has its own currency, and a strong economy, whereas all of its European neighbors have a common currency (the euro), and struggling economies, investments in Swiss assets (primarily savings accounts and government debt) have become increasingly attractive. This has caused demand for francs to rise, causing its value to increase against most currencies.
• The debt crisis in the rest of Europe, most notably in Greece and Italy, reduces certainty among investors in these European governments’ ability to repay their debt, creating further demand for investment in Switzerland, causing the franc to rise.
In India:
• According to the Associated Press, “Slowing growth, a swelling current account deficit and waning investor interest in India are adding to pressure on the rupee…” India runs a large trade deficit, equaling about 3% of the nation’s GDP. This means Indians are dependent on imported goods, while foreigners do not demand as many of its exports. This puts downward pressure on the exchange rate of the rupee.
• In addition, the “slowing growth” rate in India sends the signal that the country’s central bank may lower interest rates to try and stimulate GDP. However, the expectations of lower interest rates in the future make international investors look elsewhere for investments with relatively higher returns.
• Next, weaker growth prospects make investments in Indian assets (such as corporate stocks or bonds) less attractive to international investors, since they expect demand for Indian output to slow in the future, thus demand for rupees declines now.
• Finally, the decline in the rupee’s value itself is fueling a further increase in the value of the franc. Not all currency exchanges are for the purpose of purchasing a nation’s goods or its assets. Much currency trading is among forex brokers who buy and sell currencies to hold as assets themselves. The weakening of the rupee may be fueling speculation about the future value of the rupee, which acts as a self-fulfilling prophecy, as forex investors will continue to swap rupees for other currencies, including the Swiss franc.
All this adds up to one thing for me: A 30% discount on my ski vacation to India! Of course, for the Indian economy, a weaker rupee might be just what is needed to boost future economic growth. As the rupee falls and the Swiss franc and the US dollar gain value, not only will ski vacations to India become more attractive to foreigners, but so will other exports from the South Asian nation. That 3% trade deficit that has contributed to the rupee’s decline may begin to move towards the positive if foreigners like me begin taking more trips to and buying more goods from Indian firms.
-
The weaker rupee could, in the long-run, increase total demand for India’s output, which would improve employment and growth prospects on the sub-continent. Furthermore, if India’s growth rate picks up due to increased net exports, the Indian central bank may be able to raise interest rates a bit, reducing the incentive for investors to flee the rupee and put their money in countries with higher returns.
-
Through this process of self-balancing, in time the weaker rupee will probably lead to an improvement in India’s economic situation and eventually the rupee will begin to strengthen against the currencies of India’s trading partners. But for now, I’m going to enjoy my week of guided skiing in the Himalayas, and thank the forex traders and currency speculators for allowing me to take this dream vacation for such a bargain price!

courtesy: http://www.gulmargpowderguides.com/

Sep 06 2011

## Stability – the greatest Swiss virtue?

BBC News – Swiss National Bank acts to weaken strong franc

The Swiss pride themselves on their long history of stable democracy, domestic tranquility and international neutrality. The stability of the Swiss state and the Swiss economy is heralded as one of its greatest virtues. But in the last few months, particularly in the first two weeks of August, instability has been more the norm in the Swiss economy due to the rapid appreciation of the Swiss currency, the franc, against the euro and the US dollar, which I blogged about here a couple of weeks ago.

Well, as of this morning, the franc’s ascent looks like it has reached its end, and the value of the franc is set to be pegged at 1.20 francs per euro (or 0.83 euros per franc), which is about 8% below what it was trading at this morning.

The Swiss National Bank (SNB) has set a minimum exchange rate of 1.20 francs to the euro, saying the current value of the franc is a threat to the economy.

The SNB said it would enforce the minimum rate by buying foreign currency in unlimited quantities.

The move had an immediate effect, with the euro rising from about 1.10 francs before the announcement to 1.21 francs.

In a statement, the SNB said: “The current massive overvaluation of the Swiss franc poses an acute threat to the Swiss economy and carries the risk of a deflationary development.

“The Swiss National Bank is therefore aiming for a substantial and sustained weakening of the Swiss franc. With immediate effect, it will no longer tolerate a EUR/CHF exchange rate below the minimum rate of CHF 1.20.

“The SNB will enforce this minimum rate with the utmost determination and is prepared to buy foreign currency in unlimited quantities.”

Against the franc, the euro climbed 9%, the dollar rose 7.7% and sterling gained 7.8% within minutes of the announcment.

NPR’s Planet Money reported on the story from Berlin here:

The instability resulting from the franc’s 30% rise in the value against other major currencies throughout the year is primarily the effect it has had on Swiss exporters. Foreign consumers, who actually buy about 50% of Switzerland’s output, have seen the prices of Swiss goods rise as the value of their own currencies has declined against the franc, reducing demand abroad for Swiss exports, forcing firms in the Swiss export sector to reduce their labor force and otherwise cut costs to compensate for the falling demand for their products. The threat of rising unemployment and falling demand for its output caused the Swiss National Bank and the Swiss government great concern, leading to today’s announcement.

The “deflationary development mentioned by the SNB refers to a situation in the Swiss economy where the strong franc makes imports appear ever more attractive (and cheaper) to Swiss consumers, and Swiss goods increasingly less attractive to foreign consumers, reducing the demand for Swiss goods overall and forcing Swiss firms to lay off workers and lower their costs and prices to compensate for falling demand. Lower prices for goods and services in Switzerland reduces the incentives for firms to invest in new capital, thus reducing the demand for labor further, threatening to push the Swiss economy into a demand deficient recession. Deflation, defined as a persistent fall in the average price levels of a nation’s goods and services, can result in a downward spiral characterized by rising unemployment, falling demand, lower prices, and increased layoffs in the export sector, further exacerbating the unemployment problem.

The SNB’s decision to peg the franc to the euro will assure that foreign consumers of Swiss goods will not see their prices continue to rise, and Swiss consumers of foreign goods will not see them get any cheaper in coming months, hopefully bringing Swiss households who have recently enjoyed cheap imports back to the Swiss market to buy more Swiss-made goods and services.

Personally, I have mixed emotions about the franc’s peg with the euro. Of course, on one hand I have benefited greatly from the stronger franc, as an American working in Switzerland, earning swiss francs, the stronger currency has meant I can send the same amount of francs home as I always have, but it has translated into larger and larger quantities of dollars. Today, the dollar’s value has risen nearly 8%, meaning this month I will have a bit fewer dollars in my savings account in the United States as I would have before the peg.

As an employee in a Swiss firm, however, my continued employment depends on the continued demand for the service my school is providing, which is education to the children of multi-national corporations operating out of Switzerland. If the franc had continued to rise, the incentive for multi-nationals to locate their offices in Zurich would have become weaker over time, and more firms would have chosen to move their international employees to cities like Paris, London or Frankfurt, reducing demand for my school’s services and threating my own employment and income, just as those workers at other Swiss export firms’ jobs have been threatened in recent months.

Stability is a virtue the Swiss have always prided themselves on. Today’s announcement by the Swiss National Bank will bring greater stability to the Swiss economy, despite the disadvantages it brings to individuals who have enjoyed the benefits of a stronger franc in recent months.

The graph below explains how the SNB will enforce its currency peg against the euro:

Discussion Questions:

1. How will the weaker Swiss franc help the Swiss economy?
2. How will certain individuals in Switzerland be harmed by the weaker franc?
3. How might the weaker franc affect demand for enrollmente at Zurich International School?
4. What are two possible consequences of the Swiss National Bank making a promise to enforce a pegged exchange rate between the franc and the euro?
5. Why are pegged or fixed exchange rates sometimes considered less desirable than floating exchange rates, which is when a currency’s value is determined solely by supply and demand on foreign exchange markets?

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