Tag Archive 'Balance of payments'

Nov 27 2014

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:

  • The US and Canada are trading partners
  • 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 in Canadian dollars, then following the depreciation of the US dollar American export revenues actually appear to decrease, 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 dollar)!

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

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Nov 07 2014

The dollar’s recent rise and determinants of exchange rates – October to November 2014

In the last couple of months the exchange rate of the US dollar against the currencies of many of its trading partners has been rising steadily. The charts below show the value of the dollar in terms of Japanese Yen and Euro in the last month.

Euro per dollar Yen per dollar

 

The reasons for the rise in the dollar are simple and illustrate some of the determinants of exchange rates that we learn about in our IB Economics classes. Listen to a recent story from APM’s Marketplace radio show about the dollar’s recent rise, then answer the questions that follow.

Discussion Questions: 

  1. Discuss with your class how each of the factors mentioned in the podcast help explain the recent rise in the value of the US dollar against other major currencies:
    • “Recovery”
    • “Yields”
    • Interest rates”
  2. Why might the rising dollar…
    • help developing countries?
    • help American consumers?
    • hurt American producers?
  3. Using your knowledge of macroeconomics, discuss and explain the following claim: “the impact of more expensive exports and cheaper imports may be to stifle inflation just enough to make the Fed slow down any rate increases, which would in turn slow down the dollar’s rise.”
  4. Using diagrams for the market for US dollar in Europe and for the Euro in the United States, and referring to one of the determinants of exchange rates mentioned in the story, illustrate the rise in the dollar’s value against the Euro over the last month and the corresponding fall in the Euro’s value against the dollar. Use values from the chart above on to determine the appropriate exchange rate values for your graphs.
  5. Explain how each of the following interventions could be used to devalue the dollar, assuming the US government or Federal Reserve Bank decided the dollar’s appreciation posed a threat to the US recovery:

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