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

Be the first to comment

Nov 19 2014

Efficiency and Market Failure in “Anchorman”

As a follow up to my recent post, A Video and Audio Introduction to Market Failure, I plan to introduce the diagrams we use to illustrate and analyze negative and positive externalities and the inefficiency arising in the markets for certain goods. My fellow Econ Video Lecturer, Mr. Clifford, provides a great introduction to these diagrams in his video, EconMovies 7: Anchorman. We’ll watch the video below before beginning our notes on the subject today! Enjoy!

YouTube Preview Image

Comments Off

Nov 17 2014

Current Account Balance analysis and questions

The table below shows the trade balances for the nations from which my year two IB Economics student come. They are ranked in order from the country whose trade deficit makes up the largest percentage of its GDP  to the country whose trade surplus makes up the largest percentage of its GDP. The blue bars represent the value of the deficit or surplus of each nation. As can be seen, Zimbabwe’s trade deficit is very small in dollar terms, but since its economy is also very small this deficit makes up a large percentage of its total GDP. Click on the image to visit an interactive version of the chart on which you can study the data more closely. Then answer the questions that follow.
chart_2
Discussion Questions:

  1. Identify and define the four components of a nation’s current account balance.
  2. According to the data, which three countries are the most import dependent? Which three countries are the most export dependent? Which country has the most balance trade in goods and services? Which has the most imbalanced trade?
  3. For one of deficit countries above, answer the following two questions:
    1. Assuming its currencies’ exchange rates is floating, explain how persistent current account deficits will affect a country’s exchange rate over time?
    2. Summarize and explain the likely effects of a current account deficit on the following: a) the financial account balance, b) domestic interest rates, and c) national debt.
  4. For one of the surplus countries above, answer the following two questions:
    1. Assuming its currencies’ exchange rates is floating, explain how persistent current account surpluses will affect a country’s exchange rate over time?
    2. Summarize and explain the likely effects of a current account surplus on the following: a) domestic savings rates, b) the financial account balance.
  5. What are the various methods a country can take to reduce a current account deficit? What is the benefit of having a balanced current account as opposed to a large deficit or surplus?

Be the first to comment

Nov 17 2014

A video and audio introduction to Market Failure

Each of the following videos or audio clips illustrate an example of a market failure. Watch or listen to each and answer the questions that follow:

Stories #1 and #2: “Cowboy City” and “Toxic Cotton”

Stories #3 and #4: “Trash Island” and “Nauru is Dead”

Story #4: “E-waste”

YouTube Preview Image

Story #5 “Why is there no Ebola vaccine?”

Story #7: Sweatshops and story #8: Toxic chemicals (watch up to 11 minutes)

YouTube Preview Image

Discussion Questions:

  1. Which of the stories above is about public goods, or goods which would not be provided at all if left entirely to the free market? Explain.
  2. Which of the stories above is about demerit goods, or ones which would be over-provided by the free market due to their negative effects on the environment or human health? Explain.
  3. Which of the stories above is about merit goods, or ones which are provided by the free market, but at a quantity below which is socially optimal due to the fact that they create spillover benefits for society as a whole.
  4. Which of the stories describes a good or goods which the government currently regulates the production of? Which goods does government currently NOT regulate the production of?
  5. What makes each of the stories above examples of market failure?

10 responses so far

Nov 13 2014

Market failure blog post activity and student-created study guide

Over the years I have written many posts on this blog about market failure. The purpose of this activity is for students to re-visit some of these posts, reflect on different types of market failure, and then complete a short survey in which they demonstrate their understanding of the topic.

With the results from the survey, we will have assembled a comprehensive spreadsheet of all the different types of market failure we study, including definitions, examples, graphical representations and possible government responses. This document can then be used for review by Economics students studying for a market failure test.

First, you must get into five groups and each group must read a couple of blog posts about their assigned market failure type.

Group 1: Public Goods:

Group 2: Positive consumption externalities:

Group 3: Positive production externalities:

Group 4: Common Access Resources and the Tragedy of the Commons

Group 5: Information Asymmetry
Group 6: Income Inequality

Once your group has read and discussed the blog posts you were assigned, work together to complete the following form. Only click submit once all questions have been answered!

Google Form – Market Failure Definitions and Examples

Once each group has submitted the form, the results can be viewed publicly here:

Market Failure Definitions and Examples Study Guide

One comment so far

Next »