Econ 437 Spring 2023 Problem Set 1
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Econ 437 Spring 2023
Problem Set 1
Due Date: January 24, 2023 by Midnight
Question 1. In this question, you see the impact of taking logs of the data. To do this we consider the relationship between FDI stock and income.
Download the data Data_ps1.xlsx . The first column is the name of the country, the second column is GDP per capita, and the third column is outward FDI stock over GDP. The data is downloaded from UNCTAD statistics, and it is for 2019.
b) Plot . Let GDP per capita be on the x-axis and outward FDI stock/GDP on the y-axis. You may remove outliers, for example, remove countries if their Outward FDI Stock /GDP is higher than 10.
a) In a few sentences, describe the relationship between these two variables you observe in the plot.
a) Now convert data into logarithms (“logs”). Make sure you use the natural logarithm (log base e ). If you use Excel or Google Sheets, use the ln function. Plot the new series.
a) In a few sentences, describe what you see in the scatter plot. What is the relationship between outward FDI and GDP per capita? Is it a strong relationship? How does this plot compare to the one in part b.?
Question 2. Statistics (or econometrics) gives us a powerful tool for studying the relationship between two variables: linear regression. As you might gather from the name, this tool works well when the two variables have a linear relationship.
b) In your Excel graph from question 1c, add a linear trend line (if you need help with this, Google trend line”).
To draw the trend line, Excel is assuming that the data are related linearly,
ln ( ) = α + βln ( ) + ϵ
and tries to find the two numbers α and β to make the line fit the data as well as possible.
a) Find the option in Excel to “display trend line equation on chart.” The equation it displays is showing the values of α (the intercept of the line) and β (the slope of the line). In a few sentences, describe what the slope means.
a) (Bonus) Show that the slope coefficient (β ) also gives us the percentage increase in FDI/GDP as a result of one percentage increase in GDP per capita. (Hint: ln(1 + x) ≈ x for small x , and use properties of ln ).
Question 3. Use the heterogenous firm model that we developed in class (and in the note “Horizontal Direct Investment”) to answer the following questions. This question deals only with domestic firms.
a) How does the price charged by a domestic firm change as ϵ increases? What is the intuition for this result?
a) Let ϵ = 3 , w1 = 2 , E1 = 50 , and fp = 1.6 . What is the profit of a country 1 domestic firm with productivity φ = 1.5 ?
a) Let’s plot the profit of a firm with φ = 1.5 earns as ϵ changes and holding all other variables constant at their values given in part b. Observe that price is a function of ϵ , you need to take into account change in price also. To do this, plug the price function into the profit formula we derived in the class. To plot the graph, go to https://www.desmos.com/calculator.
Please type the profit function to the left panel. You should replace ϵ
with 北 , and the only unknown should be 北 , for other variables you should plug in their values. You may use ^ (shift+6 on Windows) to take the power, or you may use the scientific keyboard by clicking on the keyboard image at the bottom left corner of the page.
Please set the range of the x-axis to be between 2 and 10, and set the
range of the y-axis accordingly (so that plot looks nice). To set the range, click on the wrench icon () on the top right corner and set ranges accordingly.
Once you are done, click on the share button () on the top right corner.
Then click on export image () to save the image. Then, include it in your answer.
a) What is the relationship between the price elasticity of demand and firm profits? In no more than a paragraph, discuss the economic intuition for this result.
Question 4. IKEA, the flat-pack furniture company, is, in many ways, a classic multinational: its IKEA Industry subsidiaries produce furniture and other items in 11 countries throughout the world. On the retail side, however, IKEA chooses to franchise.
2023-02-04