Suppose that the United States and Canada produce clothing (C) and food (F). The U.S. has an endowment of 200 man-hours, each of which can produce either 2 units of clothi

Econ 140, Summer Session 2 2022

Problem Set 1 Due: 11:59 pm on July 30, Saturday (Pacific Time)

Instructions. To get full credits you need to provide a detailed justification of your claims.

1. (Analytical Exercise) Suppose that the United States and Canada produce clothing (C) and

food (F). The U.S. has an endowment of 200 man-hours, each of which can produce either

2 units of clothing or 2 units of food. Canada has an endowment of 300 man-hours, each

of which can produce either 1 unit of clothing or 2 units of food.

(a) Which country has an absolute advantage in each good?

(b) Derive opportunity costs and examine comparative advantages.

i. For each country, what is the opportunity cost of clothing?

ii. For each country, what is the opportunity cost of food?

iii. Which country has a comparative advantage in each good?

(c) Draw the production possibility frontiers for both economies (draw the production

of clothing on the x-axis and of food on the y-axis). Use a different graph for each

economy.

(d) On your graphs in part (c), indicate consumption of goods in each economy. You do

not need to derive exact quantities.

(e) Let PC/PF denote the relative price of clothing. In the following, we will derive the

autarky equilibrium of each economy.

i. For each country, use the production possibility frontiers above to derive the quan-

tity of production of each good.

ii. Put PC/PF on the y-axis and QC/QF on the x-axis of a graph, and draw the

relative supply curves in each economy under autarky. Use a different graph for

each economy.

iii. In each economy, the relative demand is:

DC/DF = 1

(PC/PF )

Solve the equilibrium relative prices and relative quantities in each economy.

iv. Do these curves depend on the economies endowments in terms of number of

man-hours?

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(f) Now assume that these economies open up to international trade.

i. Derive the quantity of world production for each good.

ii. The world relative demand is:

DC/DF = 1

(PC/PF )

Solve the equilibrium relative prices and relative quantities in the world economy.

(g) Graphically show the changes in welfare in each economy with free trade. Does inter-

national trade provide mutual benefits to both countries?

(h) Now think about a scenario where the U.S. labor force increased by a factor of 1.5.

i. How does this affect the production possibility frontier for the U.S.?

ii. How does the trade pattern change? Make your argument using changes in com-

parative advantages.

iii. Discuss changes in the world equilibrium with respective to the population growth

in the U.S.

(i) ([Extra Credit] Challenging) Let us go back to the initial population size in the U.S.

But, now assume that productivity changes in the U.S.: each field can produce the

same amount of clothing and food, but this amount is now a variable x > 0 (previously

x = 2). How does the equilibrium trade relative price PC/PF depend on x? Clearly

indicate how to compute PC/PF given any value of x > 0.

2. (Empirical Exercise) Is the pattern of trade consistent with the idea of comparative ad-

vantage? Sometimes it is difficult to say which nation has a comparative advantage in

producing a given item, but lets look at trade (export and import) in the following items

between the U.S. and a few other countries to see if the pattern of trade fits what we expect.

• United States: computers and machine tools; Brazil: coffee and agricultural exports

• United States: computers and machine tools; South Korea: manufactured goods

• United States: computers and machine tools; Venezuela: fuel and natural resources

Go to the U.S. Census Bureaus site on to bilateral trade statistics for the U.S. and an- other

country: https://www.census.gov/foreign-trade/statistics/country/sitc/index.html and down-

load the database.

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(a) Try the above examples or investigate other countries and goods that might be inter-

esting. Report your findings and discuss your result. (Hint: Recommended steps to

follow for this exercise.)

i. Download the database “2015-Present” from “Exports and Imports Totals 1-digit

SITC.”

ii. Open the data file using MS Excel (or any comparable software programs to open

spreadsheets that allows basic data analysis) and select the Data tab on top.

iii. Click on Filter. You will then see little arrows appear on the first row in each cell.

iv. Click on the arrow in the cell next to Country. Here, you can arrange the data

in a way that allows you to view only the country of interest. More specifically,

unselect Select All then scroll down to find the country you want to see and make

the selection.

v. Column E shows the value of exports using data from January. Click on the arrow

next to ExportsFASValueBasisJan and click descending which will then rearrange

the U.S. export data for the country of interest.

vi. Follow the same steps using Column F for U.S. import data.

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