Week 2 Tutorial Solutions
Question 1
a) Mexico has absolute advantage in TV; the US has absolute advantage in computers.
We can transform the input requirement table into a table of marginal product of labor (MPL).
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How? For example, it takes Mexico 6 hours of labor to produce 1 unit of TV. We want to know how much can one hour of labor in Mexico do. So, we divide 6hrs/ 1 unit (of TV) by 6. This tells us that 1hrs of labor can produce 1/6 unit of TV.
MPL TV Computer Mexico 1/6 1/4
US 1/3 1/3
Obviously, the gain from increasing 1 extra unit of labor in the US in both industries is higher than that in Mexico.
𝑝 𝑎 1/𝑀𝑃𝐿 𝑝 𝑎 1/𝑀𝑃𝐿
𝑝 1.5,𝑝 1
Note that unit input(labor) requirement 𝑎
Opportunity Cost Mexico
1.5 Computer 1 Computer
Computer 2/3 TV
d) The US has comparative advantage in TV because it has lower opportunity cost to produce a unit of TV; Mexico has comparative advantage in computers because it has lower opportunity cost to produce a unit of computer.
PPF is given by 𝑎𝑥 𝑎𝑦 𝐿, where 𝑎 is the unit input (labor) requirement, x, y denote two goods, L is the labor endowment. Here I denote TV as good y and computer as good x.
PPFinMexico: 4𝑥6𝑦60→𝑦𝑥10
PPFintheUS: 3𝑥3𝑦60→𝑦𝑥20
Note that the 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑃𝑃𝐹 𝑀𝑃𝐿 /𝑀𝑃𝐿 .
(The graph is easy to draw. So I don’t include it.)
The price of a country’s exports divided by the price of its imports is called the terms of trade.
For US it is ; and for Mexico.
The free-trade price ratio needs to lie between the autarky price ratios. So,
𝑝 𝑝 𝑝 𝑝 𝑝 𝑝
1 𝑝 1.5 𝑝
The terms of trade of Mexico will be another way around:
Question 2: a) D;
d) B; e) D.
2 𝑝 1 3 𝑝
Question 3
a) The US has absolute advantage in cola; Russia has absolute advantage in Kombucha.
𝑃 𝑎 1 1 𝑀𝑃𝐿
𝑃 𝑎 1 2 𝑀𝑃𝐿
𝑀𝑃𝐿3 𝑃 𝑎 1
𝑀𝑃𝐿 PPFofRussia: 𝐶𝐾10→𝐾102𝐶
PPF of the US: 𝐶 𝐾 60 → 𝐾 30 𝐶
The autarky consumption is given by 𝑀𝑅𝑆, in each country. (In this
question we cannot obtain the exact value of the consumption because utility function is not given.) Since we assume an autarky market equilibrium, production equals to consumption in each country.
3 or 2. Since 32, it is not possible to be a
world trade equilibrium. For the same reason, 0.2 1.3 is neither a world
trade equilibrium.
NB: The graph is not specific to the question.
What you really need to care about when drawing these graphs: 1) Free-trade prices always go through the “comparative advantage end” of the PPF because given the FT price the country will exhaust all its resources in production of the good it has comparative advantage on; 2) The length of perfectly elastic part of the supply/demand curves equals autarky consumption/production in each country, respectively (I use 𝑥, 𝑥∗ to denote this).
Question 3’
Again, this question cannot be precisely solved because utility function is not specified. But the key take-way for this question is that a large country may affect world-trade price (e.g., significantly large quantity supplied) and end up getting no benefits from
Question 4
a) Home has comparative advantage in cloth; Foreign has comparative advantage in wheat. Home has absolute advantage in both goods.
MPL Cloth(C) Home(H) 1/2 W Foreign(F)* 2 W
Wheat(W) 2 C
First find out the autarky prices: for Home, ∗ 2 for Foreign. ∗
is a credible world trade equilibrium price. However, it is same as the
autarky price at Home. Given this price, Home does not move to higher level of utility. However, Foreign can achieve a higher level of utility. We then conclude that Home does not gain from trade but Foreign does.
Unit labor requirement Home(H)
Foreign(F)*
Cloth(C) Wheat(W) 10 20
Now, , ∗ . There is no gain from trade for both countries. ∗
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