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II. The Ricardian Model and Paul Samuelson [3 pts each, 18 points total] Consider two countries of U.S. and China, two goods

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A).

Consider the given problem here there are two goods “good1=X1” and “good2=X2”. Now, given the information provided in the question the PPF of both country are given.

=> X1/2 + X2/(1/2) = 100, => X1 + 4*X2 = 100*2, => X1 + 4*X2 = 200, the PPF of US.

=> X1/(1/20) + X2/(2/10) = 1000, => 20*X1 + 5*X2 = 1000, => 4*X1 + X2 = 200, the PPF of China.

The opportunity cost of producing “X1” of US is given by |dX2/dX1| = ¼, => if US want to increase the production of “X1” by 1 units, => have to reduce the production of “X2” by “1/4” units. Now, the opportunity cost of producing “X1” of China is given by |dX2/dX1| = 4, => if China want to increase the production of “X1” by 1 units, => have to reduce the production of “X2” by “4” units. So, “US” having lower opportunity cost of producing “good1”, => US having comparative advantage in “good 1” and China having comparative advantage in the production of “good 2”. So, under free trade US totally specialize in the production of “good1” and China totally specialize in the production of “good2”. So, the production point of US is “good 1 = 200, good 2 =0” and the same for China is “good 1 = 0, good 2 = 200”. Consider the following fig.

Good 2 (X2) A1 200/4 50 B1 Good 1 (X1) 200/1 PPF of US 200

Good 2 (X2) A2 200/1 =200 B2 Good 1 (X1) 200/4 PPF of China =50

So, here “A1B1” is the PPF of US and “A2B2” is the PPF of China. Now, the production point of both country are “B1” and “A2” respectively.

Production Good 1 Good 2 dX1 dX2 0 200-100 100 0-25 (-25) 200 US 200 0-25 (-25) China 200-100 100 0

The above table shows that after trade the production of “X1” increases by “100” and decreases by “25” in US and China respectively. Similarly, the production of “X2” decreases by “25” and increases by “100” in US and China respectively.

B).

Now, let’s assume that the TOT is “1”, => the free trade equilibrium price of both good are same and each country spend 50% of their income on the consumption of both good, => both country will consume “50 units of good 1” and “50 units of good 2”.

free trade consumption Income per Capita good 1 good 2 GDP 100 (100*100)^0.5=100 100/100 1 100 (100*100)^0.5=100 100/1

Now, each country having same GDP, => the world share of counties GDP is “0.5” for both country.

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