Question

Assume that Colombia had 1,600,000 workers and Mexico had 800,000 workers, respectively. This is the only factor input to produce beef and fish. Units of labor required per unit of output: Colombia Mexico Beef 4 4 Fish 8 2 Now, discuss the situation when two countries agree to exchange two goods freely with Pbeef=$4 and Pfish=$4. (1) Explain why each country completely specializes to produce its comparative advantage good. (2) Assume that B (F) is the quantity of beef (fish) consumption in Colombia in the free trade equilibrium. Write a mathematical expression of the consumption possibility frontier for Colombia. (3) If consumers in these two countries share the same Leontief preferences (i.e., they would like to have the same amounts of beef and fish), how many units of beef would be traded? (4) Using the intra-industry trade (IIT) index: IITjc=min(EXjc,IMjc)/[0.5(EXjc+IMjc)] for country c' product j, calculate IITjc for Colombia's beef.

Answer 1

Answer to 1)

Number of workers employed in Colombia =1600000

Number of workers employed in Mexico=800000

Units of labour employed to produce per unit of output (Table 1)

Table 1.

	Beef	Fish
Colombia	4	8
Mexico	4	2

Now, we'll calculate the bushels of beef and fish produced by given number of inputs (labour employed in Colombia and Mexico) per hour (time assumed), given (below) in Table 2.

Table 2.

	Beef	Fish
Colombia	1600000/4= 400000	1600000/8= 200000
Mexico	800000/4= 200000	800000/2= 400000

Colombia has an absolute advantage in producing Beef over Fish. And on the other hand, Mexico has an absolute advantage in producing Fish over Beef.

Table 3. Opportunity Cost

	Beef	Fish
Colombia	200000/400000= 1/2	400000/200000= 2
Mexico	400000/200000= 2	200000/400000= 1/2

For every Beef Colombia produces, they are giving up 1/2 bushels of Fish and for every Fish they make, they're giving up 2 bushels of Beef. And on the other hand, for every Beef that Mexico makes, they're giving up 2 bushels of Fish and for every Fish they make, they're giving up 1/2 bushels of Beef.

When you come to the cost, you want that number to be low. And, as it is already cleared out that cost should be low in producing goods, Colombia has a comparative advantage in producing Beef, they only have to give up 1/2 bushels of Fish for every bushel (unit) of Beef they make. Whereas, Mexico has a comparative advantage in producing Fish, they only have to give up 1/2 (unit/bushel) of Beef for every bushel of Fish they make.

Now our question becomes, "At what ratio should they trade when they specialize?" Now, we know that Colombia has a comparative advantage in making Beef and Mexico has a comparative advantage in producing Fish and now they can trade with each other. But at what ratio is the question here.

For Colombia, the ratio of Beef to Fish they can make is 2:1, whereas, for Mexico, the ratio of Beef to Fish they can make is 1:2. No mutually beneficial trade can take place.

Now, given in this case, Colombia agrees to exchange Beef at a price of $4 per unit and Mexico also agrees to exchange Fish at a price of $4 per unit. But no mutual gains would be there.

4B=4C (case), Suppose, the wage rate in Colombia is $4 per hour. Since, one hour produces 4 B in Colombia, the price of a unit of Beef comes out to be P(B)= $1. On the other hand since one hour produces 8 F, P (F) is $0.5.

The wage rate in Mexico in £1 per hour. And if the exchange rate between dollar and pound is 1£=$2.

No mutual gains would be there, as it is clear from above that P(B) is $4 and P(F) is also $4.

Answer 2)

Mathematical expression

a LB QB + a LF QF =L, is an equation of a line whose plot represents the Consumption Possibility Frontier.