Question

Gains from Trade

Portugal and Spain produce and consume two commodities, Wine (W) and Cheese (C). Labor (L) is the only factor of production in both countries. Commodity and labor markets in the two countries are perfectly competitive. In Portugal, it takes 8 labor hours for the production of a bottle of W and 6 labor hours for the production of one kg of C. In Spain, it takes 10 labor hours for the production of a bottle of W and 14 labor hours for the production of a kg of C. The total amount of labor available in Portugal is ?�? = 360 and in Spain ?�? = 700.

a) Derive the algebraic expression for each country’s Production Possibilities Curve (PPC). What is the opportunity cost of each good in the two countries? Explain what is, and why, its relation to the relative price of the two goods in a country. [Mark: 0.75]

b) Based on the information given, in which commodity (-ies) Portugal and Spain have an absolute or comparative advantage? Explain briefly and clearly. [Mark: 0.5]

c) If the consumption of C in Portugal is 40 kgs and in Spain is 35 kgs, how much of the two commodities does each country produce/consume? [Mark: 0.75]

d) What can be said of the relation between the opportunity cost and the relative price of a good after trade? (Hint: are the two the same/different form each other, why?) [Mark: 0.75]

e) Let the international price of a bottle of W be 1.25 kgs of C. Suppose that at this price, the two countries exchange 20 bottles of W. What are the levels (i) of production and consumption of the two commodities, and (ii) of exports and imports, in the two countries?

Answer 1

First the basics:

In Portugal, it takes 8 labor hours for the production of a bottle of W and 6 labor hours for the production of one kg of C. In Spain, it takes 10 labor hours for the production of a bottle of W and 14 labor hours for the production of a kg of C.

Considering current labor availability,
In Portugal, 8x+6y = 360
In Spain, 10x+14y = 700

8x = 360 - 6y
So, x = (360 - 6y) / 8 = 45 - 0.75y
So, 10 * (45 - 0.75y) + 14 y = 700
So, 450 - 7.5y + 14y = 700
So, 6.5 y = 250
So, y = 38.46 = 38 (for ease of further calculations)
So, x = 45 - 0.75y = 45 - 29 = 16 (for ease of further calculations)

So, Portugal can produce approximately, 128 bottles of wine and 228 kg cheese with the available labor.

Spain can produce approximately, 160 bottles of wine and 532 kgs of cheese with the available labor.

a) Derive the algebraic expression for each country’s Production Possibilities Curve (PPC). What is the opportunity cost of each good in the two countries? Explain what is, and why, its relation to the relative price of the two goods in a country. [Mark: 0.75]

For production possibilities curve plot, following equations would be useful.

In Portugal, 8x+6y = 360
In Spain, 10x+14y = 700

Spain has more labor available and can produce more. So cost of goods in Spain will be nearly half of the same in Portugal.

b) Based on the information given, in which commodity (-ies) Portugal and Spain have an absolute or comparative advantage? Explain briefly and clearly. [Mark: 0.5]

Spain will have an advantage - as labor is better available there.

c) If the consumption of C in Portugal is 40 kgs and in Spain is 35 kgs, how much of the two commodities does each country produce/consume? [Mark: 0.75]

Portugal consumes 17.5% of the cheese it produces [consumes 40 kgs out of 228 kgs produced].

Spain consumes 6.5% of the cheese it produces [ consumes 35 kgs out of 532 kgs produced]

d) What can be said of the relation between the opportunity cost and the relative price of a good after trade? (Hint: are the two the same/different form each other, why?) [Mark: 0.75]

They are similar

e) Let the international price of a bottle of W be 1.25 kgs of C. Suppose that at this price, the two countries exchange 20 bottles of W. What are the levels (i) of production and consumption of the two commodities, and (ii) of exports and imports, in the two countries?

1 bottle of wine is 1.25 kgs of cheese.

So 20 bottles of wine are equivalent to 25 kgs of cheese.

Production will remain the same.

Consumption will vary in the ration 1:1.25