Question

Suppose there are two countries A and B, and they produce good X and Y. Assume perfect competitive market and labor is the only factor of production. Answer following questions based on David Ricardo's comparative advantage model.

In country A, 2 laborers are required to produce one unit of good X and three laborers are required to produce one unit of good Y. In country B, five laborers are required to produce one unit of good X and six laborers are required to produce one unit of good Y. Both countries have 150 laborers respectively.

(1) what are the relative prices of country A, (Px/Py) and (Py/Px)? What are the relative prices of country B, (Px/Py) and (Py/Px)? Assume perfect competitive market.

(2) what is the relative price range in free international trade which is beneficial to both countries in (Px/Py) and (Py/Px)?

(3) Show the wages in each country both in terms of both good X and good Y.

(4) Suppose free international trade equilibrium relative price is set at (Py/Px)=4/3. Draw export supply curve and import demand curve for both countries in good X and in good Y. You may assume equilibrium quantity of your choice.

Answer 1

Two countries A and B, and they produce good X and Y.

perfect competitive market and labor is the only factor of production.

In country A, 2 laborers are required to produce one unit of good X

and three laborers are required to produce one unit of good Y.

In country B, five laborers are required to produce one unit of good X

and six laborers are required to produce one unit of good Y.

Both countries have 150 laborers respectively.

Note that , 2 laborers are required to produce one unit of good X

= > 1 labour produces ½ units of good X………marginal productibity of labor in x sector

Therefore :- aLX = 1/2;aLY = 1/3

Also, bLX= 1/5 ;bLY = 1/ 6

LaX* aLX + Lay* aLY = 150

LbX* bLX + Lby* bLY = 150

Being a single factor economy basically the production possibility frontier acts as the budget line for the two good economy .

In competitive market prices are equal to marginal rate of substitution or

i.e., to increase a unit of good Y output amount of good X to be sacrificed:-

we need 2 labours for a extra unit of good x ;

3laboures produce one unit of Y

ð 2 lobours produces 2/3 units of Y

ð To increase oone unit of good x one needs to forego 2/3 units of good Y

Therefore For Country A:- pX/ pY = 2/3

ð

Similarly

For Country B :- pX/ pY = 5/6

Hence , the price range in which free interntional trade is beneficial for both the countries is

when 2/3< pX/pY < 5/6 -====> 0.667 < pX/pY <0.833

Note that this price range is beneficial because if free trade occurs and relative price of good x being lower in A than in B;

A shall import Y and export X and B shall import X and export Y

Consumers of A shall get good Y at lower prices and be better off, while consumers of B shall get good X at lower prices and be better off.

At equilibrium in competitive market the wage – marginal productib=vity of labor

In A:-

WX = ½ ; WY = 1/3

Wage in terms of good x = 3/2

In terms of Y = 2/3

In B ; WX = 1/5 and WY= 1/6

Wage In terms of good X = 6/5