Question

Let us consider a model with two countries (H and F), one factor of production (Labor), and two goods (A and B).

The following table provides the unit labor hours cost structure for the production of A and B in H and F respectively –

Country	1 unit of A	1 unit of B
H	80	90
F	120	100

Let us also assume that H and F has total labor hours endowment of 72,000 and 60,000 respectively.

Using the above given information answer the following questions:

d) If the F country wants to produce both the commodities in autarky, determine the autarky relative price of A. You need to provide explanations for your answer.

(e) Suppose the world price of commodity A is $ 95 per unit and that of B is $100 per unit.

If both the country engages in free trade with each other, explain under free trade how much each of the commodity each of the two country H and F will produce.  

(f) Determine, under free trade, what would be the wage rates in H and F in production line of good A and B. You need to provide explanations for your answer.

(g) Suppose the world relative demand curve is a straight line with an intercept of 1 and

slope – 1. Draw the world relative supply curve for good A and the world relative demand curve for good A. Determine the equilibrium world price. At this price determine the production structure in country H and F. You need to provide explanations for your answer.

(h) If world price of commodity A is $ 95 per unit and that of B is $100 per unit, show and explain that the foreign country can gain substantially by completely specializing in product B and exporting product B and importing product A from country H.

Calculate the level of gain that F can achieve through engaging in free trade with country H.

Answer 1

d).

Here there are two goods “A” and “B” and their respective labor requirement are “120 hours” and “100 hours”. So, the PPF of foreign country is “120*A+100*B = 60,000”. So, under the autarkic situation the relative price is exactly equal to the opportunity cost, => the autarkic relative price of good A is “120/100 = 1.2”.

e).

The PPF of home country is “80*A + 90*B = 72,000”, => the autarkic relative of good A is “80/90 = 8/9=0.89”. The world price of good A and good B are “95” and “100” respectively, => the relative price of good A is “95/100 = 9.5”. So, the world relative price of good A is more the autarkic relative of home country, => home country will fully specialize to the production of “A” only. So, the home country produce “A = 72,000/80 = 900 units” and “B = 0 units”.

Similarly, the world relative price of good A is less the autarkic relative of foreign country, => foreign country will fully specialize to the production of “B” only. So, the foreign country produce “A = 0 units” and “B = 60,000/100 = 600 units”.

f).

Under free trade the home country will produce only good A, => the wage rate in home country is “Wh = Pa*MPLa”, where “Pa=95” and “MPLa = 1/80”. So, the wage rate is “Wh = 95/80 = 1.19”.

Similarly, under free trade the foreign country will produce only good B, => the wage rate in foreign country is “Wf = Pb*MPLb”, where “Pb=100” and “MPLb = 1/100”. So, the wage rate is “Wf = 100/100 = 1”.

g).

Consider the following fig.

Here given the information provided the world relative supply of “A” is given by “OABCD” line and the relative demand is negatively sloped red color straight line. So, here the equilibrium point is “E” the intersection of “RD” and “RS”. So, here the relative price is “0.89” exactly equal to the autarkic relative price of home country. So, here home country will produce both goods but foreign country will completely specialize to the production of good B.