Question

Consider two countries Home and Foreign that can produce two goods, apples and bananas, using labour as the sole production factor. Home and Foreign have, respectively, 2400 and 1600 units of labour available and the unit labour requirements in the production of both goods are as shown in the following table: Home Foreign Apple 6 hours 10 hours Bananas 4 hours 2 hours 1. Construct the world relative supply curve and graph the relative demand curve along with the relative supply curve. (Use the ratio of apple quantity to bananas quantity on the X-axis). (10 points) Assuming that the world relative demand takes the following form: Demand for apple Price of bananas Price of apple Demand for bananas What is the equilibrium relative price of cloth? (10 points) Describe the trade pattern and show that both Home and Foreign gain from trade. (10 2. 3. points) 4. Suppose that instead of 2,400 workers, Home had 4,800. Find the equilibrium relative price. (10 points) 5. What can you say about the efficiency of world production and the division of the gains from trade between Home and Foreign in this case? (10 points)

Answer 1

1).

Consider the given problem here the labor requirement for both the goods as well as the total labor availability are given in the question, => the PPF of “Home” as well of “Foreign” country are given by.

=> “6*A + 4*B = 2400” of home country and “10*A + 2*B = 1600” of foreign country, where “A=apple” and “B=banana”. So, the opportunity cost or the autarkic relative price is given by “6/4 = 1.5 units” for home and “10/2 = 5 units” for “foreign country.

Now, if “p = relative price of apple”, => if “p < 1.5, 5”, => both the country will specialize to the production of “B”, => the production of “A” is “0”, => the relative supply of apple is “0”. Now, if “p=1.5 < 5”, => home country can produce on any point on the PPF but the foreign country will produce only banana, => the relative supply of apple is horizontal here till home will specialize to apple, => untill the relative supply of apple is “(2400/6)/(1600/2) = 400/800 = 0.5”. Now, for “1.5 < p < 5”, home will specialize to “A” and the foreign will specialize to “B”, => here the relative supply will be vertical at “400/800=0.5”. Finally, for “p = 5” home will continue to produce “A” and foreign can produce on any point of the PPF. So, the relative supply of apple is horizontal.

2).

So, here “p=relative price of apple” and “q=relative quantity of apple”, => the RD function is given by.

=> p*q = 1. Now, the “RS” is vertical at “q=0.5”, => the “RD” will cut “RS” at the vertical portion of the “RS” curve, => at equilibrium the intersection between “RD” and “RS” the equilibrium price is given by “p* = 1/0.5 = 2”. Consider the above fig where “E” be the intersection between “RD” and “RS”. So, the equilibrium price is “2” which is between the opportunity costs of both country.

3).

So, here the home’s autarkic price is less than the free trade equilibrium price, => home will totally specialize to the production of “A” and foreign’s autarkic price is more than the free trade equilibrium price, => the pattern of trade is given by, “home” will export apple in exchange of “banana” and “foreign will export “banana” in exchange of “apple”.

4).

Now, the labor supply in home increases to “4,800”, => if home specialize to the production of apple, => total production is “4,800/6=800”, => the vertical segment will shift right to “q=1”. Consider the following fig.

So, given the demand curve, “p*q=1”, if “q=1”, => “p=1 < 1.5”, => here the “RD” will cut the “RS” at the horizontal segment that at “p=1.5”. So, here the equilibrium relative price will be “p=1.5” exactly equal to the home’s autarkic relative price. So, the new equilibrium price is “p*=1.5”.