Question

# NOTE: I am interested in PART B There are two countries that produce the same good...

NOTE: I am interested in PART B There are two countries that produce the same good x and initially there is no trade or factor mobility between them (closed economies). The demand and supply functions for good x in country 1 are respectively 11100 20DP= − and 1120 10SP= + , while in country 2 the demand and supply functions for good x are respectively 2270 10DP= − and 2240 30SP = + . The good x is produced in both countries with the use of physical capital and labor. More precisely, in country 1, 1 unit of good x is produced with 1 unit of physical capital (K) and 2 units of labor (L), while, in country 2, 1 unit of the good x is produced with 3 units of physical capital (K) and 1 unit of labor (L). In country 1, there are in total 1 240 L= and 1 120 K = units of labor and capital, while, in country 2, there are in total 2 67 L = and 2 200 K = units. Part A: Under no trade and factor mobility determine: i) The price and the quantity of good x in equilibrium for each country. (Mark: 0.2) ii) How much labor and capital are used for the production of good x and how much labor and capital remain unused in each country. (Mark: 0.4) iii) If in country 1 the price of capital is twice the wage rate { }112rw= and in country 2 the wage rate is three times the price of capital { }223wr= , find the price of capital and the wage rate in each country assuming perfectly competitive markets and zero firm profits. (Mark: 0.4) Part B: Under free trade for good x and free mobility of factors (K,L) between the two countries determine: i) The importing and the exporting country of good x and the international price. (Mark: 0.3) ii) How much labor and capital are used in each country for the production of good x and how much capital and labor have been moved between the two countries. (Mark: 0.6) iii) The common international price of capital and the common international wage rate (assuming, again, perfect competition and zero firm profits). Compare to the no-trade situation of part Α). (Mark: 0.6) (Hint 1: The production of good x takes place in fixed proportions. That means, if country 1 produces q units of the good, it will use q units of capital and 2q units of labor, for every possible level of q. Similarly, if country 2 produces q units of the good, it will use 3q units of capital and q units of labor for every possible level of q again) (Hint 2: Zero profits implies that total revenue equals to total cost of production. Therefore, it is the case that j j j j jj PQ rK wL ∗∗ ∗ ∗ = + for every country { } 1,2 j= .)

the numbers seem to be inconsistent but the mechanics given here will be used. Please recheck the numbers and comment if there is any doubt