If nation A can produce 5 units of good X or 10 units of good Y and nation B can produce 4 units of good X or 12 units of good Y we can conclude that both nations would gain from trade if nation A sold _____ units of good _____ for one unit of good _____
A) 0.4; Y; X
B) 2.5; Y; X
C) 2.5; X; Y
D) 0.4; X; Y

Question

Quizplus · Accepted Answer

To determine the optimal trade ratio, we must find the opportunity cost of each good in each nation. 
For nation A, the opportunity cost of producing 1 unit of X is giving up 2 units of Y (10Y/5X). The opportunity cost of producing 1 unit of Y is giving up 0.5 units of X (5X/10Y). 
For nation B, the opportunity cost of producing 1 unit of X is giving up 3 units of Y (12Y/4X). The opportunity cost of producing 1 unit of Y is giving up 0.333 units of X (4X/12Y).

In this scenario, nation A has a lower opportunity cost for the production of X, and nation B has a lower opportunity cost for the production of Y. Therefore, nation A should specialize in the production of good X and nation B should specialize in the production of good Y.

To determine the optimal trade ratio between nation A and nation B, we need to find an exchange rate that benefits both nations. Nation A has a comparative advantage in producing X, so it would want to sell X in exchange for Y. Nation B has a comparative advantage in producing Y, so it would want to sell Y in exchange for X.

The exchange rate between nation A and nation B should be such that the opportunity cost for nation A is lower than the exchange rate, while the opportunity cost for nation B is higher than the exchange rate.

Thus, the exchange rate can be found by equating the opportunity cost for nation A with the exchange rate, and solving for Y/X.

Opportunity cost for nation A = 2Y/X
Exchange rate = Y/X
Equating the two, we get 
2Y/X = Y/X 
Y/X = 2

Therefore, nation A should sell 2.5 units of X for one unit of Y. 
Choice C is the only answer that has 2.5 as an option for units of X sold, and it correctly identifies X as the good that nation A should sell.

If Nation a Can Produce 5 Units of Good X