Question

Chuck and Crusoe are trapped on opposite sides of a tropical island. They each have 60 units of labor that they can spend on one of two activities: building shelters or fishing. Chuck can produce 1 unit of shelter with 5 units of labor, and can produce 2 units of fish with 1 unit of labor. Crusoe can produce 1 unit of shelter with 3 units of labor, and can produce 4 units of fish with 1 unit of labor. Given this information:

Suppose that Chuck and Crusoe are allowed to trade with one another. They decide that one of them should specialize in shelter and the other in fish. Which would you suggest specialize in shelter? specialize in fish?

Assuming Chuck and Crusoe are consuming at the possible and efficient point in autarky, propose a trade deal that would leave both parties better off when trade is possible. What is the total welfare of the island measured in units of shelter and fish now?

Answer 1

Consider the given problem here “Chuck” and “Crusoe” both have 60 units of labor. Chuck can produce unit of shelter with 5 units of labor, 1unit of fish with ½ unit of labor. The PPF of “Chuck” is given below.

=> 5*S + ½*F = 60……………..(1)

Crusoe can produce unit of shelter with 3 units of labor, 1unit of fish with ¼ unit of labor. The PPF of “Crusoe” is given below.

=> 3*S + ¼*F = 60……………..(2).

Now, the opportunity cost of “fishing” is “(1/2)/5 = 1/10” of “Chuck” and the same for “Crusoe” is “(1/4)/3 = 1/12”. So, we can see that “Crusoe” have lower opportunity cost of producing “F” compared to “Chuck”, => “Crusoe” has the comparative advantage in the production of “fishing” and “Chuck” has comparative advantage in the production of “building shelters”. So, “Crusoe” should totally specialize towards “fishing” and “Chuck” should totally specialize towards “shelter”.

Let’s assume that initially “Chuck” and “Crusoe” were consuming (S=5, F=70” and (S=6, F=168) respectively, where “S=Shelter” and “F=Fishing”. So, total production of “F” and “S” were “70+168=238” and “5+6=11” respectively. Now, with trade “Crusoe” will totally specialized towards “F” and “Chuck” will totally specialized towards “Shelter”, => total production of “F” is “60*4=240 > 238” and “S=60/5=12”. So, under this situation if “Chuck” will export “6 units of S” and import “71” units of “F” on the other hand “Crusoe” will import “6 units” of “S” and export “71 units” of “F”.

So, after trade the consumption bundle of “Chuck” and “Crusoe” are “(S=6, F=71) and (S=6, F=169) respectively. So, we can see that both the person will be better off with trade.

So, after trade the total welfare is “S + F = 12 + 240 = 252.