Robinson Crusoe and his friend Friday are stranded together on a desert island.

Question

Robinson Crusoe and his friend Friday are stranded together on a desert island. They each spend 10 hours a day catching fish or gathering coconuts. The following table specifies their productivity levels:

fish

coconuts

crusoe

2/hr

10/hr

friday

12/hr

4/hr

Suppose they decide to combine their efforts and produce together. What is the opportunity cost of catching the 60th fish?

a) 1/5 coconuts

b) 5 coconuts

c) 1/3 coconuts

d) 3 coconuts

**please include explaintion along with answer to help me gain some understanding**

fish

coconuts

crusoe

2/hr

10/hr

friday

12/hr

4/hr

Explanation / Answer

Crusoe can catch either 2 fish in 1 hour or can harvest 10 coconuts in 1 hour.

So, if Crusoe devotes 1 more hour to fishing, he has to sacrifice harvesting of 10 coconuts.

So, opportunity cost of catching fish for 1 hour is 10 coconuts.

On the other hand, if Crusoe devotes 1 more hour to harvest of coconuts, he has to sacrifice catching of 2 fish.

So, opportunity cost of harvesting coconut for 1 hour is 2 fish.

Friday can catch either 12 fish in 1 hour or can harvest 4 coconuts in 1 hour.

So, if Friday devotes 1 more hour to fishing, he has to sacrifice harvesting of 4 coconuts.

So, opportunity cost of catching fish for 1 hour is 4 coconuts.

On the other hand, if Friday devotes 1 more hour to harvest of coconuts, he has to sacrifice catching of 12 fish.

So, opportunity cost of harvesting coconut for 1 hour is 12 fish.

Thus, Crusoe has lower opportunity cost and thereby comparative advantage in production of coconuts while Friday has lower opportunity cost and thereby comparative advantage in production of fish.

If they both wants to combine their efforts and produce together then they will produce items as per their comparative advantage to maximize their joint production.

So, Friday will devote all his 10 hours in catching fish and will catch (12*10) 120 fish while Crusoe will devote all his 10 hours in harvesting coconuts and will harvest (10*10) 100 coconuts.

As stated above, Friday will catch 12 fish when both produce together.

In one hour, Friday can catch 12 fish or 4 coconuts. So, the opportunity cost of 1 fish is (4/12) or 1/3 coconuts.

So, when Friday catches 60th fish, he is sacrificing harvest of 1/3 coconuts.

Thus, the opportunity cost of catching the 60th fish is 1/3 coconuts.

Hence, the correct answer is option (c).

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