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1. Jack and Meg are stranded on a deserted island where they live by catching fish...

1. Jack and Meg are stranded on a deserted island where they live by catching fish and picking coconuts. In one day Jack can catch 12 fish or pick 8 coconuts while Meg can catch 5 fish or pick 10 coconuts. When they are separated, they each choose to catch 3 fish.

a. How many coconuts is each of them consuming when they are separated?

b. What is the marginal cost of a fish for Jack and what is it for Meg?

c. If Jack and Meg are able to coordinate their activities and they want to get the same number of fish that they were getting when separated, how many coconuts can they get?

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Answer #1
  1. Jack collects 12 fish in one day. He can collect one fish in 1/12 day and 3 fishes in ¼ day. Therefore, after collecting 3 fishes he is left with ¾ day.

Therefore in ¾ day Jack will collect ¾*8 = 6 coconuts.

Similarly, Meg collects 5 fish in one day. He can collect one fish in 1/5 day and 3 fishes in 3/5 day. Therefore, after collecting 3 fishes he is left with 2/5 day.

Therefore in 2/5 day Jack will collect 2/5*10 = 4 coconuts.

  1. Marginal Cost of fish for Jack = 8/12 = 2/3 coconut.

Marginal Cost of fish for Meg = 10/5 = 2 coconut.

  1. Since the marginal Cost for fish is less for Jack therefore Jack will catch fish first and Meg coconut. Thus, after catching 6 fish which he can do in half time Jack can collect coconuts.

Therefore total coconuts available will be 4+10 = 14 coconuts.

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