Question

Dan and Patrick are stranded on a deserted island.  They survive by catching fish and gathering coconuts.  In one day, Dan can pick 15 coconuts or catch 5 fish and Patrick can pick 20 coconuts or catch 20 fish.  They can divide their time in any way between the two tasks without any loss of efficiency.  When alone, Dan chooses to consume 3 fish and Patrick chooses to consume 8 fish.

a. How many coconuts does each eat when alone?  (How many is that total….?)

Answer 1

Opportunity cost of 1 fish for Dan = Total coconuts not consumed/Total fish consumed = 15/5 = 3 coconuts
So, when Dan consumes 3 fish he gives up 3*(3 coconuts) = 9 coconuts. So he is left with 15 - 9 = 6 coconuts to consume.

Opportunity cost of 1 fish for Patrick = Total coconuts not consumed/Total fish consumed = 20/20 = 1 coconut
So, when Patrick consumes 8 fish he gives up 8*(1 coconut) = 8 coconuts. So he is left with 20 - 8 = 12 coconuts to consume.

a. Dan consumes 6 coconuts and Patrick consumes 12 coconuts. In total, they consume 6+12 = 18 coconuts.