Question: 1 robinson crusoe has decided that he will spend exactly...
1. Robinson Crusoe has decided that he will spend exactly 8 hours a day gathering food. He can either spend this time gathering coconuts or catching fish. He can catch 1 fish per hour or he can pick 2 coconuts per hour.
a) Draw a graph showing Robinson’s production possibility frontier between fish and coconuts per day. Write an equation for the line segment that is Robinson’s production possibility frontier.
b) Robinson’s utility function is U(F, C) = FC, where F is his consumption of fish and C is his consumption of coconuts. If he allocates his time in the best possible way between catching fish and picking coconuts, how many coconuts will he collect? How many fish will he catch?
c) Robinson has little else to do, so he pretends that he is running a competitive firm that produces fish and coconuts. He wonders, “What would the price have to be to make me do just what I am actually doing? Let’s assume that the price of coconuts is $1. And let’s pretend that I have access to a competitive labor market where I can hire as much labor as I want at some given wage. There is a constant returns to scale technology. An hour’s labor produces 1 fish or 2 coconuts. What is the only possible wage rate that would make me choose to produce a positive finite amount of coconuts? Now what would the price of fish have to be to induce me to produce a positive number of fish? What would be my income?”