Robinson Crusoe can catch 1 fish per hour or can gather 10 coconuts in the same time. His

utility function is

U = F1/2C 1/2

where F and C represent the quantities of fish and coconuts he consumes each day.

(a) Assuming that Robinson has decided to work 8 hours per day, how many fish and

coconuts will he produce and consume each day? What implicit price ratio would support

this equilibrium?

(b) Suppose Robinson discovers that he can trade fish and coconuts freely on a neighboring

island at the rate of 8 coconuts per fish. How many fish and coconuts will he produce and

how many will he consume each day now?

(c) Suppose now that there is no neighboring island, but Robinson discovers Man Friday on

his island. Friday can catch fish at the rate of 10 per day or can gather coconuts at the rate

of 40 per day. His utility function is identical to Crusoe's. What is Friday's consumption

pattern before he meets Crusoe?

(d) Now Friday and Crusoe are discussing the possibility of trading with one another. Is the

price ratio of 8 coconuts per fish an equilibrium price ratio? Explain your answer fully.

(e) Can you find any other price ratio that would yield an equilibrium? If you can, find that

price ratio (or ratios). If you cannot, explain why not.