Suppose that Bear Grylls produces and consumes fish (F) and coconuts (C). Assume that, this month, he has decided to work 200 hours and is indifferent as to whether he spends this time fishing or gathering coconuts. Bear Grylls’ production for fish is given by
and for coconuts by
where lC and lF are the number of hours spent fishing or gathering coconuts. Consequently,
Bear Grylls’ utility for fish and coconuts is given by
a. If Bear Grylls’ cannot trade with the rest of the world, how will he choose to allocate his labour? What will the optimal levels of F and C be? What will his utility be? What will be the RPT (of fish for coconuts)?
b. Suppose now that trade is opened and Bear Grylls can trade fish and coconuts at a price ratio of pF /pC= 2/1. If Bear Grylls continues to produce the quantities of F and C from part (a), what will he choose to consume once given the opportunity to trade? What will his new level of utility be?
c. How would your answer to part (b) change if Bear Grylls adjusts his production to take advantage of the world prices?
d. Graph your results for parts (a), (b) and (c).