Question 6
Jake produces and consumes fish (F) and coconuts (C). Assume that, during a certain
period, he has decided to work 800 hours and is indifferent as to whether he spends this time
fishing or gathering coconuts. Jake's production functions for fish and coconuts are given by
F = \sqrt{l_F} and C = \sqrt{l_C}, respectively, where $l_F$ and $l_C$ are the number of hours spent fishing
or gathering coconuts. In addition, Jake's utility function is given by U = \sqrt{F \cdot C}
a) If Jake cannot trade with the rest of the world, how will he choose to allocate his labor?
What will be the optimal levels of F and C? What will be his utility? What will be
the RPT (of fish for coconuts)?
b) Now suppose that trade is opened and Jake can trade fish and coconuts at a price ratio
of $\frac{P_F}{P_C} = 3$. If Jake 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 be his new
level of utility?
c) How would your answer to Part b) change if Jake adjusts his production to take
advantage of the world prices?
d) Sketch your results for Parts a), b), and c).
e) Based on your graph in Part d), what can you say about the impact of free trade on
general equilibrium?
