Pai lives alone on a deserted island. He can spend his time gathering coconuts or bananas. He has 16 hours available each day and can gather 4 coconuts in an hour or 8 bananas in an hour.
Show the derivation process that leads to the final solution for all parts of question.
a) Given that Pai's marginal utility of bananas is always 25 and his marginal utility of coconuts is always 100, what is his optimal consumption? Draw his budget constraint and indifference curve and identify his optimal bundle in a diagram.
b) One day an individual from a neighbouring island arrives by boat and offers to exchange any number of fruits at a rate of 1 coconut for 1 banana. Plot Pai's budget constraint at this exchange rate assuming he will now spend all her time gathering bananas. Is Pai better off? What is his new optimal consumption? Show the results in the diagram.