Draw budget constraint and indifference curve using data below

Draw budget constraint and indifference curve using data below

Subject: Economics    / General Economics
Question
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.
(15 marks)
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. (10 marks)