Question1. Consider the economy of Monkey Island. For a given population-levelP, the utility of a resident is given by:

u(P) = 40P 4P².

For simplicity, assume that the population can only take integer values, i.e.P {1,2,3, }.

(a) [5 points] What is the marginal utility? Answer must be a function ofP. Do not take the derivative since function only defined on integer, derivative is not defined. Recall that (a+b)²=a²+ 2ab+b². (Hint: think about the definition of marginal utility).

The marginal utility is

MU(P) =

(b) [5 points] What is the efficient level of population? Answer must be an integer number.

The efficient level of population is

(c) [10 points] Suppose that individuals can freely migrate into Monkey Island and out from Monkey Island. Assume also that outside option does not depend on the population of Monkey Island. Explain why market equilibrium is inefficient. Would there be more people or fewer people compared to the efficient level? What might be the reason behind inverse U-shaped utility? No need to calculate anything here, just explain with words.