Suppose that you know the utility function for an individual is given by the equation U = XY where U is the total amount of utility the individual gets when they consume good X and good Y. You are also told that this individual's income is $100 and that the price of good X is $2 and the price of good Y is $4. From this information answer the following set of questions.

(a) What is the consumption bundle of good X and good Y that maximizes this individual's utility given their income, prices of the two goods, and their tastes and preferences as measured by their utility function? Support your answer with a well labelled diagram [Hint: e.g. MUx = dU/dX].

(b) What is the level of utility this individual gets when they maximize their utility given the above information?

(c) Suppose that the price of good X increases to $4 and nothing else changes. What is the new consumption bundle that maximizes the individual's utility now that the price of good X has increased? What has happened to his utility? Determine the SE and IE.