Assume a person has a utility function U = XY, and money income of $10,000, facing an initial price of X of $10 and price of Y of $15. If the price of X increases to $15, answer the following questions:

a. What was the initial utility maximizing quantity of X and Y?

b. What is the new utility maximizing quantity of X and Y following the increase in the price of X?

c. Calculate the amount of substitution and income effects.

d. What can you say about good X, is it a normal good or inferior good? Explain.