Suppose that you have two consumption choices: good X, and good Y. An indifference curve is the set of consumption choices with a CONSTANT utility. For example if and gives the same utility as consuming and , than these are both points on the same indifference curve. An indifference map is the set of all indifference curves for EVERY given utility.

Consider the following utility map:

A budget curve gives the set of possible consumption choices with a given income. If you have an income of $1106 and the price of good X is given by , and the price of good Y given by . The equation for the budget line is given by: .

A utility maximizing combination of goods X and Y occurs when the budget line is tangent to an indifference curve.

Find X as a function of its price and the price of good Y:
(If Y represents all other goods, than this function is just a demand curve for X).

(Use px for and py for )

Let be the value for X when and .

(you will lose 25% of your points if you do)

You can earn partial credit on this problem.