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 consuming 10X and 6Y gives me the same utility as consuming 11X and 5Y, then these are both points on the same indifference curve. An indifference map is the set of all indifference curves with EVERY given utility.

Consider the indifference map given by:
[math] , where [math] is a measure of utility.

A budget curve gives the set of possible consumption choices with a given income. If you have an income of $616 and the price of good X is given by [math], and the price of good Y given by [math]. The equation for the budget line is given by: [math].

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

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

[math]
(Use px for [math])

Let [math] and [math] be the values for X and U when [math] and [math].
[math]
[math]

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