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 [math] and [math] gives the same utility as consuming [math] and [math], than these are both points on the same indifference curve. An indifference map is the set of all indifference curves for EVERY given utility.

The Cobb-Douglas utility function gives a simple indifference map:
[math] , where [math] .

A budget curve gives the set of possible consumption choices with a given income. If you have an income of $196 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 an indifference curve.

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

[math]
(Use px for [math])

Let [math] be the value for X when [math] and [math].
[math]

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