Suppose that you have five consumption choices: good x1 ...5. An indifference surface is the set of consumption choices with a CONSTANT utility. For example if (x1,, x5) = (2, 1, 1, 1, 1) gives the same utility as (x1,...,x5) = (1, 1, 1, 1, 2) than these are both points on the same indifference surface. An indifference map is the set of all indifference surface for EVERY given utility. Consider the following utility map: U = 5 i=1 In(xi-ai) Where (a1,, as) = (8,7,5,7,6) 5 The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $720 and the price of good x is given by pi. The equation for the budget line is given by: 720 = Pixi i=1 A utility maximizing combination of goods 15 occurs when the surface given by the budget constraint is tangent to an indifference surface. Find x1 as a function of p1...P5 x1 = (Use p1 for p₁ and likewise for P2, P3, P4, P5- The easiest way to solve this question is using Lagrange multiplier. We define the Lagrange function to be: / 5 19:45