Problem 1 [20 pts] Consider the utility function u(x1, x2) = x1x2. Initially p1 = $1 and p2 = $2. Income is $ 15. 1. Derive the optimal consumption bundle. [05 pts] 2. If the price of good 1 doubles to $ 2, derive the new consumption bundle. [03 pts] 3. Decompose the the Change in consumption of good 1 into the income and substitution effect, and illustrate your answer with a graph. [05 pts] 4. Compute the Compensation variation (CV) and the Equivalent Variation (EV). [07 pts]