1. Suppose a consumer has a utility function U(x1,x2) = x1x2. The con- sumer has an income of $24. Initially, pi-1 and P2 2. The price of good 2 rises to $3, while the price of good 1 stays the same. The consumer's demand function is given by Di (P1,P2, m) = 2 for good 1 and D2(pi, P2, m) = 2 for good 2. Find the following: P2 a) How many units of good 1 and good 2 are demanded by the consumer before the price change? b) Find the consumer's m' at which her old bundle is affordable. c) Find the consumer's substitution effect for good 2. d) Find the consumer's income effect for good 2. Hint: For parts c and d, you can ignore good 1 and do it the way we did in class.

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.