1. Alex lives in city A and consumes two goods, 1 and 2, with the following utility function, u (x1, X2) = Ax1 2 , where A > 0 is a constant. The goods prices are p, and p2. Alex works h hours and earns w per hour. Both w and h are taken as given. (a) [20 points] Use the Lagrangean method to derive the Marshallian demand functions and the indirect utility function. (b) [10 points] Suppose the city is undergoing severe inflation. Specifically, both goods prices have risen by 10%. What percentage of a raise in the wage rate should Alex request to her boss, in order for her to maintain the same level of maximized utility without having to work more hours? Use one of the properties of the indirect utility function to prove your point. (c) [10 points] Now suppose Alex's utility function is given by u (1, 2, h) = Ax, x,/- h2, where Alex can now choose the number of hours to work, h. Solve for the optimal h*. Then derive the Marshallian demand functions again