1) (6 pts) Consider Anna, who gets a regular transfer from her parents that equals , dollars per working day. She also works for hourly wage w. Let's group everything she buys under a "composite good" x, with price P (in the textbook this is referred to as "C" for "consumption", and you can use that notation if you prefer.) Anna has the following preferences over leisure (Le) and consumption of other goods (x): lo + 24w Px U(Le, x) = Le0.75 x-0.25 lo + WL P. where Le = Leisure and L = Labor = 24 - Le. Assume Anna earns an unspecified hourly wage w and has some nonlabor income Io- Io Hours of leisure (24-L) - 24 24 #Hours worked (L) 0 a. Write and solve Anna's utility maximization problem to find the demand functions for leisure and the composite good: Le(w, Px, lo) and x (w, Px, Io) After you obtain these expressions, assume P = $1 for the rest of the problem. b. Assume for now that , =$60. Does Anna have upward sloping labor supply? Draw the leisure-consumption diagram for this level of nonlabor income, and for w=15. Show the budget constraint and the optimal choice basket. C. In the same graph, add Anna's optimal choice at the following alternate wage levels (keeping ), = 60): w = 10, 20,30, 45, and even 5 (in case Anna tries driving for Uber). d. Draw Anna's labor supply curve for lo = 60, by using the values you calculated above (at w=5,10,15,20,30,45). Add to this her labor supply curve when I, =$ 0. e. Under what conditions might Anna choose to work 8 hours/day at w=15? Show what the labor supply curve would look like in that case. Would it be upward sloping or downward sloping? f. As an added exercise, solve the expenditure minimization problem to obtain compensated demand: Le"(w, U) and x" (w, U). (Continue to assume Pr = 1)