All parts with work and explanations!

8. (40 points total) Suppose Maxine has the following utility function U = 0.9 * XiYi (MUx = 0.3Y 3 and Xi 0.6X 3 MUY = Y3 Answer the following questions and, as always, show your work. (a) (6 points) On a regular day, Maxine earns $270. She currently faces the following prices Px = $9 and Py = $1. What is her optimal consumption bundle of X and Y? (b) (2 points) How much does she spend per day on X and Y? (c) (6 points) Now suppose she leaves work early one day and only earns $148.50. How much of X and Y will she consume then? (d) (2 points) How much does she spend that day on X and Y? (e) (6 points) What would happen to Maxine's consumption of X and Y on a regular day if the price of X decreases to $3? (f) (2 points) How much would she spend on the X and Y that day? (g) (2 point) What share of her income does she spend on X and Y on a regular day? (h) (2 point) What share of her income does she spend on X and Y on the day she leaves early? (i) (12 points) Plot all three equilibria