3) Mary spends all of her income on goods X and Y. She has a monthly income of $6000, and the prices of the goods are PX = 30 and PY = 10. Draw the budget constraint, calculate Mary's optimal consumption bundle, and show it on your graph, when: a. Mary's utility function is U(X,Y) = XY b. Mary's utility function is U(X,Y) = X2Y c. Mary's utility function is U(X,Y) = XY4 [Hint: can you calculate the optimal consumption bundle for a consumer with generic Cobb-Douglas preferences, U(X,Y) = XY?]

4) Mary spends all of her income on goods X and Y. She has a monthly income of $6000, and the prices of the goods are PX = 30 and PY = 10. Draw the budget constraint, and calculate Mary's optimal consumption bundle when a. Mary's utility function is U(X,Y) = 4X+Y b. Mary's utility function is U(X,Y) = min(X,2Y) [Hint: what type of preferences are represented by this utility function? Draw the indifference curves]

5) Bob has convex indifference curves and has a monthly income equal to $1000, and pays $1 for every text message he sends. Under these conditions, Bob sends 200 text messages per month, and uses the rest of his income to purchase an aggregate consumption good, Y, whose price is PY=1. a. Draw Bob's budget constraint and his optimal consumption bundle on a graph with the number of text messages on the horizontal axis and the amount of Y on the vertical axis.

b. The cell phone company offers a new plan: Bob can pay a flat monthly fee of $180, and the price per text message will fall to $0.10. Which plan does Bob prefer, the original plan or the new one?