1) A rational consumer has a utility function that follows all of the characteristics explained in class and can choose to buy either "food" or video games. S/he is constrained by a monthly budget (M). Graphically and verbally detail the following using proper terms, labels, and vocabulary (20 pts): a. Draw this consumer's utility function and budget constraint. Indicate the optimal bundle (10 pts).

b. Consumer's income significantly increases (5 pts). c. A moderate increase in the price of video games (5 pts). EC: In addition to part c, indicates a small decrease in the price of food as at the same time (2 pts).

2) A consumer's utility function is: Upxy) = sqrt(2xy). The price of each good is: (Px, Py) = (5,10). The monthly budget is: M - 200. Using any mathematical method, answer the following (30 pts): a. What is the optimal bundle (X, Y) that maximizes the consumer's utility (9 pts)? b. If the desired level of utility the consumer is U = 20, what would be the optimal bundle (X, Y) to minimize consumer expenses (9 pts)? c. Given U - 20 from part b, what would be the new optimal bundle for both goods if Py increases to 40 [think min expenses at new prices to help solve] (6 pts)? d. Given the price increase in good Y from part c, what would be the optimal bundle for this consumer wishing to maximize its utility [ think max utility at new prices] (6 pts)