David has preferences between two goods: Pizza (denoted by P) and hamburgers (denoted by H). His preferences over the two goods are represented by the utility function U = P + H. David has an income of $36 per week. The price of a pizza is $4, and the price of a hamburger is $2. (i) How many pizzas and hamburgers will he buy each week if he maximizes utility? [7 marks] (ii) Illustrate your answer on a graph when pizza and hamburgers are shown on the horizontal and vertical axis, respectively. Make sure you draw the budget line and show its slope and intercepts. Also, draw an indifference curve that passes through the optimal choice. Show if the indifference curve intersects either axis. [3 marks] Q1b (15 points) Now, suppose that David considers two goods, pizza (P) and hamburgers (H), to be perfect substitutes, as shown by his utility function: U(P,H) = P + 4H. The price of pizza is $2, and the price of hamburgers is $4, and David's monthly income is $200. Knowing that he likes pizza, David's friend gives him a birthday gift card of $40, redeemable only at Pizza Hut. Though David is happy to get this gift, his friend did not realize that she could have made him exactly as happy by spending far less than she did. (i) How much would she have needed to give David in cash to make him just as well off as with the gift card? [10 marks] (ii) Illustrate your answer on a graph when pizza and hamburgers are shown on the horizontal and vertical axis, respectively. Show David's budget lines before and after receiving the gift card. Also, draw his indifference curves and show his optimal choices before and after receiving the gift card. [5 marks]