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ECNEIIE Summer 223 1. Max only spends mone}r on his favorite owers. His favorite owers are tulips {31] and daffodils [1:2]. Suppose the price of tulips is p] = 2, the price of daffodils is p; = 4, and his income is m = sill. {a} 1Write down Max's budget constraint {a formula] and plot all of Max's affordable bundles in the graph [his budget set). Your graph need not be precise but you need to label the intercepts. Find the slope of the budget line {number}. Give an economic interpretation for the slope of the budget line {one sentence]. J32 ECNHIE Summer 223 2. Norma consumes two goods: food {I1} and water (at?) The price of food is 31 end the price of water is $2. Korma has SSH to spend. Her preferences are given by: U(1.'1,3:2} = min-[gr] _. mg} {a} 'Write down Norma's budget constraint {a formula] and plot her budget line. Elrarl.r at least one indifference curve {no need to be precise, just make sure that the shape is correct]. Circle the optimal consumption bundle in the graph {a point; you do not need to solve it enalrticellr~ just indicate where it should be]. If? \fE-CN312 Snrnrner 223 3. Joe has preferences over clothing C and food F. The prioe of clothing is pr? = 31 and the price of food is Pf = $2. Joe has $25 to spend. {a} Suppose that the store offers a bulk discount on food. If Joe purchases more than F.- units of food, the price of the additional food is discounted by 5n%. Graph Joe's budget set, with C' on the horizontal axis and F on the vertical axis. Lahel slopes and intercepts. 372 ECN312 Surnrner 223 (h) Joe's preferences are represented by the following utility,r function: UH}, F] = 31'? + 4F Draw an indifference curve {with (3' on the horizontal axis and F on the vertical axis; no need to he precise~ just make sure that the shape is correct]. 1What is the slope of the indifference curve? 3'32 (c) Suppose that the bulk discount discussed in part (a) holds. Calculate Joe's optirnal hundle {6", F"). ECNHIE Summer 223 4. Betty can consume apples and bananas. She prefers 5 bananas and 5 apples to =1 bananas and '3 apples. She also prefers bananas and 4 apples to 4 bananas and apples. She slightly prefers bananas and 4 apples to 5 bananas and 5 apples. i'v'rite a utilityr function that represents these preferences. You only need to specify the utility levels for these three bundles or, if you cannot find a utility function. explain why