Suppose you consume goods q, and q2 and no other goods. In addition, assume that your indifference curves over bundles of goods #1 and #2 exhibit strictly diminishing marginal rates of substitution (that is, the indifference curves are convex). In year 1, assume that your income is $10 (y = $10) and the price of good #1 and the price of good #2 are both $1 (p1 = p2 = $1). During year 1, you choose to purchase 6 units of good #1 (q1 = 6) and 4 units of good #2 (q2 = 4). Suppose during the next year, year 2, the price of good #1 goes up to $2.50 (p, = $2.50) and the price of good #2 goes up to $1.25 (p2 = $1.25). Also, assume your income went up during year #2 - now y = $20. If we assume that you don't save or borrow (so you spend all of your income during the year you earn it) and we assume that your preferences don't changes across years, when are you happier - year 1 or year 2? That is, which year will you reach a higher level of utility given your consumption of good #1 and good #2? (Hint: draw the budget constraints and an indifference curve going through the bundle (q1, 92) = (6,4).) At Samie's current consumption bundle, her marginal utility for hot dogs is 5 and her marginal utility for sodas is 3. If the price of one hot dog is $1 and the price of one soda is $0.50, is Samie currently maximizing her utility? If not, how should she reallocate her spending in order to increase his utility - that is, should she increase or decrease hot dog consumption and should she increase or decrease soda consumption? Assume that an individual spends all of their income on bundles of q, and q2. Assume the price of good #1 is $1 and the price of good #2 is $2 (p, = 1, p2 = 2). In addition, assume income is always y = $12. For each of utility functions listed below in (a) through (d), solve for the utility maximizing quantity of good 1. (Note: for additional practice, also solve for the demand functions qf (P1, P2. y) and q4 (P1.P2, y) for ANY levels of p1. P2, and y.) a. U(91. 92) = 41 92 b. U(q1, 92) = 41 2/3 1/3 . 92 c. U(q1, 92) = 41 1/2 1/2 . q2 d. U(q1, 92) = 41 1/2 + q2 1/2