(Solved): 1. Lisa has \( \$ 48 \) per week set aside for coffees \( (x) \) and lunches \( (z) \). The price of ...

1. Lisa has \( \$ 48 \) per week set aside for coffees \( (x) \) and lunches \( (z) \). The price of coffee is \( \$ 4 \) and lunches are \$6. What is Lisa's budget line equation (with \( z \) on the left-hand side)? Graph the budget line, and show how it changes when the price of lunches rise to \$8 (including intercepts). What is the new budget line equation? 2. Suppose utility for a consumer of movies ( \( x \) ) and golf \( (z) \) is \( U=20 x^{0.4} z^{0.6} \). The consumer has set aside \( \$ 1000 \) to consumer movies and golf for a year. a. If the price of movies is \( \$ 20 \) and the price of golf is \( \$ 40 \), what is the utility-maximizing consumption of movies and golf? b. Show the optimal consumption bundle on a graph, showing a budget line (with intercepts), a tangent indifference curve, and the optimal choice. 3. Sam has set aside \( \$ 480 \) for entertainment this month, which is golf \( (x) \) and/or bowling \( (z) \). A round of golf is \( \$ 40 \) and a night of bowling is \( \$ 30 \). His utility function is \( \mathrm{U}=3 \mathrm{x}+2 \mathrm{z} \). a. What is his MRS? b. Solve for the optimal choice of golf and bowling. c. Draw a graph of the budget line (including intercepts), a few indifference curves, and the optimal choice for Sam.