Question

Chloe’s job pays $1,000 per week. Chloe can freely choose how many weeks she spends on working each year. Assume there are 52 weeks in a year.

Let ? denote the number of weeks spent on leisure in a year and let ? denote her annual wage income in dollars.

1. a. Write an equation relating ? and ?. [6 points]

1. b. Graph the relationship between ? and ? with ? on the horizontal axis and ? on the vertical axis. Label the axes, intercept values, and slope of the line. [4 points]

1. c. What is Chloe’s opportunity cost of leisure measured in dollars per week?

1. d. Chloe is considering a two-week long vacation trip. The table below summarizes the expenses. Calculate the accounting and economic costs of her vacation.

Item	Cost ($)
Transportation	1800
Lodging	700
Entertainment	500

Suppose now that Chloe needs to pay tax on her wage income. The tax rate is initially 0%. The tax rate increases to 10% after earning $32,000. In other words, she pays no tax for the first $32,000 she earns and pays 10 cents for every dollar she earns above $32,000.

1. e. Graph the new relationship between ? and ? with ? on the horizontal axis and ? on the vertical axis, where ? is now the disposable (after-tax) income. Label the axes, intercept values, kink points, and slopes of the line segments.

Answer 1