Problem 3 Wendy loves working, mostly because she is lucky to have a great job that pays $40/hour. She has no other source of income. Wendy has preferences over hours of leisure (N) and goods (Y) of the form: U(N, Y) = Y +240VN Wendy has 24 hours in the day to devote between work and leisure. The price of Y is $1. a) Solve Wendy's utility maximization problem. Find Wendy's optimal hours of leisure per day, hours of work per day, and level of goods consumption per day. Draw a picture of her situation on a diagram with N on the horizontal axis and Y on the vertical axis. Wendy keeps telling herself that she'll work less once she becomes rich. One day, she buys a lottery ticket on a whim and wins the "$1,000-a-day" jackpot. b) Write down the equation of Wendy's new budget constraint. Draw it on your picture. c) Now solve Wendy's utility maximization problem. Draw the optimum on your picture. Does Wendy keep to her vow to work less? I d) What is the substitution effect of Wendy's lottery winnings on the amount of goods she buys per day? What is the income effect of Wendy's lottery winnings on the amount of goods she buys per day