The goal of this exercise is to apply the income and substitution effects learned in lecture to the topic of labor supply.1 Junyi likes two goods: a consumption good c and leisure l. He maximizes the following utility function: u(c, l) = c l where , (0, 1), > 1. Junyi has H hours to spend either working or enjoying leisure time; hours worked t therefore satisfies t = H l. The consumption good's price is p, and the hourly wage is w. 1. Utility is a function of two goods: consumption and leisure. Why can we treat leisure as a good? (Hint: What is the price of leisure? Think of the wage.) 2. What is the total income that Junyi derives from working? (Hint: income is hourly wage multiplied by the number of hours.) 3. What is Junyi's budget constraint? Write it as a function of c and l. How do we know that Junyi will satisfy his budget constraint with equality? 4. Set up the utility-maximization problem, write down the Lagrangian, and take first-order conditions for c, l, and . 5. Solve for c and l as functions of , , p