Amy has preferences over the == consumption good and leisure defined by the utility function U(C,1) = Cl. Let h = 24 hours. Amy receives $80 in dividends and pays $20 in taxes. (a) (8 points) Write down Amy's utility maximization problem. Write down her optimality condition. (b) (12 points) Suppose you know that Amy's optimal level of consumption equals 150. What is Amy's wage? How many hours does she work? (c) (5 points) Suppose Amy's wage increased. Would she work more or less? Explain your answer in terms of income and substitution effects. (d) (5 points) Suppose Amy received only $20 in dividends, and still paid $20 in taxes. How would her labor supply change in response to an increase in the wage rate then? Explain your answer in terms of income and substitution effects.