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A single parent, Sue, is endowed with 600 hours per month, which can be allocated toward leisure or labor. For each hour spent on labor, Sue earns a wage of $10 per hour. Her utility function is U=lnC+sinL, where C is consumption and L is the amount of leisure. a) Assume that Sue's only source of income is her own earnings. Solve algebraically for her choice of consumption and hours of leisure and work. Then, show your results in a carefully labeled graph. (10 points) b) Now suppose that a welfare program is introduced with a benefit guarantee of $600 and a benefit reduction rate of 50%. (12 points) i) Draw and carefully label Sue's budget constraint (including intercept points and any kinks). ii) How many hours will she choose to work with this program in place? [Hint: from part (a) you should figure out where she chose to locate on the budget constraint, and use that to understand which segment of the new budget constraint is relevant for her optimization problem.] iii) What level of benefits does she receive? By how much has her consumption increased? iv) Explain how your findings relate to the concept of moral hazard that is captured by behavioral responses. c) Describe two strategies for reducing the moral hazard costs associated with this type of meanstested cash transfer program (that are beyond changing the benefit guarantee or reduction rate). Make sure to explain how each of the two strategies can be effective. ( 8 points)