6. Consider a worker whose only source of income is what he earns in the market. Each week has 168 hours that can be divided between leisure and work. If he works, his wage rate is $2 per hour. His preferences can be described by the utility function: U=YL where Y is his weekly consumption of goods measured in units that cost $1 each and L is his weekly leisure time measured in hours. His marginal rate of substitution is given by: MRSLY = Y/L a. If the worker is trying to make himself as well off as possible, how many hours will he work each week? How many hours of leisure will he consume? How much income will he earn and how many units of goods will he consume? b. Suppose the government decides to provide assistance to poor consumers by providing them with a cash grant of $100 per week, but this grant is reduced by 1A: the amount earned in the market until the grant becomes zero. Given this program, how many hours will this person work each week? How many hours of leisure will he consume? How much income will he earn and how many units of goods will he consume? How much will this program cost the government? c. Has the worker's labor supply increased, decreased, or remained the same? Is the direction of the change (or lack of a change) an artifact of the numbers used in this problem or is this a general theoretical result for such a program that will be true in any case for which indifference curves are downward-sloping and convex toward the origin? Explain. You many assume that both leisure and income are normal goods