3. (40 points) Suppose Karenna has a utility function U(C, L) = Co.5 + 10.5 de- fined over leisure (L) and consumption (C), measured as expenditure. Karenna has 200 hours in a month to divide between leisure and labor. Her wage is $14 per hour. Karenna also receives an income support benefit from the government equal to $200 a month which is unrelated to her work decision, i.e. there is a 0% benefit reduction rate. Karenna has no other income. How much will Karenna choose to work and how much consumption expenditure will she have? How does this answer change if her benefit is raised from $200 to $300? Thinking in theoretical terms, what happens to Karenna's optimal choice of work and her personal utility when her benefit is raised? Does this policy change impose any dead weight loss on society