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1. a. Naomis utility function: U C is consumption L is leisure 75 x In(C)+300 x InL) Naomis Budget Constraint is a little tricky Lets assume she is eligible for a government program that guarantees her S5000 a year for consumption and where the benefit is reduced by 50% for every dollar earned through working once she earns $10,000 she no longer receives the subsidy as it has been completely reduced by her income from working. If Sarah does decide to work she can work 2000 hours a year (50 weeks and 40 hours per week) and earn a wage of S10 an hour. How many hours a year will she work? What will be her level of consumption? What level of utility will she reach? Hint: the slope of the budget constraint will change, it helps to draw the budget constraint before jumping into the math. You must solve for the optimal level of leisure and consumption on each segment of the budget constraint.

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