Problem III. Unemployment Benefit (15 points) Sergio is a construction worker in Min- neapolis. He gets income I for his work during the current month. However, there is uncertainty for next month, say January. If the weather is bad he cannot work and gets zero income. Weather is bad with probability n. He spends his current income on current month's consumption and savings for next month's consumption. He maximizes the discounted summation of his expected utility over the two months when he decides on his current consumption and savings i.e. he maximizes u(ci) + BEU(C2) where u(c) = log(c). The interest rate on savings is r. 1. Set up Sergio's problem. Be clear about his choice variables, his objective function, and his budget constraints. Then simplify the problem to have only two choice variables. (You do not need to solve the problem.] (4 pts) 2. Now suppose there is an unemployment benefit equal to b provided jointly by the state of Minnesota and the federal government. Redo part 1. (4 pts) 3. How do Sergio's choices change with the presence of UI? How does UI impact Sergio's savings? Explain. (4 pts) 4. What other potential problems could occur because of UI? (3 pts) Problem III. Unemployment Benefit (15 points) Sergio is a construction worker in Min- neapolis. He gets income I for his work during the current month. However, there is uncertainty for next month, say January. If the weather is bad he cannot work and gets zero income. Weather is bad with probability n. He spends his current income on current month's consumption and savings for next month's consumption. He maximizes the discounted summation of his expected utility over the two months when he decides on his current consumption and savings i.e. he maximizes u(ci) + BEU(C2) where u(c) = log(c). The interest rate on savings is r. 1. Set up Sergio's problem. Be clear about his choice variables, his objective function, and his budget constraints. Then simplify the problem to have only two choice variables. (You do not need to solve the problem.] (4 pts) 2. Now suppose there is an unemployment benefit equal to b provided jointly by the state of Minnesota and the federal government. Redo part 1. (4 pts) 3. How do Sergio's choices change with the presence of UI? How does UI impact Sergio's savings? Explain. (4 pts) 4. What other potential problems could occur because of UI? (3 pts)