4. An agent expects income of 200 in period 1 and 100 in period 2. His...

 

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4. An agent expects income of 200 in period 1 and 100 in period 2. His utility, defined over consumption in periods 1 and 2 (denoted by c₁ and c2 respectively), is given by U(C₁, C₂) a ln c₁ + (1 -a) ln c₂ for 0 < a < 1. The agent could save money at 10% interest but could only borrow at 15% interest. Draw a picture of his budget set and find the values of a for which he will (i) save in period 1; (ii) neither borrow nor save; and (iii) borrow in period 1. ++ 5. Let U R → R be a continuous utility function. Suppose that u is in the range 1 + of U, i.e., there is à such that U (x) u. For any p e R+ show that the problem: min P. x subject to U(x) ≥ ū has a solution. (In other words, there is * R that minimizes px, subject to U(x) > u.) + = 4. An agent expects income of 200 in period 1 and 100 in period 2. His utility, defined over consumption in periods 1 and 2 (denoted by c₁ and c2 respectively), is given by U(C₁, C₂) a ln c₁ + (1 -a) ln c₂ for 0 < a < 1. The agent could save money at 10% interest but could only borrow at 15% interest. Draw a picture of his budget set and find the values of a for which he will (i) save in period 1; (ii) neither borrow nor save; and (iii) borrow in period 1. ++ 5. Let U R → R be a continuous utility function. Suppose that u is in the range 1 + of U, i.e., there is à such that U (x) u. For any p e R+ show that the problem: min P. x subject to U(x) ≥ ū has a solution. (In other words, there is * R that minimizes px, subject to U(x) > u.) + =

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