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Sociology

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1. For a simple two-period overlapping-generations model, utility depends on consumptions in the two periods, C and C2, and can be represented by U(C1, C2), which obeys the "law of diminishing marginal rate of substitution". Assume that income is earned only in the first period, in amount I. So the consumption in the second period is possible only by saving Sin the first period. That is, C = 1-S, C2 = S(1 + r), where r is the (exogenous) interest rate. (1) Formulate this problem as an unconstrained optimization problem. Derive the first order condition for an interior solution. (2) Formulate this problem as a one-constraint optimization problem. Derive the first order condition for an interior solution. (3) It has been argued that reducing interest rate can increase consumption in the first period, and the Chinese government was doing this way. Use the diagram to determine the effect of a reduction in the interest rate to the consumption in the first period (substitution effect, income effect, total effect). Assume both C and C 2 are normal goods. 2. On a given evening Mr. J.P. enjoys the consumption of cigars (C) and brandy (B) according to the function U(C,B) = 200-C +18B-3B. (1) How many cigars and glasses of brandy does he consume during an evening? (Cost is no object to J.P.) (2) Lately, however, J.P. has been advised by his doctors that he should limit the sum of brandy and cigars consumed to 9. How many glasses of brandy and cigars will he consume under these circumstances? 3. Over a two-year period, an individual exhibits the following consumption behavior: P P. Y Year 1 Year 2 3 4 3 2 8 6 5 6 Is this behavior consistent with the weak axiom of revealed preference?