Economics Suppose there are just two periods, today and

Economics Suppose there are just two periods, today and tomorrow. Suppose also that you have some endowments ????, and you want to decide how much to save in order to consume today and tomorrow. If you save the amount ???? for tomorrow’s consumption, you will be able to consume the remaining part of your endowment, ???? − ????, today. Suppose that you can invest your savings either in a saving account or in a bond which pays a gross interest rate ????, so you will be able to consume tomorrow ????????. a. Set your utility maximization problem in each period. Assume that you consume two goods: ????1, ????2 and you need to choose over ????. The prices for goods ????1 and ????2: ????1 and ????2 are observed in the marked and do not change across time. b. Sketch the first order conditions for this dynamic problem for each period. c. Find the inter-temporal MRS determining the decision over savings, ????. Argue under which conditions you will decide to save for tomorrow’s consumption or not.

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