申論題

1.Consider a two-period endowment model with income (y and y') and the consumer pays lump-sum tax (t and t') in the current and future period, respectively. The consumer chooses consumption (C and C') in the current and future periods, and saving (s) in the current period. The real interest rate is r. Consider that a representative consumer lives in this two-period economy and has a convex preference over the current and future consumption. [50 pts]

(a) Write down the consumer's current period budget constraint and its future-period budget constraint. Also, derive the (present-value) lifetime budget constraint of the consumer. [10 pts]