Problem 1: TwoPeriod ConsumptionSavings Framework {31] points). Consider the twoperiod economyr (with zero government spending and zero taxation}, in which the representative consumer has no control over real income {v1 \"-1? l} in period 1 and y: 3} E! in period 2). The lifetime utilitj,r mction of the representative consumer is 1 \"(51,c1)=[acf+(1a3cf}, in which the exogenous parameter 0' l:- D and the exogenous parameter p E (33, l]. The consumer begins period 1 with zero net wealth [i_e_= on = ). Keeping in mind that end-ofperiod-E net wealth must be zero (i.e., a: = U) in the twoperiod economy} the lifetime budget constraint, stated in real units, is C: c+ =- + , 1 l+r v1 l+r in which 3" denotes the real interest rate. a. {5 points) Construct the lifetime Lagrange mction for the representative consumer's lifetime utility maximization problem. Clearlyr dene any new notation