Problem 1: TwoPeriod ConsumptionSavings Framework (31] points). Consider the twoperiod economy (with zero government spending and zero taxation}, in which the representative consumer has no control over real income {v1 31* G in period 1 and y: 3';- 0 in period 2). The lifetime utility function of the representative consumer is n{c1,c1)=[J-cf +(lJ}-cf:|':-*, in which the exogenous parameter cr :- and the exogenous parameter p E (03-,1]. The consumer begins period 1 with zero net wealth (ie.= an = 0). Keeping in mind that endofperiodE net wealth must be zero (ie, a: = U) in the twoperiod economy, the lifetime budget constraint, stated in real units, is C: y c + = + ' , 1 l+r M 1+:- in which 3' denotes the real interest rate. a. (5 points) Construct the lifetime Lagrange metion for the representative consumer's lifetime utility maximization problem. Clearly dene any new notation