Macroeconomic Theory and Policy – Midterm Exam | © Sanjay K. Chugh 2 Problem 1: Two-Period Consumption-Savings Framework (25 points). Consider the two-period economy (with zero government spending and zero taxation), in which the representative consumer has no control over his real income (y1in period 1 and y2in period 2). The lifetime utility function of the representative consumer is 2211,lncu c cc. (Note:that is not a typo – it is only1cthat is inside a ln(.) function, c2is notinside a ln(.) function). The lifetime budget constraint (in real terms) of the consumer is, as usual, 22110(1)11cycyr arr. Suppose the consumer begins period 1 with zero net assets (a0= 0), and as per the notation in Chapters 3 and 4, r denotes the real interest rate. a.(7 points) Set up a lifetimeLagrangian formulation for the representative consumer’s lifetime utility maximization problem for the given utility functionDefine any new notation you introduce. .