Consumption-Savings. The representative consumer's utility function is u(C , C2 ) = In(c - y) + B.In(c2 -y), in which the exogenous constant parameters are y > 0 and B (the Greek lowercase letters "gamma" and "beta," respectively), with A fixed between zero and one (i.e., BE (0,1) ). The consumer begins period I with zero net wealth. The period-1 and period-2 budget constraints, stated in real units, are, respectively, c, +a, = y, and C2 + a2 = y2 + (1+r)a . a. Based on the utility function above, construct the lifetime Lagrange function in real terms (i.e., not in nominal terms). b. Based on the lifetime Lagrange function from part a, construct the first-order conditions with respect to c, and c2. c. Using the first-order conditions from part b, construct the consumption-savings optimality condition which should be written as U (C, C2) ... . us (G, C2) The term in ellipsis ("...") on the right-hand side is for you to determine. Provide algebraic steps as needed for clarity. (Hint: The optimality condition cannot be written as c, / c, =... given the particular utility function stated above.)