Question 1 {Consumption}. Suppose an agent lives for T = 2 periods with income stream (yl, ya} = (212}, l}, discount factor ,5 = 11 and lifetime utility function u{c1, 2} = ln[c1} + lnfc where c: denotes consumption in period t and r 2 is the interest rate. a} Find optimal consumption a; and saving s: Vt when the interest rate is r = I]. Also compute lifetime utility U5 := 1:03;, {:5} in this case. b} Find optimal consumption c: and saving 51'; Ht when the interest rate is r = 1. Compute lifetime utility U; :2 n{c,c} in this case and compare to US. Under which interest rate is the consumer better off; does this make sense? c} Now assume that the consumer's lifetime income stream is [h = (men). Solve parts a and h again and compare your answers. d} Now assume that r = i} and [yhyg] = (211}, If!) again1 but the consumer faces a bor rowing constraint such that they cannot borrow more than 5 units of the consumption good. Solve for optimal consumption and saving in this case, and compute lifetime utility I}; . Compare this to U; ; does this make sense. e} Discuss how your results wtmld change if this consumer exhibited sonle time discounting between periods [i.e. 1:: 1]