a) (2 points) To get a sense of how our household's lifetime utility UA# looks like, assume y = 0.5, 8 =0.97, r = 0.05, m = 1, and visit WolframAlpha to plot Un# as a function of s (i.e. copy-paste "plot ((1-s) "(1-0.5)-1)/(1-0.5) + 0.97((1.05*s) "(1-0.5)-1)/(1-0.5) between 0 and 1"). Like in class, use the max operator to find the optimal amount of savings s*. Using calculus, it is possible to show that our household's optimal plan must satisfy the following optimality condition, = [8(1 + r)] (OCG) Combining (OCG) with the two budget constraint allows us to solve for the following general in the sense that y, B, r, and mare left unspecified - consumption-savings solution, 4 = m k(1+r) 1 +k 8* = mo - Co where k = =(1 +r ) 7. b) (3 points) Calculate the values of (c, ci, s*) by either plugging y = 0.5, 8 = 0.97, r = 0.05, me = 1 into the above equations or, alternatively, by plugging them into the corresponding Excel sheet. Does your solution match the result you found in a)