7. (25 points) Suppose consumers have preferences over consumption of wine and beer summarized by the utility function u = u(w, b). Suppose furthermore that the price of wine 1s p,,, per unit, the price of beer is p,, and that individuals have wealth I which they split between purchases of each good, in other words, their budget constrain is Pw W+p,-b=1L Letu(w,b) = alnw+ Blnb. a) (3 points) Suppose the consumer's goal is to maximize utility. Formally state the consumer's constrained maximization problem: b) (4 points) Rewrite this problem as an unconstrained univariate maximization problem. ) (10 points) Write the first order condition and solve the first order condition to obtain the optimal wine and beer consumption. d) (8 points) Verify that the SOC holds for maximization