Suppose Officer Jim Hopper has the following utility function U = V(ge -") + V(9d) where ge is the quantity of cigarettes Office Hopper consumes, qa is the quantity of doughnuts Jim consumes, and n is Jim's nicotine habit (i.e. Jim needs to consume at least n cigarettes before he gets any utility, so we will assume that qe 2 0). a) (6 marks) Show the optimal choice of ge and qa that Jim would select using his budget constraint m = Page + Page (Hint: n will be in the optimal choice and must have qc > n). b) (3 marks) Does Jim's nicotine habit influence his optimal quantity of doughnuts? Use math to show this (i.e. how would a change in his habit change his consumption of doughnuts?). Why would this be the case? c) (4 marks) Find the own-price and income elasticity for q and qa. For this exercise, it is best to use the Quotient Rule: for a function f(z) 9(x) the derivative of(z) (8g(z)/0z) x h(z) - (Oh(z)/01) x g(z) h(I) (h(I) ) 2 (Hint: simplify your life by eliminating variables where possible.) CS Scanned with CamScanner Drag and drop your files or click to browse