Suppose Officer Jim Hopper has the following utility function U = (qc - n) + v(qa ) where q 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 q 2 0). a) (6 marks) Show the optimal choice of q and q, that Jim would select using his budget constraint m = Pcq + Paqd (Hint: n will be in the optimal choice and must have qc 2 72). 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 qd. For this exercise, it is best to use the Quotient Rule: for a function 9(I) f(I) = the derivative of(x) (3g(x) /Or) x h(x) - (Oh(x)/Or) x g(z) h(r) (h(I)) 2 (Hint: simplify your life by eliminating variables where CS Scanned with CamScanner + Drag and drop your files or click to browse