The number of patients, nA, that seek treatment from Doctor Andrew is a function of the quality of his service, q, and is given by nA(q), where nA'(q) > O, nA "(q) = 0, and q 2 0. The government pays Doctor Andrew p for every patient he treats. The cost to Doctor Andrew of treating nA patients is c(nA), where c'(nA) > 0 and c"(nA) > 0, and the cost of delivering quality q is aq. Thus, the total cost is c(nA)+ aq. (i) Express Doctor Andrew's profit as a function of q. (3 points) (ii) Doctor Andrew chooses q to maximise profit. What is the first order condition for an interior maximum? (6 points) (iii) Check that the solution to (ii) yields a maximum. (6 points) (iv) Write down the condition for the solution to Doctor Andrew's profit maximisation problem to be interior. Show on a diagram. (9 points) (v) Take the differential of the first order condition in (ii) or use implicit differentiation to find an expression for da/dp and sign it. (6 points)