using the notes/book of pricing and revenue optimization written by Robert L. Phillips

Pricing with Arbitrage. (Similar to Problem 4.8 on page 96 of PRO-attached.) A supplier is selling hammers in two cities, Pleasantville and Happy Valley. It costs her $6.00 per hammer delivered in each city. Let p1 be the price of hammers in Pleasantville and p2 be the price hammers in Happy Valley. The price-response curves (PRFs) in each city are: Pleasantville: d1(p1) = 13,000-1000 p1 Happy Valley: d2(p2) = 7,000-350 p2 a. Using the fact that, at the optimal TC maximizing price, d(p*) = -d’(p*)·(p*-c), find the optimal prices in each city (p1*, p2*). i. Pleasantville price (p1*) = $________ ii. Happy Valley price (p2*) = $________ b. Using p1 and p2, find the demands for each city at optimal prices: i. Pleasantville demand (d1(p1*)) = ________ ii. Happy Valley demand (d2(p2*)) = ________ c. Using d1(p1*) and d2(p2*), find the total revenue and total contributions: i. Total revenue = $________ ii. Total contribution = $________