Maria owns a woodfired pizza shop which imitates traditional

Maria owns a wood-fired pizza shop which imitates traditional Italian methods. She uses a unique sauce that attracts a loyal following of customers. The demand for her pizzas is q = 1650 ? 250p, and her costs are T C(q) = 0.72q + 0.0035q 2 . q is the number of pizzas sold per week, T C(q) is Maria’s weekly total cost, and p is the price of a pizza.

(a) What price and output will Maria choose to maximize profits?

(b) Maria returns to college and asks her cousin Victor to manage her pizza business. Victor faces the same demand and cost conditions as Maria, but he decides to maximize revenue. What price and output should he choose?

Solution

For profit maximization we have to equate MR and MC

TR=6.6Q-Q^2/250

MR=6.6-2Q/250

MC=0.72+0.007Q

MR=MC

solving, we get

Q=392

P=5

revenue maximization condition is MR=0

MR=6.6-.008Q=0

Q=825

P=3.3