Hello, can you please explain how to solve question 3 "Profit Maximization with third-degree price discrimination" of the problem set attached. I have answered parts 1 and 2, and they are included in the attachment for your reference.

PROBLEM SET #5 ECONOMICS 5310: MANAGERIAL ECONOMICS PLEASE SUBMIT USING BLACKBOARD DROP BOX. NAME: Problems (9 points) Profit Maximization with no price discrimination You are running a football program at a large Texas university. Your program has been losing money and you therefore want to work out the profit maximizing price for tickets. You hire a consultant who calculates that you face the following demand curve for season tickets for each game: Qa(P) = 140, 000 - 250P He notes that you have a very large stadium (92,589) seats that is never filled. He also notes that most of the costs that your football program faces (i.c., wages for staff, equipment and scholarships for players, maintenance for the large stadium) are fixed costs and do not depend on the number of season tickets that you sell. He therefore estimates that your variable cost of selling an additional season ticket is 0. Your total cost function, therefore, is only made up of fixed costs (i.e., salaries for coaching staff, maintenance for the stadium etc.) : TC (Q) = $20,000, 000 Given this level of demand and your cost structure listed above: A. (3 points) What is the profit maximizing level of output (Q*) Note: Q" is a round number in thousands. So please round your answer to the nearest 1000 Step 1: Inverse demand function Q) = 140,000 - 250P P =560 - .004Q Step 2: TR = PQ X Q TR = 560Q - .004Q2 Step 3: Profit = TR(Q) -TC(Q) 560Q - .004Q2 - 20,000,000 Step 4: Derivative Marginal Profit 560Q - .004Q2 - 20,000,000 Q = 560 - .004Q2 = 2 X -.004 X Q = .008Q MP= 560 - .008Q Step 5: Find Q* 560 - .008Q = 0 Q* = 70,000 B. (3 points) What is the price that you charge at the profit maximizing level of output (P*)? Find the optimal price P* Substitute Q* into the inverse demand function 560 - .004Q 560 - .004(70,000) P* = 280 C. (3 points) Calculate profits at the profit maximizing output level. Substitute Q* into the profit function 560Q - .004Q2 - 20,000,000 560(70,000) - .004(70,000)2 - 20,000,000 Profit = - 400,000 (9 points) Own-price elasticities discrimination. He notes that you can segment your market into students and alumni the notes that you u consider charging students and alumni different prices. Demand for students is the following Qs(PS) - 80,000 - 20OPS A. (3 points) Calculate the elasticity of demand for students Elasticity = AQ/8 P Q. 70.900 (do/de) x (P/Q) Elasticity of demand for students - 0.8 Demand for alumni is the following Q4(PA) = 60,000 - 50PA you found in Q1 (Le., with ne price discrimination) cing price that Elasticity - 40/4 p Q- 70 090 (do/dp) x papand for alumni =-so Elasticity of demand for alumni -0.2 . (3 points) Based on these elasticities, if you practice third degree price discrimination, would you expect to charge higher prices to students or alumni if you decide to price discriminate? customer is Alumni's demand cure is less elastics therefore this indicates if prices increase, many alumni will still purchase tickets. The demand for students is more elastic and this indicates that if we charge higher prices for tickets, we will lose more students. (9 points) Profit Maximization with third-degree price discrimination ion, work out what profits will be with third degree price discrimination often with charter students and alumni different For students, demand is Qs(Ps) = 80, 000 - 200Ps We will divide total costs evenly between students and alumni. Total costs for students ar TC(Q) = $10,000,000 A. (3 points) What is the profit maximizing level of output (Q:") for students Note: Q* is a round number in thousands. So please round your answer to the nearest 1000 . (3 points) What is the price that you students? ing level of output (P.") for C. (3 points) Calculate profits that yo selling tickets to students