rart A. 14 1AL RD. (Almost same as Class Test 7. This part will also be considered as Class Test 7 without bonus. Students who have done Class Test 7, may simply bring most of their class test answers to this section) Problem 6 of Ch 10, Microeconomics by Goolsbee, Levitt and Syverson , 4 Edition (p.325) Q. The promoters of a major basketball tournament try to segment their tickets into two groups: I. Adults Tickets, with a Demand: Q4 = 5000-10P II. Student Tickets, with Demand: Qs = 10000-100P The promoter's Marginal Cost per ticket is same for all output levels as $10 Please answer the following: I. For Price Segment: Adults Tickets: a. Write the Inverse Demand Curve and Marginal Revenue Curve Functions b. Determine the Profit Maximizing Quantity, Q* and Price, P* . Determine the Revenue to be generated with Q* and P* d. Determine the Producer Surplus (Hint: The area is a rectangle; not a triangle !) II. For Price Segment: Student Tickets: a. Write the Inverse Demand Curve and Marginal Revenue Curve Functions b. Determine the Profit Maximizing Quantity, Q* and Price, P* c. Determine the Revenue to be generated with Q* and P* d. Determine the Producer Surplus (Hint: The area is a rectangle; not a triangle) ITI. What is the Total Quantity (number of tickets sold to both groups), Total Revenue and Total PS generated for the two segments? IV. Suppose, instead of segmenting, the Promoters plan to follow perfect price discremination with the help of a combined demand function. a. What will be the new Demand Function (combine both demand functions)? b. What will be the combined Inverse Demand and Marginal Revenue Functions? c. Ifthe sponsors like to sell the same total number of tickets that would be sold through segmenting (as per part I1I), What will be the price (or prices) under perfect price discrimination and Total Revenue and Producer Surplus generated? How these values differ from answers to Part I11, i.e. from segmenting? d. If the promoters like to increase the number of tickets to maximum possible with the Answer No of Tickets Max. Min. Pricing Strateg from (Q*) Price Price TR PS N Segmenting Part lll | (Adult + Student) Perfect Price Discrimination Same as above Perfect Price Discrimination Maximum Possible Part B: 10 marks Suppose, the promoter plan to sell only 5000 tickets to the two groups. i. How the tickets will be allocated among the two groups if segmenting is used? That is, how many tickets are to be sold to adult group and how many to student group so as to maximise the total producer surplus from both groups (and Total Revenue)? Quantity (number of tickets) for Adults: Quantity (number of tickets) for students; ii. At what prices those tickets are to be sold? Price for Adults: Price for Students: iil. What will be the total revenue generated from selling those 5000 tickets? iv. Isita good decision to restrict the number of tickets to 5000? Please fill-in the following table and provide your observation. Your observations may target acieving higher revenue or PS or increasing revenue per ticket or comparing percentages etc. NB: For part I, consider only segmenting as option and not perfect price discrimination. | Adults | Students | Total | Number of Tickets Part | Profit Maximizing Quantity Part 1T Share of 5000 tickets sold Percentage of max tickets sold _ -- Part] TR at Profit Maximizing Quantity Part II TR at Share of 5000 tickets sold Percentage of max revenue achieved AutoSave O A A . C GD ... w- Dang_Anh_ ECON 3013_Project 5 (1) - Saved to my Mac Q Search (Cmd + Ctrl + U) Home Insert Draw Design Layout References Mailings Review View Comments Editing Share Times New... v 12 A" A Aa Ap EVENEVEE AaBbCcDdEe AaBbCcDdEe AaBbCcDc AaBbCcDdEE AaBb( , LA Paste BI Uvab X X |A LA Normal No Spacing Heading 1 Heading 2 Title Styles Dictate Sensitivity Editor Pane Please answer the following: I. For Price Segment: Adults Tickets: a. Write the Inverse Demand Curve and Marginal Revenue Curve Functions Inverse Demand Curve: P = 5000 - QA 10 ", Or P = 500 -0.1QA MR = 500- 2(0.1)QA, OR MR= 500 - 0.2QA b. Determine the Profit Maximizing Quantity, Q* and Price, P* To maximize profit, MR=MC Or, 500 - 0.2Q = 10, or Q* = 2450 P* = 500 - 0.1(2450) = $255 c. Determine the Revenue to be generated with Q* and P* AT Q* = 2450, P* =255, TR= 2450(255) = $624,750 d. Determine the Producer Surplus (Hint: The area is a rectangle; not a triangle !) PS = (255-10)(2450) = $600,250 II. For Price Segment: Student Tickets: Write the Inverse Demand Curve and Marginal Revenue Curve Functions Inverse Demnad Curve: P=10000-25, Or P=100 - 0.01Qs 100 MR=100 - 0.02Qs b. Determine the Profit Maximizing Quantity, Q* and Price, P* To minimize profit, MR = MC Or, 100 - 0.02Qs = 10, or Q* = 4,500 P* = 100 - 0.01(4500) = $55 c. Determine the Revenue to be generated with Q* and P* At Q* = 4500, P* = $55 Page 1 of 6 1110 words X English (United States) Ex Accessibility: Investigate Focus E + 153%AutoSave O A A . CG ... w- Dang_Anh_ ECON 3013_Project 5 (1) - Saved to my Mac Q Search (Cmd + Ctrl + U) Home Insert Draw Design Layout References Mailings Review View Comments Editing Share Times New... v 12 A" A Aa Ap AaBbCcDdEe AaBbCcDdEe AaBbCcDc AaBbCcDdEE AaBb( , LA Paste BIUvab X X A DAY Normal No Spacing Heading 1 Heading 2 Title Styles Dictate Sensitivity Editor Pane d. Determine the Producer Surplus (Hint: The area is a rectangle; not a triangle) PS= (55-10)(4500) = $202,500 III. What is the Total Quantity (number of tickets sold to both groups), Total Revenue and Total PS generated for the two segments? Total Quantity = QA + Qs = 2450 + 4500 = 6950 TR= TRA + TRs = $624,750 + $247,500 = $872,250 Total PS = PSA + PSs= $600,250 + $202,500 = $802, 750 IV. Suppose, instead of segmenting, the Promoters plan to follow perfect price discremination with the help of a combined demand function. a. What will be the new Demand Function (combine both demand functions)? Combined demand: QA + Qs = 5000-10P + 10000-100P, Or Q = 15000-110P b. What will be the combined Inverse Demand and Marginal Revenue Functions? Combined inverse Demand: P = 15000-Q , Or P = 15000 110 110 110 Marginal Revenue =. 15000 1 110 110 c. If the sponsors like to sell the same total number of tickets that would be sold through segmenting (as per part III), What will be the price (or prices) under perfect price discrimination and Total Revenue and Producer Surplus generated? How these values differ from answers to Part III, i.e. from segmenting? Page 2 of 6 1110 words x English (United States) Accessibility: Investigate Focus E + 153%