Knoebels Amusement Park in Elysburg, Pennsylvania, charges a lump-sum fee, L, to enter its Crystal Pool. It also charges p per trip down a slide on the pool's water slides. Suppose that 400 teenagers visit the park, each of whom has a demand function of q₁ = 6-p, and that 400 seniors also vist, each of whom has a demand function of q₂ = 5-p. Knoebels's objective is to set L and p so as to maximize its profit given that it has no (non-sunk) cost and must charge both groups the same prices. What are the optimal L and p? The optimal L and p are L=$and p=$ (Enter numeric responses using real numbers rounded to three decimal places.)

Knoebels Amusement Park in Elysburg, Pennsylvania, charges a lump-sum fee, L, to enter its Crystal Pool. It also charges p per trip down a slide on the pool's water slides. Suppose that 400 teenagers visit the park, each of whom has a demand function of q₁ = 6-p, and that 400 seniors also vist, each of whom has a demand function of q₂ = 5-p. Knoebels's objective is to set L and p so as to maximize its profit given that it has no (non-sunk) cost and must charge both groups the same prices. What are the optimal L and p? The optimal L and p are L=$and p=$ (Enter numeric responses using real numbers rounded to three decimal places.)

Microeconomics: Principles & Policy

14th Edition

ISBN:9781337794992

Author:William J. Baumol, Alan S. Blinder, John L. Solow

Publisher:William J. Baumol, Alan S. Blinder, John L. Solow

Chapter13: Between Competition And Monopoly

Section: Chapter Questions

Problem 5DQ

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Knoebels Amusement Park in Elysburg, Pennsylvania, charges a lump-sum fee, L, to enter its Crystal Pool. It also charges p per trip down a slide on the pool's water slides. Suppose that 450 teenagers visit the park, each of whom has a demand function of q₁ = 6-p, and that 300 seniors also vist, each of whom has a demand function of q₂ = 5-p. Knoebels's objective is to set L and p so as to maximize its profit given that it has no (non-sunk) cost and must charge both groups the same prices. What are the optimal L and p? The optimal L and p are L=$and p=$. (Enter numeric responses using real numbers rounded to three decimal places.)
Knoebels Amusement Park in Elysburg, Pennsylvania, charges a lump-sum fee, L, to enter its Crystal Pool. It also charges p per trip down a slide on the pool’s water slides. Suppose that 400 teenagers visit the park, each of whom has a demand function of q1 = 5 – p, and that 400 seniors also visit, each of whom has a demand function of q2 = 4 – p. Knoebels’ objective is to set L and p so as to maximize its profit given that it has no (non-sunk) cost and must charge both groups the same prices. What are the optimal L and p?
Suppose the typical LA Rams fan has the following demand curve for Bills football games: P = 200 – 5G where G is the number of games the fans attend. Suppose the Bills have the chance to offer a various multi-game season ticket packages and tickets to individual games. If the Rams want to sell a particular fan single tickets to all eight home games, what price must they charge? $___ What should be the total price for a LA Rams 8-game season ticket package? $___ What should be the average ticket price for an LA Rams 4-game season ticket package? $___ Suppose the Rams have the opportunity to sell tickets to individual games. What price should they charge? $___
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Jackistheowneroftheonlylocalbarinasmalltown.Hesellswhiskeyin one-ounce glasses. For simplicity, let’s assume it doesn’t cost Jack anything to run his business. There are two customers, Adam and Burt who are twin brothers. Adam’s demand function is yA = 16 – 2p, and Burt’s demand function is yB = 8 – p (price is measured in dollars and quantity is measured by ounces). Jack knows their demand functions, but the problem is that he cannot tell them apart since they look exactly the same to him. To increase his profits, Jack offers the following two options that his customers can choose from: (1) You can pay $T1 up front and drink as much as you want; or (2) Pay $T2 up front and the price per ounce of whiskey will be $p. 1.a If p = 4, what is the maximal T2 that Jack can charge so that Burt is willing to come to the bar? 1.b What is the maximal T1 that Jack can charge so that Adam will choose the first pricing option?
Suppose you are managing a farming company, which is one of the major producers of Tomato in the State of North Carolina. You have been provided with the following graph which shows the demand curve for the tomatoes that your company is producing. As you can see, there are two known points (X and Y) on a demand curve for tomatoes. According to the “standard" method of computing elasticity (i.e. use the standard formula of percentage change in your computations), the standard-method price elasticity of demand for tomatoes when moving from point X to point Y is approximately Demand 10 20 30 40 50 60 70 80 90 100 QUANTITY (Thousands of pounds of tomatoes)
Suppose that managers at Honda are deciding how to price the new Honda Accord. The managers estimate that their total costs increase by $20,000 for each car they produce. They also estimate the demand curve they face; it is described by the equation: Q = -0.4 P + 16,000, where Q represents the quantity of Honda Accords they will sell and P represents the price they charge in US dollars. We can re-write that demand curve as: P = 40,000 - 2.5 Q. Take every possibly quantity that the managers might choose between and 7,000 in units of 100. For each possible quantity, calculate the associated price the managers would need to charge, the revenue they would earn, and the total costs. You can then calculate profits for each level of quantity. Highlight the cell that contains the highest value of profit. Finally, you can also approximate marginal revenue here as the change in total revenue after the next 100 cars are produced. At what quantity does marginal revenue roughly equal marginal cost?…
Suppose that managers at Honda are deciding how to price the new Honda Accord. The managers estimate that their total costs increase by $20,000 for each car they produce. They also estimate the demand curve they face; it is described by the equation: Q = -0.4 P + 16,000, where Q represents the quantity of Honda Accords they will sell and P represents the price they charge in US dollars. We can re-write that demand curve as: P = 40,000 - 2.5 Q. Take every possibly quantity that the managers might choose between 0 and 7,000 in units of 100. For each possible quantity, calculate the associated price the managers would need to charge, the revenue they would earn, and the total costs. You can then calculate profits for each level of quantity. Highlight the cell that contains the highest value of profit.
Suppose the typical Buffalo Bills fan has the following demand curve for Bills football games:P= 120-10G where G is the number of games the fans attend.If the Bills want to sell the fan a ticket to all eight home games, what price must they charge?
A manager of a nightclub realizes that demand for drinks is more elastic among students and is trying to determine the optimal pricing schedule. Specifically, he estimates the following average demand for his customer types: Under 25: qr =18-5p Over 25: q=10-2p The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the club $2 to make. If the manager can charge a separate entry fee and a price per drink for each group, what two-part price will the manager set for reach group. Now suppose that once again it is impossible to identify which group the customers belong. Suppose the manager lowers the price of drinks to equal to marginal cost and still wanted to attract both customers, what entry fee would the manager set? Compare the profits earned in parts a) to d). Which scheme would you choose if you could not identify customer type and which would you choose if you could identify customer type.
There are two types of consumers in Melbourne: students and non-students. The student population is 10, and each student’s demand of printing paper is Q=1−?, for ?<1.The non-student population is 40, and each non-student’sdemand of printing paper is Q=3−?, for ?<3. Suppose OfficeMax is the only seller of printing paper in Melbourne. Assume zero production cost. Suppose OfficeMax offers a student discount, d, so students only pay d*p and non-students pay the full price, p. What are the profit maximizing price and discount d?
What is the difference between bundle pricing and random pricing?