A baseball team plays in a stadium that holds 54,000 spectators. With ticket prices at $10, the average attendance had been 16,000. When ticket prices were lowered to $8, the average attendance rose to 24,000. (a) Find the demand function (price p as a function of attendance x), assuming it to be linear. P(x) = (b) How should ticket prices be set to maximize revenue? (Round your answer to the nearest cent.)

A baseball team plays in a stadium that holds 54,000 spectators. With ticket prices at $10, the average attendance had been 16,000. When ticket prices were lowered to $8, the average attendance rose to 24,000. (a) Find the demand function (price p as a function of attendance x), assuming it to be linear. P(x) = (b) How should ticket prices be set to maximize revenue? (Round your answer to the nearest cent.)

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter3: Demand Analysis

Section: Chapter Questions

Problem 1.8CE

See similar textbooks

Similar questions

A theater company presents a play in a theater with a capacity of 2,000 spectators. With the ticket price at $20, the average attendance at recent games has been 1,000. Market research indicates that for every dollar the ticket price drops, attendance will increase by 100. Identify the feature that maximizes ticket revenue.
The marketing department of a business has determined that the demand for a product can be modeled by p=2000−10x, where p is the price per unit (in dollars) and x is the number of units. The cost (in dollars) of a producing x units is given by C=2000+500x. What price will yield a maximum profit?
There is no demand for a certain make of one-time use camera when the unit price is $ 12. However, when the unit price is $ 8, the quantity demanded is 8000/week. The supplier will not market any cameras if the unit price is $ 2 or lower. At $ 4/camera, however, the manufacturer will make available 5000 cameras/week. Given that both the supply and demand equations are linear: Determine the associated linear demand function Determine the linear supply function. At what price should the camera be sold so that there is neither a surplus nor a shortage?
An industrial firm makes two products, A and B. These products require water resources where they are very scarce. The products they make are unique, and hence they can set the unit price of each product at any value they want to. However, experience tells them that the higher the unit price for a product, the less amount of that product they will sell. The relationship between the unit price and quantity that can be sold is given by the following two demand functions: Assume for simplicity that the unit price for product A is (16 - A) and for product B is (18-2.5B). Suppose the total amount of A and B could not exceed the total amount of Tmax. Where Tmax = 10. Please use "Lagrange Multiplier" method to determine what are the amounts of A and B, and their unit prices, that maximize total revenue (Set the marginal increments at 1).
The total cost function will be given by Total Cost = 200 + 2Q + 0.01 Q^2 and demand function is Q = 1000 - 0.02 p, where p is a price. Find the demand Q at which Total net benefit is maximized. Find the associated values of price, total net benefit, profit, and consumer surplus.
Supply is said to be inelastic when the quantity supplied changes* more than the change in its price. less than the change in it price. 2 equal to the change in its price. none of the above. Elasticity of supply tends to be greater when* inputs are specialized. time period allowed for adjustment is fairly long. degree of advertising is great. demand for the product is inelastic The supply curve overtime is more elastic than the supply curve over the short period of time because, given sufficient time* production techniques become more expensive. new firms can enter the industry and old firms can increase their plant size. producers become more competitive. consumers become more demanding.
After an analysis of a large number of small businesses with two to nine employees, it was determined that, in a certain market sector, the operating costs C, in thousands of dollars, could be modeled by the function(pic#2)...., where p is the number of employees working for the firm. On the other hand, the realized revenue, R, of a firm could be determined as a function of the operating costs C, where R=(pic#1)... R and C are expressed in thousands of dollars. a) Based on the analysis, what would be the operating costs for a business with three employees? b) What would be the revenue for a company with three employees? c) Determine the equation that would model the realized revenue, R, as a function of the number of employees.
A local store will buy 20 doorbell cameras from a supplier if the price is $77 each. If the price drops to $27 , then the store will buy 30 . The supplier is willing to sell 66 doorbell cameras for the price of $50.50 each, but only 49 at a price of $42.00 each. Find the supply and demand functions and the market equilibrium point. Assume both the supply and demand are linear. Use integers, fractions or decimals to describe the slopes and p-intercepts. A) What is the equation for the demand? p= B) What is the equation for the supply? p= c) What is the market equilibrium point?Explain in details
A company wants to issue a coupon for a product. The marginal cost of the product is $1. If the elasticity of demand for coupon users is -5 and the elasticity of demand for non-coupon users is -2, then in order to maximize profit, what should the value of the coupon (in dollars) be? Group of answer choices: 1) 0.50 2) 0.75 3) 1.00 4) 1.50
A retail chain will buy 900 cordless phones if the price is $30 each and 800 if the price is $40. A wholesaler will supply 350 phones at $40 each and 1400 at $70 each. Assuming that the supply and demand functions are linear, find the market equilibrium point and explain what it means.
A toy company is trying to determine the optimal price for their weekly supply to meet the demand for a toy they are about to release. They estimate that the supply function follows p= 0.006q^2 + 0.14q+ 8.62 and the demand function follows p= -1.25q+ 65 , where p is the price of the toy (in dollars) and q is the weekly quantity of the toy (in hundreds). If the company tries to sell the toy for $24, will there be a shortage or surplus of toys each week?
The daily cost to manufacture generic trinkets for gullible tourists is given by the cost function C(x) = −0.001x2 + 0.3x + 500 dollars where x is the number of trinkets. a. As x increases, the marginal cost(A) increases (B) decreases (C) increases, then decreases. (D) decreases, then increases. b. As x increases, the average cost(A) increases (B) decreases (C) increases, then decreases. (D) decreases, then increases. c. The marginal cost is(A) greater than (B) equal to (C) less than the average cost when x = 100.