6) Elasticity of Demand: You are the manager of a bus line. You estimate the demand function to be y = D(p) = 81 – p² on thousands of tickets), where p is the price in dollars. (0 < p < 9) (It means y units will be sold (in demand) for a price of p.) a) At what price should the ticket be in order to maximize the revenue? (Hint: Revenue = price • unit-sold) b) Determine the elasticity at the price of $3 and interpret your result. Should you raise or lower the price from the present lever of $3?
6) Elasticity of Demand: You are the manager of a bus line. You estimate the demand function to be y = D(p) = 81 – p² on thousands of tickets), where p is the price in dollars. (0 < p < 9) (It means y units will be sold (in demand) for a price of p.) a) At what price should the ticket be in order to maximize the revenue? (Hint: Revenue = price • unit-sold) b) Determine the elasticity at the price of $3 and interpret your result. Should you raise or lower the price from the present lever of $3?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Elasticity of Demand:**
As the manager of a bus line, you need to estimate the demand function for your service. The demand function is given by:
\[ y = D(p) = 81 - p^2 \]
where:
- \( y \) is the number of units (in thousands of tickets) sold.
- \( p \) is the price of a ticket in dollars.
- \( p \) ranges from 0 to 9 dollars (\( 0 \leq p \leq 9 \)).
This means that \( y \) units will be sold (in demand) at a price \( p \).
### Task Breakdown:
#### a) Revenue Maximization:
To determine the ticket price that maximizes revenue, you should use the formula for revenue:
\[ \text{Revenue} = \text{price} \times \text{units sold} \]
Determine the optimal price and the corresponding units sold to maximize the revenue.
#### b) Calculation of Elasticity:
Compute the elasticity of demand at the price point of $3. Based on the result, decide whether it is beneficial to raise or lower the ticket price from the current level of $3.
Understanding the elasticity will help you gauge how sensitive the demand for tickets is to changes in price, guiding your pricing strategy for maximizing revenue and optimizing passenger numbers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb226293-e139-4051-bc95-6fe5cac3a2f7%2F18d42e01-29da-401d-a096-1bcb1e36edb8%2Fjbrcs9_processed.png&w=3840&q=75)
Transcribed Image Text:**Elasticity of Demand:**
As the manager of a bus line, you need to estimate the demand function for your service. The demand function is given by:
\[ y = D(p) = 81 - p^2 \]
where:
- \( y \) is the number of units (in thousands of tickets) sold.
- \( p \) is the price of a ticket in dollars.
- \( p \) ranges from 0 to 9 dollars (\( 0 \leq p \leq 9 \)).
This means that \( y \) units will be sold (in demand) at a price \( p \).
### Task Breakdown:
#### a) Revenue Maximization:
To determine the ticket price that maximizes revenue, you should use the formula for revenue:
\[ \text{Revenue} = \text{price} \times \text{units sold} \]
Determine the optimal price and the corresponding units sold to maximize the revenue.
#### b) Calculation of Elasticity:
Compute the elasticity of demand at the price point of $3. Based on the result, decide whether it is beneficial to raise or lower the ticket price from the current level of $3.
Understanding the elasticity will help you gauge how sensitive the demand for tickets is to changes in price, guiding your pricing strategy for maximizing revenue and optimizing passenger numbers.
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