Chapter 4, Review Exercises, Question 061 The demand for a product is q = 2000 – 4p where 4 is units sold at a price of p dollars. Find the elasticity E if the price is $40 . Round your answer to two decimal places. The demand i v elastic. the absolute t inelastic. neither elastic nor inelastic.
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
![### Chapter 4, Review Exercises, Question 061
#### Problem Statement:
The demand for a product is given by the equation \( q = 2000 - 4p \), where \( q \) is the number of units sold at a price of \( p \) dollars. Find the elasticity \( E \) if the price is $40.
Round your answer to two decimal places.
\[ E \approx \, \_\_\_\_\_ \]
#### Elasticity Calculation:
To determine whether the demand is elastic, inelastic, or neither (absolute thresholds), you can use the following multiple-choice options provided:
1. elastic.
2. inelastic.
3. neither elastic nor inelastic.
Please select the appropriate option by considering the calculated elasticity value.
---
#### Detailed Explanation of Graphs/Diagrams (If present):
There are no specific graphs or diagrams included in this question. However, the interface indicates that a dropdown menu with the choices mentioned above is available for selection.
### Steps for Solving the Problem:
1. **Find the Derivative of the Demand Function**: The demand function is \( q = 2000 - 4p \).
\[ \frac{dq}{dp} = -4 \]
2. **Calculate the quantity demanded at \( p = $40 \)**:
\[ q = 2000 - 4(40) = 2000 - 160 = 1840 \]
3. **Use the elasticity formula**:
\[ E = \left| \frac{p}{q} \frac{dq}{dp} \right| \]
Substituting the values:
\[ E = \left| \frac{40}{1840} \cdot (-4) \right| = \left| \frac{40 \cdot -4}{1840} \right| = \left| \frac{-160}{1840} \right| \approx 0.09 \]
4. **Compare the calculated elasticity**:
- If \( E > 1 \), the demand is elastic.
- If \( E < 1 \), the demand is inelastic.
- If \( E = 1 \), the demand is unit elastic.
Finally, based on the calculated elasticity value, select the appropriate option from the dropdown menu.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92ac4bd1-ce2e-4c9a-a27a-d1c524faff08%2Ff709a16a-0e65-4b1b-aceb-b54a5d1e5fbd%2Fvekq28q.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
