If the two points on the demand for Norman's rooms lie on a straight-line demand curve, what then is the point price elasticity of demand at a nightly price of $150? Please show your work and report your answer to one decimal place. Suppose Norman Bates, the owner-manager of a small local hotel, projects the following demand for his rooms: Price $110 130 Quantity purchased (per night) 10 8
If the two points on the demand for Norman's rooms lie on a straight-line demand curve, what then is the point price elasticity of demand at a nightly price of $150? Please show your work and report your answer to one decimal place. Suppose Norman Bates, the owner-manager of a small local hotel, projects the following demand for his rooms: Price $110 130 Quantity purchased (per night) 10 8
Chapter1: Making Economics Decisions
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![**Task: Calculating the Point Price Elasticity of Demand**
If the two points on the demand for Norman's rooms lie on a straight-line demand curve, what then is the point price elasticity of demand at a nightly price of $150? Please show your work and report your answer to one decimal place.
**Scenario Description:**
Suppose Norman Bates, the owner-manager of a small local hotel, projects the following demand for his rooms:
| **Price** | **Quantity purchased (per night)** |
|-----------|-------------------------------------|
| $110 | 10 |
| $130 | 8 |
**Instructions:**
Calculate the point price elasticity of demand at a given price point using the provided data. The point price elasticity of demand formula is given by:
\[ E_d = \left( \frac{\Delta Q}{\Delta P} \right) \times \left( \frac{P}{Q} \right) \]
Where:
- \( \Delta Q \) is the change in quantity.
- \( \Delta P \) is the change in price.
- \( P \) is the price at which elasticity is being calculated.
- \( Q \) is the quantity demanded at that price.
Show all steps in your calculations and round the final answer to one decimal place.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab7a93e1-40d3-4bdc-a63d-a1a4acc86cc1%2F6a8e0551-65bd-4462-89d0-c65adc57379f%2Fu59z41a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Task: Calculating the Point Price Elasticity of Demand**
If the two points on the demand for Norman's rooms lie on a straight-line demand curve, what then is the point price elasticity of demand at a nightly price of $150? Please show your work and report your answer to one decimal place.
**Scenario Description:**
Suppose Norman Bates, the owner-manager of a small local hotel, projects the following demand for his rooms:
| **Price** | **Quantity purchased (per night)** |
|-----------|-------------------------------------|
| $110 | 10 |
| $130 | 8 |
**Instructions:**
Calculate the point price elasticity of demand at a given price point using the provided data. The point price elasticity of demand formula is given by:
\[ E_d = \left( \frac{\Delta Q}{\Delta P} \right) \times \left( \frac{P}{Q} \right) \]
Where:
- \( \Delta Q \) is the change in quantity.
- \( \Delta P \) is the change in price.
- \( P \) is the price at which elasticity is being calculated.
- \( Q \) is the quantity demanded at that price.
Show all steps in your calculations and round the final answer to one decimal place.
Expert Solution
Step 1
Given: At the price of $110 quantity purchase is 10, and at a price of $130 quantity purchase is 8.
We have to find out Norman's demand curve using the given information.
It is given that Norman's room lies on a straight-line demand curve.
So, the equation for a straight-line demand curve is:
P = mQ + c (1)
Here P = price, Q = Quantity, m= slope and c = constant
Slope m = = = -10
Putting the value of m in equation (1)
P = -10Q +C (2)
Now, it has to satisfy the points that lie on a straight-line demand curve.
So, putting P = $110, Q = 10 in equation (2)
So, 110 = -10*10 +c
c = 210
Putting the value of c in equation (2)
P = -10Q +210 (3)
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