To address the question regarding the price elasticity of demand for serving 3,000 commercial patients and 1,000 HMO members, we'll first need to understand some key concepts and determine if we have sufficient information.
### Understanding Price Elasticity of Demand
Price elasticity of demand measures how the quantity demanded of a good responds to a change in its price. Mathematically, it's given by the formula:
[tex]\[ \text{Price Elasticity of Demand} (E_d) = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}} \][/tex]
A high price elasticity means that the quantity demanded is highly sensitive to price changes, while a low price elasticity indicates that demand is relatively insensitive to price changes.
### Analyzing the Question
You are given that you serve 3,000 commercial patients and 1,000 HMO members. To determine the price elasticity, we need additional specific information, such as:
- The percentage change in quantity demanded in response to a certain percentage change in price.
- Historical data showing how the demand has varied with price changes.
- Any specific price elasticity values determined through previous studies or market analysis.
### Given Information and Options
From the question:
1. There are 3,000 commercial patients and 1,000 HMO members.
2. You need to set prices correctly considering the price elasticity of demand.
Given options:
a. [tex]\( E_d = 4.00 \)[/tex]
b. [tex]\( E_d = 4.25 \)[/tex]
c. [tex]\( E_d = 2.75 \)[/tex]
d. [tex]\( E_d = 3.00 \)[/tex]
However, the problem does not provide specific numeric changes in demand or price or any historical data to directly calculate elasticity.
### Conclusion
Based on the information provided in the question, without additional context or specific numerical data on how quantity demanded changes with price, we cannot accurately determine which price elasticity value is correct from the provided options.
Therefore, the conclusion is:
Insufficient information to determine the correct value of price elasticity from the given options.
