Chapter1: Making Economics Decisions
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![# Problem 6: Analyzing Price-Demand Relationship
A highly traded commodity has a price-demand relationship given by the equation:
\[ q = 120 - \sqrt{p} \]
## Tasks
### a) Construct the Elasticity Function
The elasticity function is defined as:
\[ E = -\frac{dq}{dp} \cdot \frac{p}{q} \]
Construct and simplify this elasticity function for the given price-demand relationship.
### b) Find the Elasticity at a Given Price
Calculate the elasticity when the price is $100. Be sure to express the answer in fractions, not decimals.
### c) Determine the Price Where Revenues are Maximized
Identify the price point at which revenue from the commodity is maximized.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c307513-d57a-4587-a417-fdbdd2c400b3%2Ffecdf15c-b917-4695-a99c-65a43676956a%2Fuhhklm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Problem 6: Analyzing Price-Demand Relationship
A highly traded commodity has a price-demand relationship given by the equation:
\[ q = 120 - \sqrt{p} \]
## Tasks
### a) Construct the Elasticity Function
The elasticity function is defined as:
\[ E = -\frac{dq}{dp} \cdot \frac{p}{q} \]
Construct and simplify this elasticity function for the given price-demand relationship.
### b) Find the Elasticity at a Given Price
Calculate the elasticity when the price is $100. Be sure to express the answer in fractions, not decimals.
### c) Determine the Price Where Revenues are Maximized
Identify the price point at which revenue from the commodity is maximized.
Expert Solution

Step 1
Given a highly traded commodity's demand(dd) function as:
where q is the quantity(q) demanded(dd) while p is the price.
Step by step
Solved in 2 steps

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