# Problem 6: Analyzing Price-Demand RelationshipA highly traded commodity has a price-demand relationship given by the equation:\[ q = 120 - \sqrt{p} \]## Tasks### a) Construct the Elasticity FunctionThe 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 PriceCalculate the elasticity when the price is $100. Be sure to express the answer in fractions, not decimals.### c) Determine the Price Where Revenues are MaximizedIdentify the price point at which revenue from the commodity is maximized.

Given a highly traded commodity's demand(dd) function as: q=120-p where q is the quantity(q)…

Answered: commodity has -Sp. traded price -…

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commodity has -Sp. traded price - demand highly Pelation ship A of こ 12o-

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

# 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:

$q = 120 - \sqrt{p}$

where q is the quantity(q) demanded(dd) while p is the price.

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