Math

CalculusApplied CalculusGiven that the demand q is a differentiable function of the unit price p, show that the revenue R = p q hasa stationary point when q + p d q d p = 0. Deduce that the stationary points of R are the same as the points of unit price elasticity of demand. (Ordinarily, there is only one such stationary point, corresponding to the absolute maximum of R .) [ HINT: Differentiate R with respect to p .]BuyFind*arrow_forward*

7th Edition

Waner + 1 other

Publisher: Cengage Learning,

ISBN: 9781337291248

Chapter 5.6, Problem 37E

Textbook Problem

Given that the demand *q* is a differentiable function of the unit price p, show that the revenue

Deduce that the stationary points of *R* are the same as the points of unit price elasticity of demand. (Ordinarily, there is only one such stationary point, corresponding to the absolute maximum of *R*.) [**HINT:** Differentiate *R* with respect to *p*.]

Expert Solution

To determine

**To calculate:** The deduction that stationary points of

**Given Information:**

The demand

**Formula used:**

Income Elasticity of Demand

The income elasticity of demand

And the demand is elastic if

**Calculation:**

The demand

Differentiate

Stationary point

Applied Calculus

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Income Elasticity of Demand: Live Concerts The...Ch. 5.6 - Income Elasticity of Demand: Broadband in 2010 The...Ch. 5.6 - Income Elasticity of Demand: Broadband in 2007 The...Ch. 5.6 - Income Elasticity of Demand: Computer Usage in the...Ch. 5.6 - Income Elasticity of Demand: Internet Usage in the...Ch. 5.6 - Price Elasticity of Supply Given a supply equation...Ch. 5.6 - Price Elasticity of Supply Given a supply equation...Ch. 5.6 - Income Elasticity of Demand (based on a question...Ch. 5.6 - College Tuition (from the GRE Economics Test) A...Ch. 5.6 - Complete the following: When demand is inelastic,...Ch. 5.6 - Complete the following: When demand has unit...Ch. 5.6 - Given that the demand q is a differentiable...Ch. 5.6 - Given that the demand q is a differentiable...Ch. 5.6 - Your calculus study group is discussing price...Ch. 5.6 - Another member of your study group claims that...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - In Exercises 18, find all the relative and...Ch. 5 - 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In Exercises 1722, sketch the graph of the given...Ch. 5 - Revenue Demand for the latest best-seller at...Ch. 5 - Revenue Demand for The Secret Loves of John O, a...Ch. 5 - Profit Taking into account storage and shipping,...Ch. 5 - Profit Taking into account storage and shipping,...Ch. 5 - Office Space Although still a sophomore at...Ch. 5 - Recreation Space As a result of complaints by the...Ch. 5 - Box Design The sales department at...Ch. 5 - Box Redesign The sales department at...Ch. 5 - Sales OHaganBooks.com modeled its weekly sales...Ch. 5 - Sales The quarterly sales of OHagan oPods...Ch. 5 - Chance Encounter Marjory Duffin is walking north...Ch. 5 - Company Logos OHaganBooks.coms website has an ani-...Ch. 5 - Elasticity of Demand (Compare Exercise 23.) Demand...Ch. 5 - Elasticity of Demand (Compare Exercise 24.) Demand...Ch. 5 - Elasticity of Demand Last year OHaganBooks.com...Ch. 5 - Elasticity of Demand JungleBooks.com (one of...

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