Chapter 5.6, Problem 14E

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248

Chapter
Section

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
Textbook Problem

# Demand for Fried Chicken A fried chicken franchise finds that the demand equation for its new roast chicken product, “Roasted Rooster,” is given by p = 40 q 1.5 , where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price. Express q as a function of p, and find the price elasticity of demand when the price is set at $4 per serving. Interpret the result. To determine To calculate: The price elasticity of demand if price was set at$4 per chicken serving and also express q as a function of p when p=40q1.5.

Explanation

Given Information:

The demand for chicken serving is p=40q1.5 where q is the number of chicken servings.

Formula used:

Price Elasticity of Demand:

The price elasticity of demand E is the percentage rate of decrease of demand per percentage increase in price. E is given by the formula:

E=âˆ’dpdqâ‹…pq

The demand is elastic if E>1, the demand is inelastic if demand is unitary elastic if E=1.

Calculation:

The demand for chicken serving is p=40q1.5 where q is the number of chicken servings.

Solving for q to get:

q1.5=40pq=(40p)11.5â‰ˆ11.6961p23

Taking derivative of q to get:

dqdp=âˆ’23(11.6961p53)

Consider the formula:

E=âˆ’dqdpâ‹…pq

Substituting value of derivative of q as âˆ’23(11

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