Use the price-demand equation at theindicated value of p and the formula-pf '(p)E (p) =f(p)to answer the followingquestions givena = f(p) = 7, 260 – 20p² and p = 12:a. Calculate the elasticity of demand (roundto one decimal place). Answer:b. Is demand elastic, inelastic, or unit?Answer:

Given: x = f(p) = 7,260 - 20p2P= 12 The formula: E(p) = -p * f'(p)f(p)Where,E(p) - Elasticity of…

Answered: Use the price-demand equation at the…

Economics Today and Tomorrow, Student Edition

1st Edition

ISBN:9780078747663

Author:McGraw-Hill

Publisher:McGraw-Hill

Chapter7: Demand And Supply

Section7.2: The Demand Curve And Elasticity Of Demand

Problem 6R

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Step 1

Given:

$\begin{array}{rcl} x & = & f (p) = 7, 260 - 20 p^{2} \\ P & = & 12 \end{array}$

The formula:

$\begin{array}{rcl} E (p) & = & \frac{- p * f' (p)}{f (p)} \\ W h e r e, \\ E (p) - E l a s t i c i t y o f d e m a n d \\ f' (p) - F i r s t o r d e r d e r i v a t i v e o f d e m a n d e q u a t i o n w i t h r e s p e c t t o p . \end{array}$

Ans. (a)

First, we need to calculate the value to substitute in the formula.

$\begin{array}{rcl} x & = & f (p) = 7, 260 - 20 p^{2} \\ w h e n p & = & 12 \\ f (12) & = & 7, 260 - 20 {(12)}^{2} \\ f (12) & = & 7, 260 - 20 (144) \\ f (12) & = & 4, 380 \\ ∴ f (p) & = & 4, 380 \end{array}$

Now, to calculate f'(p), take the first-order derivative with respect to p.

$\begin{array}{rcl} w h e n p & = & 12 \\ f (p) & = & 7, 260 - 20 p^{2} \\ f' (p) & = & - 2 x 20 p \\ f' (p) & = & - 2 x 20 (12) \\ ∴ f' (p) & = & - 480 \end{array}$

Now, substitute the values in the formula.

$\begin{array}{rcl} E (p) & = & \frac{- p * f' (p)}{f (p)} \\ E (p) & = & \frac{(- 12) x (- 480)}{4, 380} \\ E (p) & = & \frac{5, 760}{4, 380} \\ ∴ E (p) & = & 1.315068 ≅ 1.4 \end{array}$

The correct answer to be filled in the box would be 1.4

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