Chapter 3, Problem 1CACQ

To determine

(a)

The revenue at different price levels and check the elasticity at that price range.

Answer to Problem 1CACQ

Revenue increases and demand is elastic in this range.

Explanation of Solution

If price is fall from $12 to $10,

When P = $12,

Revenue = P*Q

= $12*1

= $12

When P = $10

Revenue = $10*2 = $20

Therefore, if price is fall from $12 to $10 then the revenue is rises from $12 to $20.

In this range, the ratio of price and quantity is greater than 1, i.e.,

$\begin{array}{c}\frac{p}{q}=\frac{12}{1}=12>1\\ \frac{p}{q}=\frac{10}{2}=5>1\end{array}$

So, demand is elastic here.

Economics Concept Introduction

Elasticity shows the responsiveness of quantity demanded due to the change in the price of a commodity. The change in revenue due to the change in price depends upon the elasticity of the demand curve.

If demand is elastic, an increase (decrease) in price will lead to a decrease (increase) in total revenue. If the demand is inelastic, an increase (decrease) in price will lead to an increase (decrease) in total revenue. Total revenue is maximized at the point where demand is unitary elastic.

To determine

(b)

Revenue and elasticity at given price level.

Answer to Problem 1CACQ

Revenue is decreases here and demand is inelastic.

Explanation of Solution

If price is fall from $4 to $2

When P = $4,

Revenue = P*Q

= $4*5

= $20

When P = $2

Revenue = $2*6 = $12

Therefore, if price is fall from $4 to $2 then the revenue is fall from $20 to $12.

In this range, the ratio of price and quantity is less than 1, i.e.,

$\begin{array}{c}\frac{p}{q}=\frac{4}{5}=0.8<1\\ \frac{p}{q}=\frac{2}{6}=0.33<1\end{array}$

So, demand is inelastic here.

To determine

(c)

Revenue and elasticity at given price level.

Answer to Problem 1CACQ

Revenueis maximum at p = $7 and elasticity at this price is equal to 1.

Explanation of Solution

Total revenue is maximized at the point where demand is unitary elastic.

When the percentage change in price is equal to the percentage change in quantity demanded, then the demand is unitary elastic.

At P = $7

Q = 3.5

Revenue = $24.5

When p = $7 and Q = 3.5, the elasticity is equal to 1.

$\begin{array}{c}{\epsilon }_p=\frac{dQ}{dP}\cdot \frac{P}{Q}\\ =\frac{1}{2}\cdot \frac{7}{3.5}\\ =1\end{array}$