Chapter 5, Problem 5.1P

(a)

To determine

The number case of beer that would need to produce to increase the tax revenue by $20,000.

Explanation of Solution

The original tax revenue received from 20,000 case of beer is $40,000$\left(\$2\text{ per case}\times \text{20,000}=40,000\right)$. According to the Mr. S’s advice, the total tax revenue received by increasing tax as $1 is $60,000$\left(\$1\text{ per case}+\$2\text{ per case}\times \text{20,000}=60,000\right)$. Thus, it gives extra $2,000 tax revenue.

According to the Mr. M’s advises, the brewery would need to produce 15,000 case beers. The total tax revenue received by increasing tax at $1 is $60,000$\left(\$2\text{ per case}+\$2\text{ per case}\times 15\text{,000}=60,000\right)$. Thus, it gives extra $2,000 tax revenue.

According to the Mr. F’s advises, the brewery would need to produce 15,000 case beers. The total tax revenue received by increasing tax at $1 is $60,000$\left(\$2\text{ per case}-\$0.50\text{ per case}\times 40\text{,000}=60,000\right)$. Thus, it gives extra $2,000 tax revenue.

Economics Concept Introduction

Income elasticity of demand: Income elasticity refers to the percentage change in the demand for goods and services due to change occurred in the income level.

Normal goods: A normal good is a good which demand increases when income of the consumer increases.

(b)

To determine

The price elasticity of demand for beer if tax revenue increased by $20,000.

Explanation of Solution

The general formula for calculating the price elasticity of demand is shown below:

$\text{Price elasticity of demand}=\left[\frac{\frac{\left({\text{Quantity }}_{\text{Present}}-{\text{Quantity }}_{\text{Previous}}\right)}{\frac{\left({\text{Quantity }}_{\text{Present}}+{\text{Quantity }}_{\text{Previous}}\right)}{2}}}{\frac{{\text{Price }}_{\text{Present}}-{\text{Price }}_{\text{Previous}}}{\frac{{\text{Price }}_{\text{Present}}+{\text{Price }}_{\text{Previous}}}{2}}}\right]$ (1)

According to the Mr. S’s advice, the price elasticity of demand for beer is shown below:

Substitute the values in Equation (1).

$\begin{array}{c}\text{Price elasticity of demand}=\left[\frac{\frac{\left(20,000-20,000\right)}{\frac{\left(20,000+20,000\right)}{2}}}{\frac{20-20}{\frac{20+20}{2}}}\right]\\ =\frac{\frac{0}{2,0000}}{\frac{0}{20}}\\ =0\end{array}$

The price elasticity of demand is 0.

According to the Mr. M’s advises, the price elasticity of demand for beer is shown below:

Substitute the values in Equation (1).

$\begin{array}{c}\text{Price elasticity of demand}=\left[\frac{\frac{\left(15,000-20,000\right)}{\frac{\left(15,000+20,000\right)}{2}}}{\frac{22-20}{\frac{22+20}{2}}}\right]\\ =\frac{\frac{-5000}{17500}}{\frac{2}{21}}\\ =-3\end{array}$

The price elasticity of demand is -3.

According to the Mr. F’s advises, the price elasticity of demand for beer is shown below:

Substitute the values in Equation (1).

$\begin{array}{c}\text{Price elasticity of demand}=\left[\frac{\frac{\left(40,000-20,000\right)}{\frac{\left(40,000+20,000\right)}{2}}}{\frac{19.5-20}{\frac{19.5+20}{2}}}\right]\\ =\frac{\frac{20000}{30000}}{\frac{-0.5}{19.75}}\\ =\frac{0.6666}{-0.0253}\\ =-26.3\end{array}$

The price elasticity of demand is -26.3.

Economics Concept Introduction

Price elasticity of demand: Price elasticity of demand refers to the responsiveness of changes or the change in quantity demanded due to the change in price.

(c)

To determine

The total revenue receive if the tax revenue increased by $20,000.

Explanation of Solution

The Burpee Beer currently receive $36,000. As per Mr. S’s plane, the total revenue received is $36,000$\left(18\times 20,000=36,000\right)$ and it remains the same revenue level. As per Mr. M’s plane, the total revenue received is $270,000$\left(18\times 15,000=270,000\right)$. It is less than the current revenue. As per Mr. F’s plane, the total revenue received is $720,000$\left(18\times 40,000=720,000\right)$ and it is greater than the current revenue.