Chapter 2, Problem 11AP

(a)

To determine

The arc price elasticity of demand for health care consumers in Japan

Explanation of Solution

The arc price elasticity of demand can be calculated using the following equation:

$\begin{array}{c}\text{Arc Price elasticity of demand}=\frac{{\text{Q}}_2-{\text{Q}}_1}{{\text{P}}_2-{\text{P}}_1}\times \frac{{\text{P}}_2+{\text{P}}_1}{{\text{Q}}_2+{\text{Q}}_1}\\ =\frac{1.50-1.25}{10-20}\times \frac{20+10}{1.25+1.50}\\ =\frac{0.25}{-10}\times \frac{30}{2.75}\\ =0.025\times 10.90\\ =0.2727\end{array}$

The calculated value shows that the arc price elasticity of demand for healthcare of consumers in Japan is 0.27.

Economics Concept Introduction

Price elasticity of demand: Price elasticity of demand refers to the degree of responsiveness of demand for a commodity after a change in its price.

(b)

To determine

The effect of a higher income in Tokyo than Hokkaido on arc price elasticity of demand.

Explanation of Solution

Incomes are generally higher in Tokyo. This means that demand must also be higher in Tokyo. At an income level equivalent to that in Hokkaido, the quantity demand would be lower in Tokyo. That is, keeping income constant at the income level of Hokkaido, the number of outpatient visits would be lower than 1.25 at the price of 20. This means an increase in price from 10 to 20 would cause a greater decrease in the number of outpatient visits than shown in the given data. Therefore, the answer to the past question is an underestimation of price elasticity.

(c)

To determine

The effect of change in price per visit on the demand for health care.

Explanation of Solution

Elasticity of demand of Tokyo can be calculated as follows:

$\begin{array}{c}\text{Elasticity of demand}=\frac{\text{Percentage change in quantity}}{\text{Percentage change in price}}\\ \text{Change in price}=\frac{30-20}{20}\\ =0.5\\ -0.27=\frac{\text{Percentage change in quantity}}{0.5}\\ \text{Percentage change in quantity}=0.5\times 0.27\\ =-0.135\end{array}$

The calculated value shows that the change in quantity demand for healthcare in Tokyo is -0.135. Therefore, an increase in price would reduce the demand for health care.

Elasticity of demand of Hokkaido can be calculated as follows:

$\begin{array}{c}\text{Elasticity of demand}=\frac{\text{Percentage change in quantity}}{\text{Percentage change in price}}\\ \text{Change in price}=\frac{5-10}{10}\\ =0.5\\ -0.27=\frac{\text{Percentage change in quantity}}{0.5}\\ \text{Percentage change in quantity}=-0.27\times 0.5\\ =-0.135\end{array}$

The calculated value shows that the change in quantity demand for healthcare in Hokkaido is -0.135. Therefore, a fall in price would reduce the demand for health care in Hokkaido.

(d)

To determine

Price elasticity of demand for healthcare in Japan.

Explanation of Solution

$\begin{array}{c}\text{Elasticity of demand}=\frac{-0.2}{\frac{1}{2}\left(1.2+1.0\right)}\times \frac{\frac{1}{2}\left(30+15\right)}{15}\\ =\frac{0.2}{1.1}\times \frac{22.5}{15}\\ =0.27\end{array}$

(e)

To determine

Calculate the elasticity of demand for healthcare for Tokyo and Hokkaido separately.

Explanation of Solution

Elasticity of demand for Tokyo can be calculated as follows.

$\begin{array}{c}\text{Elasticity of demand}=\frac{-0.25}{\frac{1}{2}\left(1.0+1.25\right)}\times \frac{\frac{1}{2}\left(30+20\right)}{10}\\ =\frac{0.25}{1.125}\times \frac{25}{10}\\ =0.55\end{array}$

The calculated value shows that the elasticity of demand for Tokyo is 2.18.

The elasticity of demand for Hokkaido can be calculated as follows:

$\begin{array}{c}\text{Elasticity of demand}=\frac{0.5}{\frac{1}{2}\left(1.2+1.5\right)}\times \frac{1.25}{5}\\ =0.22\times 2.5\\ =0.55\end{array}$

The calculated value shows that the elasticity of demand for Hokkaido is 0.55.

(f)

To determine

The effect of an increase in price on the demand for healthcare.

Explanation of Solution

Elasticity of demand for Tokyo can be calculated as follows:

$\begin{array}{c}\text{Percentage change in price}=\frac{60-15}{15}\\ =3\\ \text{Elasticity of demand}=\frac{\text{Percentage change in quantity}}{\text{Percentage change in price}}\\ 0.27=\frac{\text{Percentage change in quantity}}{3}\\ \text{Percentage change in quantity}=\mathrm{0.81.}\end{array}$

The calculated value shows that the demand for healthcare is 0.81 percentage.

(g)

To determine

The combined elasticity of demand for Tokyo and Hokkaido. 

Explanation of Solution

$\begin{array}{c}\text{Combined elasticity of demand}=\frac{{\text{E}}_{\text{t}}{\text{P}}_{\text{t}}+{\text{E}}_{\text{n}}{\text{P}}_{\text{n}}}{{\text{P}}_{\text{t}}+{\text{P}}_{\text{n}}}\\ {\text{When P}}_{\text{t}}={\text{5P}}_{\text{n,}}\\ =\frac{{\text{5E}}_{\text{t}}{\text{P}}_{\text{n}}+{\text{E}}_{\text{n}}{\text{P}}_{\text{n}}}{{\text{5P}}_{\text{n}}+{\text{P}}_{\text{n}}}\\ =\frac{{\text{5E}}_{\text{t}}+{\text{E}}_{\text{n}}}{6}\\ =-0.556\end{array}$

The calculated value shows that the combined elasticity of demand would be 0.556.