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This is your chance to calculate demand elasticities for health care. Suppose you are collecting data from a country (like Japan), where the government sets the price of health care. Each prefecture in Japan has a different set of prices (for example, Tokyo has higher prices than rural Hokkaido). Suppose you observe the following data for 1999: Outpatient visits Price/visit Tokyo 1.25/month 20 Yen Hokkaido 1.5/month 10 Yen What is the arc price elasticity of demand for health care consumers in Japan (using only these data)?

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Answer:

Arc price elasticity of demand = -0.273

Explanation:

This problem is solved as follows:

1. Identify the data.

                   Outpatient visit       Price / visit

Tokyo           1.25 / month                  20y

Hokkaido      1.5 / month                   10y

Outpatient visits equal the quantities demanded of the service. Therefore, we can say that:

Qt (Outpatient visits in Tokyo) = 1.25 / month

Qh (Outpatient visits in Hokkaido) = 1.5 month.

With the following prices:

Pt (Price in Tokyo) = 20y

Ph (Price in Hokkaido) = 10 y

2. Apply the formula to calculate arc-elasticity of demand:

[tex]Ep^{arc} = \frac{Pt+Ph}{Qt+Qh} *\frac{Qh-Qt}{Ph-Pt}[/tex]

We replace the data:

[tex]Ep^{arc} = \frac{20+10}{1.25+1.5} *\frac{1.5-1.25}{10-20}[/tex]

[tex]Ep^{arc}= \frac{30}{2.75} *\frac{0.25}{-10} = 10.91 *-0.025[/tex]

[tex]Ep^{arc} = -0.27275[/tex]

Final answer: -0.27275 or -0.273

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