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An individual has the following demand function for gasoline:

QDGAS = 15-3PriceGAS + 0.02Income + 0.11PriceBT - 0.008PriceAUTO

Where income and car price are measured in thousands, and the price of bus travel is measured in average dollars per 100 miles traveled. Assuming the average automobile price is $22,000, income is $40,000, the price of bus travel is $25, and the price of gasoline is $30, calculate and interpret the income elasticity of gasoline demand and the cross price elasticity of gasoline demand with respect to the price of bus travel.

Sagot :

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Answer:

Explanation:

From the information given:

[tex]Q^d_{gas} = 15 - 3 P_{gas} + 0.02 I +0.11 P_{BT} -0.008P_{AUTO}[/tex]

[tex]Q^d_{gas} = 15 - 3 (30) + 0.02(40000) +0.11 (25) -0.008(22000)[/tex]

[tex]Q^d_{gas} = 15 - 90 + 800+2.75 -176[/tex]

[tex]Q^d_{gas} = 551.75[/tex]

So, Income elasticity = [tex]\dfrac{dQ^d}{dI}*\dfrac{I}{Q^d}[/tex]

[tex]= 0.02 *\dfrac{40000}{551.75}[/tex]

= 1.45 which is greater than 1

It is positive → i.e. Normal good

The cross elasticity = [tex]\dfrac{dQ^d}{dPBT}*\dfrac{PBT}{Q^d}[/tex]

[tex]= 0.11 \times \dfrac{25}{551.75}[/tex]

= 0.0049 which is greater than 0

It is positive →  hence they are substituents.

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