Question

# See the multivariate demand function below. Please show work so I can learn how this is...

See the multivariate demand function below. Please show work so I can learn how this is done.

Setting: U.S. Auto manufacturers are trying to develop a multivariate function with which to estimate the demand for their gas-electric hybrid compact cars. Here is one that Motors General developed for its Jolt: Qj = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A

Where:

Qj = the number of Jolts demanded per week.Pj = the price of each new Jolt (in \$). Pf = the price of each new Ford gas-electric hybrid (in \$). Pt = the price of each new Toyota gas-electric hybrid (in \$). Pb = the price of replacement batteries for the Jolt (in \$). Tc = the amount of tax credit incentive offered with the purchase of a new hybrid (in \$). Y = average weekly disposable income of a typical Jolt purchaser (in \$). Mg = the miles per gallon of gas rating of the Jolt (in miles per gallon). A = average weekly Jolt advertising expenditure (in \$).

1. What is the partial derivative of the demand for Jolts with respect to the gas mileage rating (Mg) of Jolts?

Qj = 65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A

Qj = the number of Jolts demanded per week.

Pj = the price of each new Jolt (in \$).

Pf = the price of each new Ford gas-electric hybrid (in \$).

Pt = the price of each new Toyota gas-electric hybrid (in \$).

Pb = the price of replacement batteries for the Jolt (in \$).

Tc = the amount of tax credit incentive offered with the purchase of a new hybrid (in \$).

Y = average weekly disposable income of a typical Jolt purchaser (in \$).

Mg = the miles per gallon of gas rating of the Jolt (in miles per gallon).

A = average weekly Jolt advertising expenditure (in \$).

(dQj)/dMg= d(65000 – 20Pj + 20Pf + 35Pt – 5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04 A)/dMg

= > (dQj)/dMg = 10

Note :- 65000 is a constant

dPj /dMg = 0   ;   Since, Pj is independent of Mg i.e., exogenoeus hence any change in Mg doesn’t   affect or cause any change in Pj.

Similarly all other variables are independent of Mg.

Hence the Partial derivative of Qj with respect to Mg yields the number 10. Therefore for a unit change in miles per gallon of gas rating of the jolt increases the demand of jolts per week by 10 units.

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