The multivariate demand function (below) is needed for questions 6-12. Setting:

Question

The multivariate demand function (below) is needed for questions 6-12. 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 Genera developed for its Jolt: Qi-65000-20Pi + 20Pf + 35Pt-5Pb + 0.2Tc + 0.05Y + 10Mg + 0.04A Where: Oi the number of Jolts demanded per week. PL = the price of each new Jolt (in $) Pf- the price of each new Ford gas-electric hybrid (in S). Pt- the price of each new Toyota gas-electric hybrid (in $). Pb- the price of replacement batteries for the Jolt (in S). Tc -the amount of tax credit incentive offered with the purchase of a new hybrid (in S) Y average weekly disposable income of a typical Jolt purchaser (in S). Mg the miles per gallon of gas rating of the Jolt (in miles per gallon), A E average weekly Jolt advertising expenditure (in S) 6. If all variables remain unchanged except that the price of Jolts (Pi) increases by $1000, then the quantity demanded of Jolts will: 7. If all variables remain unchanged except that the average weekly disposable income (Y) increases by $350 then demand for Jolts will: S. You can tell by looking at the sign of the price of Toyota hybrids (P) that they are considered

Explanation / Answer

Question 6

Demand function of Jolts -

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

Calculate the partial derivative of demand function with respect to the price of Jolt -

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

Calculate the change in quantity demanded of Jolts -

Change in quantity demanded = Increase in price of Jolts * (dQj/dPj)

Change in quantity demanded = 1,000 * (-20) = -20,000

Negative change means the decrease in the quantity demanded.

So,

The quantity demanded of Jolts will decrease by 20,000.

Question 7

Demand function of Jolts -

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

Calculate the partial derivative of demand function with respect to the average weekly disposable income (Y) -

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

Calculate the change in demand of Jolts -

Change in demand of Jolts = Increase in weekly disposable income * (dQj/dY)

Change in demand of Jolts = 350 * 0.05 = 17.5

Positve change implies increase in demand.

So,

The demand for Jolts will increase by 17.5.

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