Setting: U.S. Auto manufacturers are trying to develop a multivariate function w

Question

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. If all variables remain unchanged except that the price of Ford’s hybrid (Pf) decreases by $500, then the demand for Jolts will:

2. Economic conditions are recessive.  Average weekly disposable income (Y) has decreased by $350.  Thus demand for Jolts will:

3. If the sign of average weekly disposable income (Y) were negative (-), this would indicate that Jolts are considered:

Explanation / Answer

1. A decrease in price of Pf by 500 would lead to 20*500 = 10,000 increase in number of jolts demanded.

2. A decrease in Y by $350 would lead to 0.05*350 = 17.5 increas in number of jolts demanded.

3. If the sign of disposable income was negative, jolts would have been considered as inferior good.

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