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 $).

6. If all variables remain unchanged except that the price of Jolts (Pj) decreases by $1000, then the quantity demanded of Jolts will:

SELECT ONE:

a. decrease by 20000

     b. decrease by 10000

     c.   increase by 10000

     d.   increase by 20000

   e.   increase by 17500

     f.   decrease by 17500

7. Average weekly Jolt advertising expenditure (A) has decreased by $450. The manager of the advertising department should point out that demand for Jolts will:

SELECT ONE:

    a. increase by 18 Jolts

   b. decrease by 17.5 Jolts

   c. increase by 17.5 Jolts

   d. decrease by 18 Jolts

     e. increase by 100 Jolts

     f. decrease by 100 Jolts

8 You can tell by looking at the sign of average weekly disposable income (Y) that Jolts are being considered:

SELECT ONE:

  a. substitutes for Jolts

   b. complementary to Jolts

c. normal goods

   d. inferior goods

9. The partial derivative of the demand for Jolts with respect to the gas mileage rating (Mg) of Jolts is:

Possible answers:  

-20     -5 +.04 +10   +20   +35

Explanation / Answer

6. d. Increase by 20000

Change in Qj = -20*change in Pj= -20(-1000)= 20000

7. d. Decrease by 18 jolts

Change in Qj= 0.04*change in A= 0.04(-450)= -18

8. c. Normal goods

Normal goods are positively related to income which is shown by + sign.

9. +10 is correct

Coefficient of MG gives you the partial derivative of Qj with respect to Mg.

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