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
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 Toyota hybrids (Pt) increases by $500, then the demand for Jolts will:
7. The Internal Revenue Service (IRS) decreases the amount of tax credit incentive offered (Tc) by $500. The manager of the advertising department should point out that demand for Jolts will:
8. If the sign of Toyota hybrids (Pt) were negative (-) instead of positive this would indicate that Toyota hybrids are being considered (_____________) to Jolts.
9. The partial derivative of the demand for Jolts with respect to the price of Jolts (Pj) is:
10. Enter the following values into your Jolt demand function (be very careful with the calculation because the resulting quantity of Jolts demanded will be used in several questions to follow). Circle your answer on the answer sheet. Pj = $25000 Pf = $40000 Pt = $35000 Pb = $5000
Tc = $7000 Y = $1200 Mg = 55 A =$70000
11. What is the point cross-price elasticity of Jolt demand with respect to the Toyota price (Pt) of $35000? Work out completely and show the sign (+ or -); carry out to 3 decimal places. The formula is:
12. What is the point elasticity of Jolt demand with respect to the advertising expenditure (A) of $70000. Work out completely and show the sign (+ or -); carry out to four decimal places. The formula is: