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 $).

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: ag, P. EE apg 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: ag А е,

Answer 1

Ano Q j = 65000 - 20 Pj+20 ff + 35 Pt-5 Pb +0.2TC +0.05 4 +10 mg +0.04 A Q; = 65000 - 20(25000) + 20(40000) +351 35000) - 5(5000) +0.2(7000) +0.05 (200) +10(55) +0.04170000) 1= 65000 – 500.000 + 800.000 + 1225000 – 25000 + 1400 + 60 + 550 + 2800 oj = 1569810 Angll E= doix PT a PT Qi ooi =+ 35 dpi The &= 35 x 35000 = 1225000 0.780 1569810569810 price elastiuty is +0 1780 re thise are portes subsitute goods. cross

AN 12 E=dQ7 x AB dA B do O/A - + 0.04 = 0.04 X 70000 1569810 11 0.00178 0.002 is +0.002 The elasticity is ie admitisment has a positive effect of the cars. it on the sale