Question

10-12 please answered with work please? 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 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 = $45000 Pf = $40000 Pt = $45000 Pb = $7000 Tc = $8000 Y = $1000 Mg = 55 A =$20000

11. What is the point cross-price elasticity of Jolt demand with respect to the Toyota price (Pt) of $45000? Work out completely and show the sign (+ or -); carry out to 3 decimal places.

12. What is the point elasticity of Jolt demand with respect to the advertising expenditure (A) of $20000. Work out completely and show the sign (+ or -); carry out to four decimal places.

Answer 1

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

10.

Pj = $45000 Pf = $40000 Pt = $45000 Pb = $7000 Tc = $8000 Y = $1000 Mg = 55 A =$20000

So, Qj = 65000 – (20*45000) + (20*40000) + (35*45000) – 5*7000 + (0.2*8000) + (0.05*1000) + (10*55) + (0.04*20000)

Qj = 65000 - 9,00,000 + 8,00,000 + 15,75,000 - 35,000 + 1600 + 50 + 550 + 800

Qj = 24,43,000 - 9,35,000

Qj = 15,08,000

11.

From the demand equation, if we take the derivative of Quantity Demanded wrt Toyota Price i.e dQj / dPt = 35

So, Cross Price Elasticity = (dQj/dPt)*(Pt/Qj)

= 35 * (45000/15,08,000)

= +1.044

12.

From the demand equation, if we take the derivative of Quantity Demanded wrt Advertising Expenditure A i.e (dQj / dA) = +0.04

So, Point Elasticity of Jold Demand = (dQj/dA)*(A/Qj)

= 0.04 * (20000/15,08,000)

= +0.0005 (up to four decimals)

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