The multivariate demand function (below) is needed for questions 6- 12 Setting:
ID: 2429448 • Letter: T
Question
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 Genera developed for its Jolt: Qi 65000-20Pj + 20Pf+ 35Pt-5Pb +0.2Tc +0.05Y+ 10Mg +0.04A Where: Qi.m, the number of Jolts demanded per week. Pi the price of each new Jolt (in S) Pf the price of each new Ford gas-electric hybrid (in S). Pt the price of each new Toyota gas-electric hybrid (in S). Pb = the price ofreplacement batteries for the Jolt (in $). Tc- the amount of tax credit incentive offered with the purchase of a new hybrid (in S). Y average weekly disposable income of a typical Jolt purchaser (in S). Mg the miles per gallon of gas rating of the Jolt (in miles per gallon). A average weekly Jolt advertising expenditure (in S)Explanation / Answer
8.
Correct Answer:
A
Gas electric hybrid and jolts are substitute to each other, because with increase in price of gas electric hybrid, the demand for jolts, increase.
9.
Qj = 65000 – 20*Pj + 20*Pf + 35*Pt -5*Pb + .2*TC + .05*Y + 10*Mg + .04*A --------------- (1)
Differentiation of eq. 1 w.r.t. Pb, will give the required partial derivative.
dQj/dPb = -5
10.
Correct Answer:
D.
Working note:
Qj = 65000 – 20*Pj + 20*Pf + 35*Pt -5*Pb + .2*TC + .05*Y + 10*Mg + .04*A
At the given set of values,
Qj = 65000 – 20*35000 + 20*35000 + 35*45000 -5*10000 + .2*10000 + .05*1000 + 10*50 + .04*10000
Qj = 1592950
11.
Income elasticity of demand = (dQj/dY)*Y/Qj
dQj/dY = .05
At Y = 1000
Qj = 1592950 (already calculated in Q. 10)
Income elasticity of demand = (.05)*(1000/1592950)
Income elasticity of demand = +.000031
12.
When Pb = 100000
Qj = 1592950 (already calculated in Q. 10)
dQj/dPb = -5
Cross elasticity = (dQj/dPb)*Pb/Qj = (-5)*(10000/1592950)
Cross elasticity = -.031