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 the Toyota hybrid (Pt) decreases by $500, then the demand for Jolts will:

7. Engineering increases the miles per gallon of gas rating (Mg) by 10 miles per gallon. The manager of the advertising department should point out that demand for Jolts will:

8. You can tell by looking at the sign Ford hybrids (Pf) that Ford hybrids are being considered:

9. The partial derivative of the demand for Jolts with respect to advertising (A) 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 = $30000 Pf = $45000 Pt = $55000 Pb = $6000 Tc = $10000 Y = $1500 Mg = 60 A =$50000

11. What is the point cross-price elasticity of Jolt demand with respect to the Toyota price (Pt) of $55000? 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 $50000. Work out completely and show the sign (+ or -); carry out to four decimal places. The formula is:

Explanation / Answer

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

(6) Ceteris paribus,

If Pt decreases by $500, Qj decreases by (35 x 500) = 17,500.

(7) Ceteris paribus,

If Mg increases by 10, Qj increases by (10 x 10) = 100.

(8) Coefficient of Pf is positive (= 20). So, Ford hybrids are substitutes of Jolts - as price of Ford Hybrid increases (decreases), quantity demanded of Jolts increases (decreases).

(9) Partial derivative of Qj with respect to A = 0.4

Note: First 4 sub-questions are answered.

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