Question

6. You are a manager at the Tesla Motors. The new Tesla roadster is due for release. If your marketing department estimates that the annual demand for the Tesla Roadster Car is: Q = 1,400,000 – 4.0P.

a. What price should you charge in order to maximize revenues from sales of the Roadster?

b. Tesla’s marketing department estimates the income elasticity of demand for it's Model S ($69,500) luxury car to be 3.5. Suppose the US, due to global trade wars, is plunged into a severe recession. How will sales be affected if consumers’ incomes fall by 24% over the next year? Answer with a percentage decline.

Answer 1

(a)

Q = 1,400,000 – 4.0P => P = (1/4)(1,400,000 – Q)

Max: Revenue(R) = PQ = (1/4)(1,400,000 – Q)Q

First Order condition:

dR/dQ = 0 => (1/4)(1,400,000 – 2Q) = 0 => 1,400,000 – 2Q = 0=> 1,400,000 - 2Q => Q = 700000

Hence, P = (1/4)(1,400,000 – Q) = (1/4)(1,400,000 – 700000) = 175000

Hence In order to maximize revenue we should charge Price = $175000

(b)

Formula:

Income Elasticity of Demand = % change in quantity demand / % change in Income

It is given that Income Elasticity of demand = 3.5 and % change in Income = (-)24% where -ve sign implies that there is decrease in Income

Hence Using above formula:

Income Elasticity of Demand = % change in quantity demand / % change in Income

=> 3.5 = % change in quantity demand /(-) 24 => % change in quantity demand = (-)84%.

Hence, if consumers’ incomes fall by 24% over the next year Then quantity demand will decrease by 84%