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 its 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 26% over the next year? Answer with a percentage decline.

Answer 1

Annual demand is: Q = 1,400,000 – 4.0P.

a. To maximize revenues, we must have an elasticity of demand = -1

-1 = price coefficient x p/q

-1 = -4 * p/(1400000 - 4p)

-1400000 + 4p = -4p

p = 175000

Hence the revenue maximizing price is 175000

b. Income elasticity of demand = 3.5. Now incomes fall by 26% over the next year. Then the % change in quantity demand / % change in sales = 3.5 x -26% = -91%. Hence sales would drop by -91%.