The car manufacturer Edison is the sole producer of electric cars in the market, selling to two different types of customers. All else equal, travelers (type t) prefer batteries that go longer distances between charges and are willing to pay for this luxury. Urban drivers (type u) do not require as great a battery. Edison knows the willingness-to-pay of each type, and that there are q percent of type ts in the market. The willingness-to-pay for each type for different battery sizes are,

Vt(k = 100) = $160, 000 Vt(k = 60) = $80, 000

Vu(k = 100) = $100, 000 Vu(k = 60) = $60, 000

where k is the battery life in kilowatt hours (kWh).

Producing 60 kWh battery costs $30,000, which is half the cost of a 100 kWh battery.

(a) Edison showroom salesmen believe they can perfectly identify (1st/3rd-degree) which type of buyer walks through the door. Find the profit-maximizing prices (pi) and battery sizes (ki). What is Edisons average profit per customer?

(b) It turns out Edison salesmen are not as smart as they think, and cannot identify any type of customer. If Edison offered the packages in (a), demonstrate who would buy which type?

(c) If Edison has no way of price discriminating, what should they do? Consider all possible options for different values of q.

(d) Sensing a better option, Edison hires some economists to help. Write out the participation/rationality constraints and the self-selection/incentive compatibility constraints. Which ones hold with equality?

(e) Determine the profit-maximizing pricing strategy for Edison for any distribution of buyers (meaning for all values of q).