There are two primary sellers of toy cars, Ferrari and Lambo. Suppose there are 100 consumers, each of whom wishes to buy at most one car: a toy car is worth $5 to a consumer. Half of the consumers are Matchbox fans; the other half are Lambo fans. However, fandom is fickle: a consumer will buy the cheapest car unless both cars are equally costly to the consumer, in which case the consumer buys according to his fandom. The marginal cost of producing a car is $1 for both firms. Matchbox chooses its price, and then Lambo chooses its price; afterwards, each consumer decides which car to buy, if any. Note that no calculus is required to understand the strategies in this case. a) Predict Matchbox’s profits. Be sure to explain your reasoning. b) Suppose now that Matchbox can issue $1 coupons to its fans (and only its fans). Determine an optimal pricing strategy for Matchbox assuming the coupons are issued. What are your expected profits? Is issuing the coupons helpful? c) Suppose now that Lambo can issue its $1 coupon to its fans after Matchbox issues its own coupon. Will Lambo wish to issue the coupon? Will Matchbox, anticipating Lambo’ action, decide to issue a coupon? What are the final expected profits and prices? d) Explain intuitively how Matchbox and Lambo enhance their profits through “differentiating” their products by issuing these coupons.