Assume that both HotWheels and Matchbox have the same unit costs = c (c > 0). First assume that neither offers a rebate. What price(s) will HotWheels and Matchbox rationally charge? Why? 2. Now assume that Matchbox but not HotWheels offers a rebate (r = $1) - issuing coupons only to Matchbox fans [half the market] for $1 off the price of a Matchbox car. Suppose HotWheels is the 'price leader' [it sets its price first and Matchbox then sets its price and then consumers buy one or the other car]. What is the highest price HotWheels can charge without being undercut by Matchbox? What price will Matchbox then charge? What are the expected profits to each firm now? [HINT: in 'steps' - moving from one firm to the next, weighing the alternative scenarios of pricing for only its segment versus for the whole market] 3. Finally, assume that both Matchbox and HotWheels offer a rebate (r = $1) - with each issuing one coupon to each of its own fans only [half the market] for $1 off the price of its car only. Suppose HotWheels again is the 'price leader' [it sets its price first and Matchbox then sets its price and then consumers buy one or the other car]. What is the highest price HotWheels can charge without being undercut by Matchbox? [HINT: again, in steps until it seems like each firm is happy with its pricing] What price will Matchbox then charge? What are the expected profits to each firm now? 4. Why do you think in this simplified game that rebates help sellers [HINT: how does it reduce pricing pressures?]