If you were a decision-maker at BMW, would you make side-impact airbags standard equipment? Use game theory to support your answer.

Apple and Samsung claim the duopoly over the premium part of the smartphone market. The two firms produce differentiated products, with constant marginal costs, engaging in price competition. The two demand functions are given by𝑞𝑞𝑎𝑎(𝑝𝑝𝑎𝑎,𝑝𝑝𝑠𝑠)=700−𝑝𝑝𝑎𝑎+𝑝𝑝𝑠𝑠𝑞𝑞𝑠𝑠(𝑝𝑝𝑎𝑎,𝑝𝑝𝑠𝑠)=700−𝑝𝑝𝑠𝑠+𝑝𝑝𝑎𝑎The two cost-functions are:𝐶𝐶𝑎𝑎=𝑐𝑐𝑎𝑎𝑞𝑞𝑎𝑎𝐶𝐶𝑠𝑠=𝑐𝑐𝑠𝑠𝑞𝑞𝑠𝑠a) Derive the best-response functions (BRF). (8 points)Hint: Profits in Bertrand competition depend on prices and costs only, e.g. for Apple: 𝜋𝜋𝑎𝑎(𝑝𝑝𝑎𝑎,𝑝𝑝𝑠𝑠)=𝑞𝑞𝑎𝑎(𝑝𝑝𝑎𝑎,𝑝𝑝𝑠𝑠)∗𝑝𝑝𝑎𝑎−𝑐𝑐𝑎𝑎𝑞𝑞𝑎𝑎(𝑝𝑝𝑎𝑎,𝑝𝑝𝑠𝑠)=(𝑝𝑝𝑎𝑎−𝑐𝑐𝑎𝑎)∗𝑞𝑞(𝑝𝑝𝑎𝑎,𝑝𝑝𝑠𝑠) and vice versa for Samsung. Then, profits are differentiated with respect to price, not quantity!

b) Determine equilibrium prices and profits, if the marginal costs for both firms are 𝑐𝑐𝑎𝑎=𝑐𝑐𝑠𝑠=300. (6 points)

c) Samsung and Apple are in an awkward relationship. They compete fiercely in the market for premium smartphones, yet Samsung is Apple’s most important supplier. You are part of the strategy team to the newly appointed CEO for Samsung Electronics, who has made it clear to you that it is his mission to humiliate Apple before the launch of the new Galaxy S9 later this year. Samsung is Apple’s sole supplier for the OLED screens used in the iPhone and you are considering to leverage your supplier power to implement a price hike for the screens in order to raise your rival’s costs (raising rival’s cost RCC strategy).As a result of raising your prices for the OLED components, you estimate that Apple’s marginal costs would increase to 𝑐𝑐𝑎𝑎=450, while your own marginal costs would remain unchanged (𝑐𝑐𝑠𝑠=300). What would happen to equilibrium prices and profits? (6 points)

7. Suppose Volkswagen (VW) and BMW must decide whether to make the latest breed of side-impact airbags standard equipment on all models. Side-impact airbags raise the price of each automobile by 1,000€. If both firms make side-impact airbags standard equipment, each company will earn profits of 250 million €. If neither company adopts the side-impact airbag technology, each company will earn 100 million € (due to lost sales to other automakers). If one company adopts the technology as standard equipment and the other does not, the adopting company will earn a profit of 300 million € and the other company will lose 150 million €. If you were a decision-maker at BMW, would you make side-impact airbags standard equipment? Use game theory to support your answer. (10 points)