Problem 5. Two firms are engaged in sequential differentiated Bertrand competition in the widget industry. Als Super-widget sells nationally branded widgets are considered to be higher quality. However, he must report and announce his price, pa, to corporate head- quarters and is unable to change it after the annoucement of his price. Bobs Ok-widget is unbranded and lower quality. As an independent owner, Bob is free to change his price, pb, and always waits to observe Als price before setting his own.

Demand for at Als Super-widgets is,

qa = 13 5/4pa + pb

Demand for widgets from Bobs Ok-widgets is, qb = 6 2pb + pa

Both firms face the same cost function. Marginal cost is constant at $1 per hundred widgets for both firms, and there are no fixed costs.

What is Bobs optimal strategy in a subgame-perfect Nash Equilibrium (SPNE)?

What is Als optimal strategy in a SPNE?

In the SPNE, what are the prices posted by each firm? What are the total profits of each firm?