Problem 4. (42 points, each part is weighted equally) Two firms are engaged in sequential differentiated Bertrand competition in the widget industry. Al's Super- widget sell's nationally branded widgets are considered to be higher quality. However, he must report his price, Pa, to corporate headquarters and is unable to change it during the day. Bob's Ok-widget is unbranded and lower quality. As an independent owner, Bob is free to change his price, pa, and always waits to observe Al's price before setting his own. Demand for at Al's Super-widgets (in hundreds of widgets) is, 5 da = 13 - -Pa + Pb Demand for widgets from Bob's Ok-widgets (in hundreds of widgets) is, 9b = 6 - 2pb + Pa Both firms face the same cost function gasoline. Marginal cost is constant at $1 per hundred widgets for both firms, and there are no fixed costs. Prices are quoted in hundreds of widgets. 1. Write down the optimization problem of Bob's Ok-widgets. 2. What is Bob's optimal strategy in a subgame-perfect Nash Equilibrium (SPNE)? 3. Write down the optimization problem of Al's Super-widgets