Consider a firm that is a sole producer of Soybean Helper. The manufacturer's cost of producing soybean helper is $3 per patty. Soybean Helper is used to make soy burgers. There are two outlets for soy burgers, and at these outlets the demand curves for Soybean Helper are p(q ) = 100 q1 and p(q ) = 80 0.5 q2 .

a. If the Soybean Helper producer can charge the two soy burger outlets different prices, what are the optimal prices and profits in each market, and what is the total profit?

b. Now suppose that the Soybean Helper firm cannot charge market-specific prices but can engage in second degree price discrimination. Specifically, using the two prices calculated in part (a), suppose Soybean Helper charges the higher price for quantities below a threshold level and the lower price for quantities above the threshold. What would be the optimal threshold and what would be the company's profits in each market, and what is the total profit?