Consider a differentiated-products Bertrand market with three firms. The demand curves for Firms 1, 2, and 3 are below

Q₁= 300 - 10P₁+ 3P₂+ 2P3

Q₂= 300 - 8P₂+ 2P₁+ P3

Q₃= 50 - 3P₃+ P₁+ P₂

Firms 1 and 2 both have marginal costs of 10, and Firm 3 has a marginal cost of 15. First, calculate the equilibrium prices and quantities. Round off to two decimal points.

After consider, would the two lead federal antitrust agencies be likely to regard a merger between Firm 2 and Firm 3 as one that would raise serious competitive concerns?

Calculate the UPPIs for the merging parties, i.e., Firm 2 and Firm 3. Assume that cognizable efficiencies cause Firm 3's marginal cost to fall from 15 to 10. Do these UPPIs give cause for concern about potential harm to competition? Suppose that you do not know that these three firms have the linear demand curves shown above. You only know prices, margins, and market shares for each firm. Assume that they have the values that you calculated in parts (a) and (b) above. You assume (incorrectly) that these prices, margins, and shares were produced by a market with logit demand curves. How would this mistaken assumption affect the UPPI calculations?