Please explain what the Bertrand model is. How to set up this problem, capacity constraint, residual demand, optimal price

2.- Each of two firms, firms 1 and 2, has a cost function C(q) = % q; the demand function for the firms' output is Q =; - p, where Q is the total output. Firms compete in prices. That is, firms choose simultaneously what price they charge. Consumers will buy from the firm offering the lowest price. In case of tying, firms split equally the demand at the (common) price. The firm that charges the higher price sells nothing. (Bertrand model.) (a) Formally argue that there could be no equilibrium in prices other than p1 = p2 = i. (That is, consider all cases: p1> p2>.5, p1 >.5 > p2, .5> p1 > p2, p1 = p2>.5, and p1= p2