Suppose there are 10 identical firms, each of which have a Total Cost function TC = 16 + q2, where q is the quantity of output. Thus, the marginal cost of production is MC = 2q. There are 40 consumers. Let α be the proportion informed consumers who know the prices of all 10 firms. 0 < α < 1. Therefore, 1 - α is the proportion of uniformed consumers. Each consumer wants to buy 1 unit of the good sold by these firms as long as the price is not greater than $10. Suppose all firms are charging a price P = MC = ATC.
a) Suppose α = ¼. Draw the demand curve that one of these firms faces. Make sure to be accurate, including specific quantities for the prices of P = 10, P = 8, and P < 8. On the same graph, draw the firm's ATC curve. Your graph should go up to 15 units of output, but you only need to draw the ATC curve up to 6 units of output.
b) Is all firms charging P = MC = ATC an equilibrium in prices when α = 1/4
c) Find the value of α that would lead to a two-price equilibrium.