Price Signaling

Signalling Through Prices Lex Chemicals has developed a new plastic usable for insulation in new homes. Production costs for the new plastic are c = 6 per unit. Demand for the insulating material is given by Q = 16 -p, where p is the price set by Lex. Hence, per-period profits are given by (p - c) Q. Lex Chemicals will have 5 periods (including this one) of being the only producer of this particular type of insulation if no one else enters before the patent runs out and lower cost competitors enter and take the market. (For simplicity, assume no discounting of future periods.) Unfortunately for Lex, a competitor, Edge Plastics, has developed a competing product and is considering entering the market immediately after this period (and would then remain in the market for the remaining four periods); if Edge Plastics does not enter after the first period, then Edge Plastics will never enter the market (and so Lex will have a monopoly for the final four periods). The plastic developed by Edge Plastics has a production cost of 7. There is a fixed cost of 2 for Edge Plastics to enter the market. Edge, however, is uncertain of the cost structure of Lex Chemicals. Edge believes there is a 50%% chance that Lex has a marginal cost of production of 8, and a 50% chance that Lex has a marginal cost of production of 6. a) What are your per-period profits as a monopolist? What would your per-period profits as a monopolist be if you had the higher marginal cost of 8? (5 points) b) Will you attempt to signal to Edge that you are, in fact, the low cost producer? If so, what price will you set in the first period? (20 points)