Question

Advertisement as a signal of quality: Assume that there are n potential customers. Each of them is willing to by a maximum of 2 units of a product (not necessarily at the same time). The willingness to pay for the first unit is v while for the second unit it is v 0.4, where v is 0.4 for a low quality product and 0.9 for a high quality product. The producer knows the quality of the product, however each customer can only get to know this quality after he/she buys the first unit. The probability that v is high a priori amounts to 50%. In any case, the average cost of producing the good is c 〈 1 and it is independent of its quality. a) The unit price of the product is 1. The producer considers whether to launch an advertisement campaign. This campaign does not impact v. The costs of the campaign do not depend on the quality of the product. Find the cost interval within which this campaign is profitable only for the producer selling the high quality product (separating equilibrium). b) The market for advertisements does not exist, however the producer is free to choose the price of the product, potentially differentiating between the first and second unit bought by the given customer: pi and p2, respectively. The producer must, however, announce these prices a priori. Additionally, assume that the following inequality holds: 0.8 <c <0.9. Find the optimal price levels dependent on the quality of the product such that p'-p11, p2"zpt (separating equilibrium), assuming that there is anything sold at all.

Answer 1

There are 3 types of equilibrium. POOLING EQUILIBRIUM,SEPARATING EQUILIBRIUM,PARTIALLY SEPARATING/POOLING EQUILIBRIUM.Separating equilibrium is an equilibrium in which all types of sender send different types of messages.In a partially separating/pooling equilibrium is an equilibrium in which some types of sender send the same messages while others send some other messages.