Consider a market with an incumbent firm I and a new entrant F producing a homogenous product and competing in quantities. The incumbent has a technology with cost function C;(q) = 20g while the entrant produces with C'z(q) = 10g. The inverse market demand is given by P(q) = 240 q. Suppose the entrant is credit-constrained and had to repay an amount of D = 1600 at the end of the period. If the entrant is not able to cover this amount with his profits, the firm has to leave the marketplace. What is the minimum quantity ; that makes sure that the entrant is unable to repay the amount of D = 16007 A competition authority introduces the following leniency program. The first firm to come forward to reveal a cartel receives a fine reduction of 60% off the full fine F' > 0. All other convicted cartel members pay the full fine of F'. Now consider an industry in which two firms have formed a cartel. The cartel has stopped its activities. However, there is still a probability p [0, 1] that, in the absence of any leniency application, the competition authority discovers the cartel and imposes the fine F' on both firms. Suppose firms simul- taneously choose whether to report or not. If both firms apply at the same time, each is getting the fine reduction with probability 1/2. Give the highest value of p for which an equilibrium exists in which both firms do not self-report [maximum two decimals]|