Suppose there are two firms competing through prices in a market. Here the inverse demand function is given by P(Q) = 2042 4Q 2 where 1/) is a random variable that may take two values. With probability 0.4, we have 1/: = tph = 10 and with probability 0.6 we have 1/) = 1/1, = 5. Thus, market demand itself is a random variable that may take two values. On the other hand, firms are assumed to be symmetric, having the same cost function given by C (q) = 4q. Both firms discount future expected profits with the same discount factor 5 E (0, 1). a) (2 points) What is the monopolistic collusion price when demand is high (h)? b) (2 points) What is the monopolistic collusion price when demand is low (1)? c) (2 points) What is the monopolistic collusion profit when demand is high (h)? d) (2 points) What is the monopolistic collusion profit when demand is low (1)? e) (12 points) For which values of 6 can we ensure that firms will be able to sustain monopolistic collusion (7n, = 7'91)\"I and 71, = 711M) as a SPE