Suppose we have two types of consumers, each buying exactly one unit of the product a monopolist is selling so long as their consumer surplus is non-negative. If the consumer has a choice, she or he will buy the product that gives them the highest consumer surplus. the monopolist has estimated the indirect utility (C3) of each type of consumer as V1: p1+9'Z19 V2 = p2 + 5 -22 where z is the quality chosen by the monopolist i.e. vertical differentiation. The monopolist does not know each consumer's type. There are 151 type one consumers and 115 type two consumers. Finally suppose the marginal cost for all quantities is zero. The rm can choose any quality between 2 and 12 What is the lowest quality type 1 consumers will demand What is the lowest quality type 2 consumers will demand What is the participation constraint for type 'I What is the participation constraint for type 2 What is the Incentive compatibility constraint for type 'I What is the Incentive compatibility constraint for type 2 In terms of prices (p1,p2]and number of consumers. what is the profit function of the monopolist In terms of choice of quality (21.22)) and number of consumers. what is the prot function of the monopolist What is the optimal value for Z1 What is the optimal value for 12 What is the price charged to consumers of type 1 What is the price charged to consumers of type 2 What are the profits of the monopolist How much consumer surplus do consumers of type 1 have How much consumer surplus do consumers of type 1 have