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3. (40 points) Risk-neutral rms simultaneously offer menus of employ- ment contracts to a population of agents. An employment contract is a pair (110,8), where w is the agent's wage and e is the agent's observable and contractible effort. An agent's utility when accepting employment contract (11), e) is w 62/6, where 6 is the agent's type. There are two types in the population, 6' = 1 and 6 = 2, and the proportion of 0 = 2 types is A. Both types of agents have an outside option with utility 0. The output of an agent with type 6 is 6 independently of her effort. (a) (20 points) Show that there is no COmpetitive equilibrium that involves any pooling of the different types of agents. Explain the intuition. (b) (20 points) Identify the A for which there is no perfectly separat- ing COmpetitive equilibrium. Explain the intuition