1. Assume a firm wants to hire a worker. The firm knows that the worker is risk-neutral but does not know the disutility of effort at work, e. This could be of two types e2 or 2e2, that is the worker of second type (Bad type) has a greater disutility of work than first type (Good type). The payoff function of worker can either be uG(w,e)=we2 or uB(w,e)=w2e2 where w is wage received by the worker. The proportion of Good types is q. Both workers have reservation utility level U=0. The firm values the effort of the worker as II(c) =ke, where k is sufficiently large so that the it wants to hire both agents, independent of their type. (a) (15 points) If the firm had full information, what will be the effort levels demanded by the firm and the wages paid? (b) (15 points) Now suppose that there is asymmetric information so that the firm does not know the workers' types and wants to find the separating contract. Explain which constraints will you expect to be bindingon-binding for each worker? Using this solve for the optimal separating contract and compare these to the full information contract