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 u(w. e) = w-e² or us (w. e) = w-2e² 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(e) = ke, where k is sufficiently large so that the it wants to hire both agents, independent of their type. (a) If the firm had full information, what will be the effort levels demanded by the firm and the wages paid? (b) 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 binding/non-binding for each worker? Using this solve for the optimal separating contract and compare these to the full information contract

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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Answer with the theoretical content of advanced microeconomics.such as :1. Hidden information: Adverse selection, screening, insurance markets, credit
rationing.
2. Signalling: Spence model, intuitive criterion, capital structure, cheap talk.
3. Hidden information: Moral hazard and contracting, credit rationing.
4. Institutional Design: Optimal income tax, auctions, contracting.
5. Voting, Gibbard-Satterthwaite Theorem, VCG mechanism.
6. Theory of social choice.

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 u(w.e) = w-e²
or u (w. e) = w-2e² 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(e) = ke, where k is sufficiently large so that the it wants to hire both
agents, independent of their type.
(a)
If the firm had full information, what will be the effort levels demanded
by the firm and the wages paid?
(b)
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 binding/non-binding for each worker? Using this
solve for the optimal separating contract and compare these to the full information
contract.
Transcribed Image Text: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 u(w.e) = w-e² or u (w. e) = w-2e² 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(e) = ke, where k is sufficiently large so that the it wants to hire both agents, independent of their type. (a) If the firm had full information, what will be the effort levels demanded by the firm and the wages paid? (b) 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 binding/non-binding for each worker? Using this solve for the optimal separating contract and compare these to the full information contract.
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