= Consider the following principal agent problem with adverse selection. A firm faces a worker who may be one of two types, with equal probabilities. The firm's profits from a type i worker are given by Ti ei Si, i 1, 2, where e; is the effort supplied by a type i worker and s; is the payment to a type i worker. The cost function of the more productive worker (type 1) is given by c₁ = el and the cost function of the less productive worker (type 2) is given by c₂ = 2e2. The utility function of a worker of type i is given by: ui = si' c; and his opportunity cost utility is u = 0. Find the solution to the firm's problem (assuming that effort is observable and contractible). 1/2 =

ENGR.ECONOMIC ANALYSIS
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Hi, questions are in the screenshot image. below is the advanced microeconomics course, lecture: Imperfect Information, I include the topics as if they do any help.

 

Lecture: Imperfect Information syllables

1 Asymmetric Information

1.1 Principal-Agent Problems with Hidden Actions

1.2 General Discussion

 

2 TheGeneral-Principal Agent

 

3 A Simple Example of a Principal-Agent Problem

3.1 CASE1: FULL INFORMATION

3.2 Case2- Unobserved Effort

 

4 Principal-Agent - Hidden Information

4.1 CaseI: Complete Information

4.2 Diagram

4.3 CaseII: HiddenInformation

 

5 Education as a Signal

5.1 Perfect Information

5.2 Imperfect Information

5.3 Equilibrium (perfect Bayesian, PBE)

 

6 The Market for Lemons

6.1 Warranties as a Signal for Quality

 

7 Static Price Competition with Asymmetric Information

7.1 Revelation of Information 

2
Consider the following principal agent problem with adverse selection. A firm faces
a worker who may be one of two types, with equal probabilities. The firm's profits
from a type i worker are given by π₁ = е₁ - Si, i = 1,2, where e; is the effort
2 ei
supplied by a type i worker and s; is the payment to a type i worker. The cost
function of the more productive worker (type 1) is given by c₁ = e² and the cost
function of the less productive worker (type 2) is given by C₂ = 2e2. The utility
function of a worker of type i is given by: u₁ = s¹/² — c; and his opportunity cost
utility is u = 0. Find the solution to the firm's problem (assuming that effort is
observable and contractible).
1/2
Si
0
Transcribed Image Text:2 Consider the following principal agent problem with adverse selection. A firm faces a worker who may be one of two types, with equal probabilities. The firm's profits from a type i worker are given by π₁ = е₁ - Si, i = 1,2, where e; is the effort 2 ei supplied by a type i worker and s; is the payment to a type i worker. The cost function of the more productive worker (type 1) is given by c₁ = e² and the cost function of the less productive worker (type 2) is given by C₂ = 2e2. The utility function of a worker of type i is given by: u₁ = s¹/² — c; and his opportunity cost utility is u = 0. Find the solution to the firm's problem (assuming that effort is observable and contractible). 1/2 Si 0
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Hi, where is P comes from? In the question, it says profit = ei - ci, how does pi*ei makes sense?

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