Question

and 12 e, In the principal-agent model the agent's utility function is given by: U(w.e)-w only two effort levels are possible: e-0 (low) and e- 1 (high). The agent has the possibility to undertake work elsewhere and his utility level will then be U. If the principal can observe the agent's effort, what remuneration should he offer the agent so as to make sure that the latter will not leave to work elsewhere?

Answer 1

Principal needs to manage that the utility obtained to Agent from working elsewhere should be at least better than or equal to U=1

therefore wage offered by Principal would be

sqrt(w*)-e>=1

Now assumes that in worse scenario where e=0 agent should get utility higher than 1 therefore

w^0.5-e>=1

w^0.5-0>=1

therefore w=1

and as higher efforts are expected then

w^0.5-1>=1

w>=2

Hence to make sure that agent will not work elsewhere he must pay remuneration of w*=2