Suppose that a certain agent has the following utility over her money u(M) = M (which...

  

Transcribed Image Text:

Suppose that a certain agent has the following utility over her money u(M) = M (which is the fourth root of M- just to be clear) Suppose that this agent has a yearly income of 20 000 USD. In any year, she has a 5% chance to be laid off from her job, in which case her yearly unemployment allowance will be 5 000 USD. a) What is going to be this agent's certainty equivalent? (2 marks) b) How much is this agent willing to pay for unemployment insurance, which fills the full gap between the agent's unemployment benefits and the wage she used to receive, for a period of one full year? (2 marks) c) Does the insurer who proposes this insurance necessarily have to be risk-neutral or risk-loving? If it can also be risk-averse, write down an example utility function and prove that with that particular utility function that you have come up with, it will insure the agent. (4 marks) 2) Consider the following estimated model: Y₁ = bo + b₁X₁i + b₂Xzi + ei a) Is the correlation between b, and b₂ important in this context? Why? Why not? Explain. (3 marks) b) Is the correlation between X₁ and X₂ important in this context? Why? Why not? Explain. (3 marks) c) Explain mathematically and using intuition, what consequences the correlation of b₁ and b₂ (or of X₁ and X₂ - whichever of the two pairs you think is important) has on your model estimates. (3 marks) Suppose that a certain agent has the following utility over her money u(M) = M (which is the fourth root of M- just to be clear) Suppose that this agent has a yearly income of 20 000 USD. In any year, she has a 5% chance to be laid off from her job, in which case her yearly unemployment allowance will be 5 000 USD. a) What is going to be this agent's certainty equivalent? (2 marks) b) How much is this agent willing to pay for unemployment insurance, which fills the full gap between the agent's unemployment benefits and the wage she used to receive, for a period of one full year? (2 marks) c) Does the insurer who proposes this insurance necessarily have to be risk-neutral or risk-loving? If it can also be risk-averse, write down an example utility function and prove that with that particular utility function that you have come up with, it will insure the agent. (4 marks) 2) Consider the following estimated model: Y₁ = bo + b₁X₁i + b₂Xzi + ei a) Is the correlation between b, and b₂ important in this context? Why? Why not? Explain. (3 marks) b) Is the correlation between X₁ and X₂ important in this context? Why? Why not? Explain. (3 marks) c) Explain mathematically and using intuition, what consequences the correlation of b₁ and b₂ (or of X₁ and X₂ - whichever of the two pairs you think is important) has on your model estimates. (3 marks)

Answer rating: 100% (QA)

Question One a The certainty equivalent of the agents income is the amount of money that would give her the same utility as her expected income If the agent has a 5 chance of being laid off and receiv... View the full answer