Problem 1. Insurance Consider a risk-avers agent who owns an asset worth 100 USD

Question

Problem 1. Insurance Consider a risk-avers agent who owns an asset worth 100 USD. The agent can choose one of two actions: being cautious a1 or being negligent (a0). The agent’s payoff from having wealth w and taking action a is given by u(w_1,a_0 )=x and u(w_1,a_1 )=x-3. There are two possible states of nature: either damage occurs, in which case the asset is lost, or no damage occur, in which case nothing happens to the asset. The probability that damage occurs equals 50% if the agent’s negligent, and 25% if he’s cautious. a.) What is the optimal action for the agent?

Explanation / Answer

Expected payoff if agent is negligent

Probability that Asset gets damanged = 0.5

Payoff = 0

Probability that Asset does not get damanged = 0.5

Payoff = 1000.5 = 10

Expected Payoff = 0.5*0 + 0.5*10 = 5

Expected payoff if agent is cautious

Probability that Asset gets damanged = 0.25

Payoff = -3

Probability that Asset does not get damanged = 0.75

Payoff = 1000.5 -3 = 7

Expected Payoff = 0.25*(-3) + 0.75*7 = 4.5

It is better for the agent to be negligent as the expected payoff is higher in that case

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