Modul IV

• Risk-averse insured with utility function u and initial wealth W

• Insured can either reduce loss size L(e) or probability of loss p(e) by effort e

• Wealth in no-loss state: YI=W-e, and in the loss state: YII:W-e-L

The insured maximizes expected utility by choosing effort e, given by: max E(u(Y))=(1-p(e))u(W-e)+p(e)u(W-e-L). Effort is optimal if it sufficiently reduces the loss probability.

Moral hazard occurs when insured individuals reduce their effort to prevent losses because the insurance shields them from the full financial consequences of the loss.

• ex-ante moral hazard: Behavior before the loss event, reducing the probability of a claim (e.g., risk mitigation efforts)

• ex-post moral hazard: Behavior after the loss, influencing claim size (e.g., overstating damages)

Full insurance optimizes risk allocation but leads to reduced incentives for loss prevention (moral hazard). Partial insurance balances these by maintaining some incentives for loss prevention.

• RAND Health Insurance Experiment: Found that more cost-sharing reduced medical visits but did not impact life expectancy (except for the poorest).

• Oregon Medicaid Experiment: Increasing insurance led to more medical visits, but both necessary and unnecessary care increased.