A risk averse agent has initial wealth w0 . With probability he will suffer a loss that will reduce his wealth by w0 . Otherwise his wealth will stay the same. The individual can insure against the loss. Denote by the premium per dollar of insurance coverage. Insurance is supplied by firms in a competitive insurance market. If a claim of x arises, the company must incur and administrative cost of cx with c>0 to investigate the claim. Will the agent fully insure against the loss? Show your work.