The utility function of a consumer is u(m)=ln (m). The value of m may be 3 or 9, with 0.2 and 0.8 being possibilities. If she takes no effort to lessen risk, the chance of m=3 increases to 0.4. e=0.5 is the cost of effort. 1) Will the customer make an effort to decrease risk if insurance is not available? 2) Assume that an insurance firm can observe customers' efforts and charge break-even premium rates based on their efforts. Will she put out the effort? 3) Assume the insurance company is unable to observe customers' efforts. As a result, the insurance firm will charge two different break-even premium rates, but only those paying the 0.4 rate will be able to completely insure. Determine a partial insurance limit F for 0.2 rate-payers that encourages them to make the effort.