Samantha's utility function is UK) = Y0.5. She tries to maximize her expected utility. She owns a car for business that she will have to replace if it is stolen. If her car is not stolen, her net income will be $122,500. If the car is stolen, her net income will be reduced by the car's replacement cost of $20,100. The probability that the car will be stolen is 20%. Use Excel to answer the following questions. a. Samantha learns that she can purchase an antitheft device that will lower the probability the car will be stolen to 10%. Would Samantha purchase the device at prices of $1,900, $2,000, or $2,100? b. Samantha can buy insurance that will pay the full replacement cost of the car if it is stolen. The price of this insurance is $4,090. For each of the prices of the anti-theft device given in part a, determine whether Samantha would buy insurance, buy the anti-theft device, or buy neither. Explain why she would not buy both. c. If Samantha buys insurance, how much would the insurance company gain in expected value if the anti- theft device was installed in Samantha's car? d. The insurance company is willing to offer a rebate to Samantha if she purchases the antitheft device. However, the company would need to incur a monitoring cost to insure that Samantha installs and retains the device (to avoid moral hazard). If the price of the device is $2,000, determine the largest monitoring cost the company would be willing to incur while still offering a large enough rebate to cover the cost of the device? How would your answer change if the price of the anti-theft device were $2,100?