DC2-4

No insurance Outcome Probability Income Utility No Loss 0.8 122500 350 Loss 0.2 102400 320 Expected Utility 344 Price of anti-theft device 1900 Outcome Probability Income Utility No Loss 0.9 120600 347.28 Loss 0.1 100500 317.02 Expected Utility 344.25 Price of anti-theft device 2000 Outcome Probability Income Utility No Loss 0.9 120500 347.13109 Loss 0.1 100400 316.85959 Expected Utility 344.10394 Price of anti-theft device 2100 Outcome Probability Income Utility No Loss 0.9 120400 346.98703 Loss 0.1 100300 316.70175 Expected Utility 343.95850 Samantha’s utility function is U ( Y ) = Y 0.5 . She tries to maximize her expected utility. She owns a car that she will have to replace if it is stolen. If her car is not stolen, her net income will be $122,500. stolen, her net income will be reduced by the car’s replacement cost of $20,100. The probability th 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 stolen to 10%. Would Samantha purchase the device at prices of $1,900, $2,000, or $2,100? 1. If the anti-theft device costs $1900, would Sa it or not? (i.e., Compare the expected utilities w without the device.) Yes, she would buy the device. 2. If the anti-theft device costs $2000, would Sa it or not? (i.e., Compare the expected utilities w without the device.) Yes, she would buy the device. 3. If the anti-theft device costs $2100, would Sa it or not? (i.e., Compare the expected utilities w without the device.) No, she would not buy the device. 1

device of $1900 (or, $2000 and/or $2100) to lower the probability of her car being stolen?) She would not buy both. If she bought both insurance and the anti-theft device, her income would de more because of higher costs. This will then lead to a decrease in expected utility. 2

Insurance Company's income, payout and profit No anti-theft device installed Outcome Probability Income Payout Profit No Loss 0.8 4090 0 4090 Loss 0.2 4090 20100 -16010 Expected Value of profit 70 Anti-theft device installed Outcome Probability Income Payout Profit No Loss 0.9 4090 0 4090 Loss 0.1 4090 20100 -16010 Expected value of profit 2080 Insurance company's gain from anti-theft device 2010 Samantha’s utility function is U ( Y ) = Y 0.5 . She tries to maximize her expected utility. She owns a car that she will have to replace if it is stolen. If her car is not stolen, her net income will be $122,500. stolen, her net income will be reduced by the car’s replacement cost of $20,100. The probability th will be stolen is 20%. Use Excel to answer the following questions. c. If Samantha buys insurance, how much would the insurance company gain in expected value if the device was installed in Samantha’s car? The company would gain $2,010 . 1

for business If the car is at the car vice. etains the g cost the device? e., Is the what is the e would be 2