Economics In Action: Should You Buy Insurance?

Economics In Action Should You Buyinsurancealisa Tazhitdinovaeconom

Economics in Action: Should You Buy Insurance? Alisa Tazhitdinova Economics 10A, UCSB Many Types of Insurances Mandatory/Semi-mandatory: Car insurance Home insurance Earthquake insurance Health insurance Government-provided: Unemployment Insurance Disability Insurance Optional Retail products insurance Insurance Offered Every Step You Go... Should You Buy the Insurance? Our example: vacuum costs $70 and 2-year insurance plan $8. Economics tells you: compare expected utility with or without insurance With insurance: U(“Life†+ vacuum −$78) Without insurance pworksU(“Lifeâ€+vacuum−$70)+(1−pworks)U(“Lifeâ€âˆ’$70) Oh-oh: What is my U(·)...? Hmmm What is pworks....? Hmmm And what does your “Life" have to do with any of this? Let’s work through these questions step by step! Types of Preferences Remember, there are 3 types of individuals Risk-loving Risk-neutral Risk-averse What kind of person are you? Ask yourself Do you prefer $100 for sure or 50/50 chance of $0 or $200? Do you prefer the Econ 10A grade you earn, or a 50/50 gamble of grade you earn+1 letter up or -1 letter down? Types of Preferences If you... prefer the sure thing, you are probably risk-averse. (Most people are). prefer the gamble, then you are probably risk-loving! If you were indifferent, then increase the stakes! What if the stakes are $100,000,000 vs $0/$200,000,000? If you still are indifferent then you are probably are risk-neutral. If you are risk-loving, then you shouldn’t buy the insurance. What if you are risk-neutral or risk-averse? Risk-Neutral Decisions Simply assume that your utility U(x) = x. Then, you want to buy if: (“Life†+ vacuum −$78) −[pworks(“Lifeâ€+vacuum−$70)+(1−pworks)(“Lifeâ€âˆ’$70)] > 0 Simplifying, we find: (1 − pworks) · vacuum > $8 Much simpler and All about “fairness" Can simply further by remembering that vacuum costs $70. You shouldn’t spend $70 if the vacuum is worth less to you. As long as you don’t get attached to this particular vacuum (fond memories?), you can always replace it for $70.  buy insurance if you think the probability of vacuum breaking in 2 years is 8/70≈12% or more Result # 1 You cannot make a decision under uncertainty without having some idea of probabilities. How can you obtain such information? Brochures? Google? Consumer reports? Your own past experience Own experience is most important if outcomes occur frequently (e.g. cell phones) Own experience is less important if outcomes are infrequent (e.g. house flooding) Risk-Averse Decisions Fact 2: Risk-neutral logic is your upper bound: If a “risk-neutral You" would buy insurance, you should definitely buy insurance What if a “risk-neutral You" doesn’t want the insurance. Then the key to keep in mind is that you should account for “Life": So buy if U(“Life†+ vacuum −$78) −[pworksU(“Lifeâ€+vacuum−$70)+(1−pworks)U(“Lifeâ€âˆ’$70)] > 0 Why Should You Account For “Life"? Decision (1): Choose between: (A) sure gain of $2.40, and (B) 25% chance to win $10.00, a 75% chance to gain $0. Decision (2): Choose between: (C) A sure loss of $7.50, and (D) 75% chance to lose $10.00, a 25% chance to lose $0. Why Should You Account For “Life"? Decision (1): Choose between: (A) sure gain of $2.40, and (B) 25% chance to win $10.00, a 75% chance to gain $0. Decision (2): Choose between: (C) A sure loss of $7.50, and (D) 75% chance to lose $10.00, a 25% chance to lose $0. Most of you probably chose A+D However: Choice A+D implies that you have a 75% chance to lose $7.6 and 25% chance to gain $2.40 On the other hand: choice B+C would give you a 75% chance to lose $7.5 and 25% chance to gain $2.5 Result #2 Your decisions are not made in isolation! A lot of empirical evidence shows that people make decisions separately from each other This is not “rational" So what does this mean in case of our example with the vacuum? In the grand scheme of things: the vacuum purchase is negligible. (Relative to other decisions, relative to your wealth, etc!)  You should behave as a risk-neutral decision maker! Remember from Class Utility Function for a Risk Averse Individual consumption utility 7 $0 $1,000,000 U($0) U($1,000,000) $500,.5U($1,000,000)+0.5U($0) Is U($500,000) here? Or here? Remember from Class Utility Function for a Risk Neutral Individual consumption utility 9 $0 $1,000,000 U($0) U($1,000,000) $500,.5U($1,000,000)+0.5U($0) So When Should You Decide as a Risk-Averse Individual? When transactions can have profound effects on your life, your livelihood: Home insurance Earthquake insurance Car insurance (liability in an accident can easily exceed millions of $!) Upper tail of health insurance risk (cancer treatments are costly!) Same applies to other risky choices, e.g. where to go to school, who to marry, etc. But for small stakes... Such as electronics purchases insurance deductibles deductibles limits the out-of-pocket expenses  your loss is limited to the size of deductible  typically small stakes etc only buy insurance if it is a good deal for you!

Paper For Above instruction

Insurance plays a crucial role in managing financial risks and safeguarding individuals from sudden losses, particularly for significant assets or health-related expenses. Understanding when and why to purchase insurance depends heavily on individual risk preferences, the nature of the risk involved, and the stakes of specific decisions. The decision to buy insurance involves analyzing expected utility, which varies according to whether one is risk-averse, risk-neutral, or risk-loving, and assessing the probability of adverse events.

Risk preferences fundamentally influence insurance decisions. Risk-averse individuals prefer certainty and tend to favor purchasing insurance to eliminate uncertainty, especially when the potential loss can be devastating or existential. In contrast, risk-loving individuals are willing to accept risk and often forgo insurance coverage unless the premium is very low or the stakes are negligible. Risk-neutral individuals focus solely on the expected monetary outcomes and make decisions based on the expected utility, assuming their utility function is linear in wealth.

For example, when considering buying insurance for a vacuum costing $70 with an annual premium of $8, individuals evaluate whether the expected utility of insuring exceeds that of not insuring. If their utility function is linear, they compare the subjective probabilities of the vacuum breaking with the cost of replacement. If the perceived probability of the vacuum breaking exceeds roughly 12%, purchasing insurance becomes rational. This simple threshold depends on the individual’s subjective probability assessments, which can be informed by past experience, expert reports, or other sources.

Decision-making under uncertainty involves understanding and estimating probabilities. Accurate probability assessments are integral because they influence the utility calculations and the ultimate decision. Broader experiences, market reports, or personal history help individuals form these subjective probabilities. For frequent outcomes (e.g., health issues or recurring damages), personal experience is more reliable; for rare events, statistical data are essential. Empirical studies show that humans often deviate from purely rational decision-making, influenced by cognitive biases and heuristics, leading to inconsistent choices that may favor or oppose insurance purchase irrationally.

Risk-averse individuals tend to buy insurance for significant risks that could drastically affect their lives and livelihoods, such as home or health insurance. For small or purely financial risks, like electronics replacement, the calculus shifts—insurance becomes less attractive unless it is available at a fair premium or provides significant value relative to the stake. The deductible system in insurance policies limits out-of-pocket expenses, making insurance advantageous only when the potential loss exceeds the deductible or when the loss would be financially catastrophic.

Furthermore, the behavioral tendency to separate decisions about insurance from broader financial contexts results in over-insuring or under-insuring relative to the actual risk. Behavioral economics suggests that people often make decision errors, such as overweighting small probabilities or ignoring low-probability events entirely. Recognizing these biases, insurance companies tailor policies to appeal to various risk preferences, and individuals should critically evaluate their personal risk appetite, the accuracy of their probability estimates, and the stakes involved.

When considering insurance options, it is essential to weigh the benefits of risk reduction against the costs of premiums and the importance of the insured asset or health condition. For large, life-altering risks, purchasing insurance is often rational for risk-averse individuals. Conversely, for trivial risks or negligible stakes, the transaction costs and premiums may outweigh the benefits, leading rational individuals to decline coverage. Overall, prudent decision-making regarding insurance involves a nuanced analysis of personal risk preferences, the magnitude of potential losses, and the probabilistic assessment of adverse events.

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