Explain the Significance of the St. Petersburg Paradox, Common Ratio Effect and Simultaneous Gambling and Insurance, and Their Implications for Expected Utility Theory

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Explain the significance of the St Petersburg Paradox, the Common Ratio effect, and simultaneous gambling and insurance, and their implications for Expected Utility theory The analysis of choice under risk departs from the standard theory of consumer choice, because we have to introduce uncertainty to the model. Uncertainty arises because the consequence of at least one option is not known to the decision maker (Gravelle and Rees 2004), but the probabilities of all possible outcomes are known. Examples of uncertain outcomes are represented by gambling and insurance. An individual who buys insurance is accepting a certain loss of a small sum, the insurance premium, in preference to a combination of a small chance of a much larger loss and a large chance of no loss. He is choosing certainty over uncertainty, and is risk averse. An individual who purchases a lottery ticket is subjecting himself to a large chance of losing a small amount (£1 for lottery ticket) and a small chance of winning a large amount, rather than keeping his £1 to avoid risk all together (Friedman and Savage. 1948). Any decision under risk can be represented by a choice among lotteries. The general form of a lottery is [(x1,p1),(x2,p2),(x3,p3),…,(xn,pn)] where xi are objects, usually units of wealth that the individual will get if state i occurs, and pi the probability that state i occurs. The probabilities sum up to 1. For example, you could have £1 for sure, or if you rob a bank you have a 20% chance of getting £40m or an 80% chance of getting caught, and receiving nothing. This lottery would take the form [£1,1] and [(£40m, 0.2), (£0, 0.8)]. The St Petersburg Paradox was first proposed by Bernoulli in 1778. He used a theoretical lottery game to highlight that by taking into account the expected value as the only decision criterion, the decision maker will be misguided into making an

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