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States of the world

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From a public economics perspective, states of the world refer to the set of outcomes that are possible in an uncertain future.[1] This abstract term is commonly used in reference to consumption smoothing, or being able to consume consistently regardless of outcomes, which are uncertain and vary across these states of the world.[2]

States of the world vary in terms of probability of occurrence and the utility one can derive from each state. According to economic theory, individuals seek to equalize consumption across states of the world to maximize their utility, as proven by the expected utility model, which is the key driver for why individuals value insurance.[3]

Insurance Theory[edit]

In public economics, specifically insurance theory, the term states of the world is used to understand why individuals choose to purchase insurance. In an unknown world, with unknown and potentially costly outcomes, people seek to reduce the affects of potentially negative and costly outcomes on their lives.[4][5] The fundamental notion of insurance theory is that individuals will demand full insurance to fully smooth their consumption over time. Smoothing consumption over time, or, put differently, having consistent consumption regardless of a good or bad outcome, is a utility maximizing behavior.[6] Intuitively, while not having to pay an insurance premium and therefore consuming more in a good state of the world yields high utility, the substantial decrease in utility associated with little consumption in a bad state of the world without insurance, ultimately yields lower utility compared to consistently smooth consumption from year to year, which is obtained by full insurance. Put simply, consumption smoothing across states of the world maximizes utility, which is proven by the expected utility model discussed below.

Expected Utility Model[edit]

An expected utility model is the weighted sum of utilities across states of the world, where the weights are the probabilities of each state occurring. The expected utility model used to maximize an individual's utility across states of the world is:[7]

EU = (1 - q) x U(consumption with no adverse event) + q x U(consumption with adverse event)

EU = (1-q) x U(W-p) + q x U(W - p - d + b)

  • EU is expected utility
  • q is the probability of an adverse event (e.g. car crash, problematic medical condition)
  • W is an individual's income or wage
  • p is the price of the insurance premium
  • d is the damages or cost of the adverse event
  • b is the insurance pay out or benefit obtained

(1-q) x U(W-p) represents the expected utility obtained from the good state of the world, while q x U(W - p - d + b) represents the expected utility obtained from the bad state of the world, both given the probability of an adverse event either occurring or not. This model is applied to examine an individual's decision over how much insurance coverage to buy.

Assuming actuarially fair premiums are sold in the insurance market, the expected utility theory proves that individuals will want to fully insure themselves in order to maintain consistent levels of consumption across states of the world.

References[edit]

  1. Gruber, Jonathan (2016). Public Finance and Public Policy. Worth Publishers. p. 339. ISBN 978-1-4641-4333-5. Search this book on Amazon.com Logo.png
  2. Gruber, Jonathan (2016). Public Finance and Public Policy. Worth Publishers. p. 338. ISBN 978-1-4641-4333-5. Search this book on Amazon.com Logo.png
  3. Schoemaker, Paul (1980). Experiments on Decisions under Risk: The Expected Utility Hypothesis. Martinus Nijhoff Publishing. pp. 11–13. Search this book on Amazon.com Logo.png
  4. Liedtke, Patrick (2007). "What's Insurance to a Modern Economy" (PDF). The Geneva Papers. 32: 211–221.
  5. Rothschild, Michael (1970). "Increasing Risk: I. A Definition" (PDF). Journal of Economic Theory. 2: 225–243.
  6. Gruber, Jonathan (2016). Public Finance and Public Policy. Worth Publishers. p. 339. ISBN 978-1-4641-4333-5. Search this book on Amazon.com Logo.png
  7. Gruber, Jonathan (2016). Public Finance and Public Policy. Worth Publishers. pp. 339–340. ISBN 978-1-4641-4333-5. Search this book on Amazon.com Logo.png

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