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Advanced Microeconomics-Uncertainty Essay

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Below is an essay on "Advanced Microeconomics-Uncertainty" from Anti Essays, your source for research papers, essays, and term paper examples.

Expected Utility Theory

Decisions under risk Outcome of at least one of the options is uncertain (& the probabilities of the possible outcomes are known.) Keep £ 1 N
1 14M

Buy a lottery ticket

r HH H

£ 7 million

HH H H Y H r H 1 1HHH 14M H H

£0
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£0 N Rob a Bank
r H HH

£ 40 million
H H HH Y H r

0.2
H HH H 0.8 H H

Life in prison

Any decision under risk can be represented by choice among lotteries.

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The General Form of a lottery:

[(x1 , p1 ), (x2 , p2 ), (x3 , p3 ), . . . , (xn , pn )]
x1 , x2 , . . . xn can be any objects, n any number p1 + p2 + + pn = 1. e.g., £ 1 for sure: [(£ 1, 1)] Rob a bank: [(£ 40m, 0.2), (prison, 0.8)] How do individuals choose among lotteries?

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Expected Utility Theory (Hypothesis): Each individual has a utility function u ( ), Given P = [(x1 , p1 ), . . . , (xn , pn )], Q = [(y1 , q1 ), . . . , (ym , qm )] P Q () p1 u (x1 ) +

+ pn u (xn )

q1 u (y1 ) +

+ qm u (ym )

(EU of P (calculated using u ( ))

EU of Q)

u ( ): von Neumann-Morgenstern (VNM) utility function. “EU maximizers”: individuals who behave according to the EU hypothesis.

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Attitudes towards risks
[(w1 , p1 ), . . . , (wn , pn )], (w1 , . . . , wn : sums of money). Expected value (EV) = p1 w1 + p2 w2 + + pn wn .
An individual is risk-averse if he prefers getting the expected value of any lottery with certainty to getting the lottery itself; risk-loving if the opposite is true; risk-neutral if he is indi¤erent between any lottery and its expected value. Equivalent De…nition : An individual is risk-averse if he rejects all fair gambles. Fair gamble : a lottery whose EV is zero or a lottery whose price is equal to its EV. 1 e.g. [( 50, 1 )(50, 2 )] 2 [(0, 1 )(100, 1 )] and the price is 50 2 2 1 (EV of the lottery = 0 1 + 100 2 = 50). 2
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"Advanced Microeconomics-Uncertainty". Anti Essays. 17 Dec. 2018

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Advanced Microeconomics-Uncertainty. Anti Essays. Retrieved December 17, 2018, from the World Wide Web: https://www.antiessays.com/free-essays/Advanced-Microeconomics-Uncertainty-146966.html