choice under uncertainty

expected value

sum of possible values Xi, weighted by their probabilities

E(X) = Σ pr(Xi) ⋅ Xi

cons of expected value measurement when making decisions

dosnt take into account people may have different attitudes toward risk

expected utility theory

E(U) = P1 U(X1) + P2 U(X2) + .... + Pn U(Xn)

utility must be cardinal

diminishing marginal utility

marginal utility falls as consumer consumes more

diminishing marginal utility of income

implies risk aversion, utility function is concave to origin, as income rises the marginal utility falls as wealthier value £1 less

what is the link between risk and inequality aversion

'the veil of ignorance' : if we were unsure about what life we would be born into then risk aversion would mean we would want a fair life for all

Rawlsian social welfare function

maximises welfare of the poorest person

types of risk preferences

1) fair gamble : expected value 0

2) risk averse : due to diminishing marginal utility of wealth

3) risk seeking : due to increase marginal utility of wealth

4) risk neutral : cte marginal utility of wealth

measures of risk aversion

coefficient of absolute risk aversion

coefficient of relative risk aversion

coefficient of absolute risk aversion

r(W) = U''(W) / U'(W)

for a risk averse U''(W)<0 so r(W)>0

coefficient of relative risk aversion

rr(W) = Wr(W) = -W ⋅ U''(W)/U'(W)

responses to risk

informal risk pooling

formal insurance

how does informal risk pooling work

law of large numbers, sharing risk amount more people means if the event happens independently, mean of X will approach population mean as sample size grows