RISK SHARING: MUTUAL INSURANCE AND CARTELS
In zero-sum ventures where one person's gain is another person's loss, there is no clear societal interest in what anyone's attitude towards risk is. However, in ventures that involve actually expending and creating resources or wealth, more total wea lth will be created if everyone is risk neutral, since the law of large numbers will apply and gains will balance losses to the GNP even if they do not balance for individuals.

Mutual insurance and cartels are two ways that individuals can band together to share the risks from many ventures. They allow risk averse individuals to achieve higher expected utility and society to achieve higher EMV than if the individuals each ac ted alone.

In the simplest form of mutual insurance, gainers cover the losses of losers and keep the remainder, while in the simplest form of cartel gaain and losses are pooled and shared equally.

EXAMPLE
U(x) = 1.1 -1.1 * exp(-0.0001499*(x+10000)

Individual Acting Alone
 
  P $  U($)   PxU  EU CME
I win 0.5 3500 0.9546 0.4773 0.8486 ($153)
I lose 0.5 -2500 0.7426 0.3713
0.8543 = utility of doing nothing > 0.8486 so do not take the venture

Note the EMV of the venture is $500 but its CME is negative

Two party mutual insurance

outcome P  $  U($)  PxU  EU CME
We both win 0.25 3500 0.9546 0.2387 0.8600 $157
I win,youlose 0.25 1000 0.8885 0.2221
I lose,youwin 0.25 0 0.8543 0.2136 
we both lose  0.25 -2500   0.7426 0.1857
($ column is payoff to me net of insurance claims paid or received)

Two party cartel

outcome  P  $ U($) PxU EU CME
We both win 0.25 3500 0.9546 0.2387 0.8603 $166
I win, you lose 0.25 500 0.8721 0.2180
I lose, you win 0.25 500 0.8721 0.2180
we both lose 0.25 -2500 0.7426 0.1857

($ column is payoff to me when the cartel is liquidated)

If the venture is independently available to n people, as individuals they will not take it, so the contribution to GNP is zero; but if they form insurance pools or cartels they will take the venture and the contribution to GNP will be very close to $5 00n if n is large.

Insurance example: Roger Bucks