UncertaintyThe expected utility function has some very convenient properties of analysing choice under uncertainty. Since to insure or not to insure is a choice we can apply it to an insurance problem. Indifference curves is used to measure utility or level of satisfaction as will be seen later.An individual’s certainty equivalent (CE) of a lottery is the amount of money that the individual is willing to pay to avoid the risk of the lottery i.e. to get the expected value (EV) instead of the lottery. For a risk averse individual CE lt. EV for all lotteries. An individual’s risk premium ( ∏) of a lottery is the maximum amount the individual is willing to pay to avoid the risk of a lottery, which is to get the expected value instead of the lottery.∏ = EV – CE. For the risk averse individual ∏ gt. 0 for all lottery.In the real world insurance is not actuarially fair. In the previous example it was assumed that the insurance did not charge anything to cover operating expenses or to allow for profit. In the cases that follow a loading factor is added to cover operating expenses and thus makes insurance actuarially unfair. This implies that ∏ gt. EV of the insurance benefit.The options available to the individual is a lower line with slope = p1/p2. At the initial point E is larger and therefore the line is lower. An indifference curve through the original point yields the diagram above (right).In diagram above (right) E (fixed loading) is larger this implies x = 0 with fixed loading and the optimal choice is no insurance in this case as the indifference curve lies above the actuarial line which is suggestive that it does provide the level of utility required by the individual.It is optimal for the consumer to choose F where w – (1 + m)px = w – L + x – px –mpx which implies x = 1 (representative of full insurance). A fair line F implies that an indifference curve is tangent to the line at F. see diagram (left)