Consider a consumer who consumes one physical good but faces uncertainty. With prob- ability 7 this consumer will have wj units of the good, but with probability (1 - 7) the consumer will have w2 units instead. We assume that w is much bigger than w2. For sim- plicity of reference, we will refer to the event that the endowment is high as "state I" and to the event that the endowment turns out to be low as "state 2". The consumer can change actual consumption away from the endowment amount by purchasing insurance. Let / denote the amount of insurance contracts the consumer pur- chases. Each insurance contract will cost p units of consumption paid in the case that the endowment is wj (i.e. paid only in "state 1" ). It will pay out 1 unit of consumption in the case that the endowment is w2 (i.e. in "state 2"). Therefore, if the consumer buys / units of insurance, the actual consumption of the consumer becomes c, = w1 - pl with probability 7, and c2 = w2 + / with probability (1 - #). The consumer is a strictly risk averse expected utility maximizer. The expected utility from consuming c units with probability 0, u"(.)