A risk adverse agent

In state of nature 1 the individual has income w, whereas in state of nature 2 the individual's income is y < w. The probabilities that these states will occur are (1 - p) and p, respectively. The individual can purchase insurance before the state of nature is known; an increase in income of s in state 2 can be purchased by a reduction in income of ∏s in state 1. Prove that a risk-averse von Neumann-Morgenstern individual will over-insure, fully-insure, or under-insure according as the insurance is available at a price ∏ lower than, equal to, or higher than the actuarially fair price.