Question: 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 \(\pi s\) in state 1. Prove that a risk-averse von Neumann-Morgenstern will over insure, fully insure, or under-insure according as the insurance is available at a price \(\pi \) lower than, equal to, or higher than the actuarially fair price