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Kala is operating an ATV on the beach. The level of care he chooses influences whether there is an accident in which his ATV harms a sunbather. Kala's cost of exerting care of x is given by wx. That is, Kala has a constant marginal cost of exerting care which is w. The probability of an accident is given by p(x), which is decreasing in x, and the harm imposed on a sunbather in the event of an accident is given by A.
(a) Suppose there is an accident, and it turns out that w < -p 0 (x)A. What does the "Hand Rule imply about whether Kala was negligent? Explain.
(b) Disregard the information in part (a) above. Suppose that A = 1000 and w = 100. Suppose that x must be a whole number between 0 and 5, and the corresponding value of p(x) is given in the table below. For which values of x would the "Hand Rule" imply that Kala is not negligent?
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