Prudence and preference for flexibility gain

We investigate the properties of the premium that a risk-averse individual is willing to pay to benefit from flexibility before an irreversible decision is made. Her decision concerns the quantity of some specific good to be acquired, knowing that the unit cost of the acquisition is either the mean value of a uniform distribution, or it is drawn from that distribution. The benefit of the latter technology, which we call a “flexibility gain”, is that after choosing the technology and before choosing the quantity, the individual learns the true unit cost. A richer individual values the flexibility more than a poorer individual if and only if her coefficient of absolute prudence is larger than a coefficient that is directly proportional to the rate at which the monetary benefit decreases when the state of nature drawn from the uniform distribution is above its mean value. We apply this result to an investment timing problem and show that the optimal waiting period increases with the ratio between the two coefficients. We next show that when the decision consists of exerting a preventive effort, the individual is more likely to prefer flexibility when she is more risk averse, but less likely to prefer flexibility when she is more prudent. Finally, we show how the identified link between the flexibility gain and degree of prudence determines the preference over specific lotteries. Moreover, when the individual is risk-neutral, the flexibility gain increases with the mean value of the distribution if and only if the marginal benefit function with respect to the unit cost is convex. Consequently, the individual has a stronger preference for an interval with lower mean, or lower mean and higher spread, when the marginal benefit function is concave rather than convex.