Uncertain Paternity, Power Utility, and Fractional Moments: The Case of Binomially Distributed Reproductive Success

In this paper, Newton's Theorem is used to derive a formula for the fractional moment of the binomial distribution. The formula is general enough to handle a continuous number of draws and thereby facilitates the analysis of representative agent models where discrete quantities are typically reflected by continuous variables. An application of the formula illustrates that it is easily implemented and can be quickly calculated using standard mathematical software.