Constructing the CES Production Function Based on the Discrete Weibull Distribution

Abstract. This paper considers a probabilistic approach to obtaining the CES production function. It consists in calculating the mean and median of the Leontief function (the quantity of output) as a random variable depending on the capacities of production factors, i.e., the ratios of the factors to their per-unit values. The type of the cumulative distribution function of the minimum from a set of independent random variables is substantiated. Explicit expressions are derived for the mean and median of the quantity of output as CES functions when the factor capacities have (continuous) Weibull distributions. Discretely distributed production factors are considered using the example of a geometric law. An attempt is made to derive the CES function when the factor capacities have discrete Weibull distributions. The difficulties arising in the analytical use of the mean of the Leontief function are described.

Keywords: production function, CES production function, probabilistic approach, Weibull distribution, discrete Weibull distribution, geometric distribution, mean, median.