The goals of this paper are to present a two-stage programming model for the capacity expansion problem under uncertainty of demand and explore the impact of this uncertainty on cost. The model is a mixed integer nonlinear programming (MINLP) model with the consideration of uncertainty used to maximize the expected present value of utility profits over the planning horizon, under the constraints of rate of return and reserve margin regulation. The results reveal that the uncertainty harms the profit seriously. In this paper both microeconomics and mathematical programming are used to analyse the problem. We try to observe the economic behaviour of the utility with uncertainty involved. We also investigate the influence on the cost of uncertainty of each economic parameter.