The impacts of joint energy and output prices uncertainties in a mean-variance framework

In this paper, we analyze the impacts of joint energy and output prices uncertainties on the inputs demands in a mean-variance framework. We find that the concepts of elasticities and variance vulnerability play important roles in the comparative statics analysis. If the firms' preferences exhibit variance vulnerability, increasing the variance of energy price will necessarily cause the risk averse firm to decrease the demands for the non-risky inputs. Further, we investigate two special cases with only uncertain energy price and only uncertain output price. In the case with only uncertain energy price, we find that the uncertain energy price has no impact on the demands for the non-risky inputs. Besides, if the firms' preferences exhibit variance vulnerability, increasing the variance of energy price will surely cause the risk averse firm to decrease the demand for energy.