This study employs duality theory to develop a theoretical model for small commercial and industrial (CIS) electricity usage. The CIS production function is posited such that output is a function of three variable inputs (electricity, natural gas, and labor) and one fixed input (capital). A profit function dual to this production function is specified using a normalized quadratic functional form. CIS profits are functionally dependent upon output price, an electricity input price, and natural gas and labor input prices for a fixed quantity of capital. The derived input-demand equation results from differentiating the profit function with respect to the price of electricity. The input-demand equation for electricity is dependent upon the own-price of electricity, the CIS output price, and input cross-prices. The model may be of use to utilities and regulators for the analysis of CIS electricity usage.

Small commercial and industrial (CIS) electricity demand is an important category of electric energy consumption. Historically, it has received substantially less research attention than residential usage, potentially due to data constraints. This study seeks to partially fill that gap in the energy economics literature by employing a fairly unique data set for the El Paso, Texas, USA metropolitan economy that includes private capital stock estimates from 1978 through 2017. The empirical model is specified using a recently developed analytical framework based on duality theory and a derived input demand function. Parameter estimation is completed using an Autoregressive-distributed lag model and an error correction model. In the long-run, CIS customers in El Paso respond only to own-price and the quantity of capital stock per capita. In the short-run, CIS customers adjust their electricity usage in response to changes in all variables except for the price of electricity. The most unexpected result from this analysis is a short-run income elasticity of −0.32, indicating that CIS electricity usage decreases with economic expansion in El Paso, Texas.