Profit-maximizing input demand under rate-of-return regulation. Pathological substitution and output effects

Cost-minimizing and profit-maximizing input demand for the firm subject to rate-of-return regulation are examined. Unregulated cost and profit functions which are conditional on the rate of employment of the rate-base input are shown to be identically equal to the regulated cost and profit functions, evaluated at the regulated optimum. Shephard's lemma and Hotelling's lemma applied to the conditional cost and profit functions, evaluated at the regulated optimum, yield the regulated input demands. For both the profit-maximizing and cost-minimizing demands, own-price effects are not necessarily negative nor are the cross-price effects in general equal. Moreover, the profit-maximizing output effect is not necessarily negative. Various decompositions of input demand are explored to explain these conclusions.