Optimal Regulatory Lag under Price Cap Regulation

We present an model of monopoly regulation in which the probability of cost being low rather than high depends on the firm's effort. The regulator chooses price and regulatory lag (i.e., the length of time until the next price review) to maximize welfare subject to an expected break-even constraint for the firm. Between reviews the firm has a finite horizon cost minimization problem. We characterize its solution and the resulting dilemmas for the regulator. Starting from a high cost state, longer lag postpones the date at which price might be reduced, but lowers price in the interim and improves the chance that cost will be low at the next review. These pros and cons are reversed starting from a low cost state. With inelastic demand infinite lags are optimal. If costs are unresponsive to efforts, then minimal lags are best. Numerical simulations indicate the importance of the demand elasticity and effort responsiveness more generally. Finally, the desirability of non-constant prices between reviews is analyzed.