Tariffs time-dynamics in competitive electricity retail markets with differentiated consumer reactions

Time-varying retail tariffs play a key role in activating demand-side flexibility in power systems.In retail markets, such tariffs compete with constant-in-time, or flat, tariffs. We investigate how the coexistence of these two tariff types influences their respective pricing levels and adoption rates among a diverse consumer base. To this end, we propose a multi-leader-followers model featuring a continuum of consumers characterized by their penalization of responding to price changes at the lower level and two competing retailers at the upper level. One retailer offers a time-varying tariff and the other a flat one. We derive the equilibria of the retail market under various assumptions about each retailer's responsiveness to the other's decisions, and compare the outcomes with those under a regulated monopolist retailer. We then provide a numerical application of the results based on the French electricity retail market. At equilibrium, the time-varying tariff's dynamics is dampened relative to the first-best real time price due to competitive pressure from the flat tariff and the distribution of consumers. When the time-varying tariff is known ex-ante, competition leads to lower or more uncertain adoption of the time-varying tariff compared to a monopolistic retailer offering both tariffs. When it is not, the monopolistic retailer option seems less attractive in terms of mobilized demand-side flexibility than retail competition, notably if consumers overestimate electricity prices on average. In that case, less flexible consumers bear the cost of imperfectly forecasting the tariff levels.