Nonlinear pricing, biased consumers, and regulatory policy

Journal of Economics https://doi.org/10.1007/s00712-022-00812-9 Nonlinear pricing, biased consumers, and regulatory policy Phuong Ho1 Received: 21 March 2021 / Accepted: 13 November 2022 © The Author(s) 2022 Abstract Recent empirical analyses show consumers in electricity and water markets respond to average price rather than marginal price, calling for information provision policies that help correct the consumers’ bias. This paper characterizes the regulated tariff if the regulator is informed about the average-price response of consumers. I find the regulated tariff for biased consumers promotes equity gains by featuring quantity premia and providing access to utility consumption for a larger population than in the world of rational consumers. The world of biased consumers can also yield higher total welfare. These results bring up the opportunity costs of the information provision programs that help consumers correct the bias. Keywords Average-price bias · Nonlinear pricing · Price discrimination · Quantity premia · Ramsey pricing JEL Classification D42 · D82 · D91 · L51 · L98 1 Introduction Although standard economic theory assumes firms and consumers optimize with marginal prices, recent empirical analyses show it is not the case for electricity consumption (Ito 2014; Shaffer 2020) and water consumption (Ito 2013). They find that given the nonlinearity of the price schedules of electricity and water, consumers respond to average price rather than marginal price.1 Their findings suggest the suboptimizing behavior would make nonlinear pricing be inefficient and generate welfare loss, compared to the case of rational consumers. However, the comparison assumed rational consumers and biased consumers face the same price schedule. 1 De Bartolome (1995); Rees-Jones and Taubinsky (2020) find by experiment that individuals use average tax rates rather than marginal rates when making marginal economic decisions. * Phuong Ho 1 SNF – Centre for Applied Research at NHH, Helleveien 30, 5045 Bergen, Norway 13 Vol.:(0123456789) P. Ho This paper formally examines the welfare comparison between the world of rational consumers and the world of average-price-biased consumers. The key point is I take into account the adjustment in the nonlinear price schedules. What is the efficient price schedule if the regulator were informed about the biased responses of consumers and considered them when designing the price schedule? Would it be better to live in the biased world? This paper characterizes the optimal regulated price schedule (tariff) that maximizes total surplus subject to a specified net revenue requirement for the utility and that consumers respond to average price rather than marginal price.2 I find the optimal regulated tariff features quantity premia even under the consumers’ preferences that lead the tariff for rational consumers to have quantity discounts. This quantity premia feature suggests the regulated tariff for biased consumers supports the equity and conservation goals of increasing block tariffs that a regulator often uses to discourage excessive use of utilities (e.g. electricity and water) and protect low-income consumers from high prices, by charging higher price rates for high consumption. I also find the regulated tariff in the world of biased consumers provides utility consumption for a larger population than in the world of rational consumers. The population that has access to the utility consumption in the world of biased consumers equals the first-best population in which the utility is priced at marginal cost, whereas consumption in the world of rational consumers is restricted to consumer types that are above the first-best marginal type. Besides those features that favor the equity and distribution goal, the regulated tariff in the world of biased consumers may offer higher total welfare and consumers’ surplus than in the world of rational consumers. For example, with constant unit costs, quadratic utility preference, and uniformly distributed consumer type, I show the regulated tariffs in the two worlds provide the same total welfare. In the case of Pareto distribution of the consumer type, the total welfare in the world of biased consumers is higher.3 An intuitive reason is the population that can consume the utility is larger in the world of biased consumers than in the world of rational consumers. This paper is related to a growing literature of behavioral economics and bounded rationality in industrial organization that examines how firms react to and in some cases exploit consumers’ suboptimal responses. These studies consider types of bias apart from average-price bias, such as loss aversion, present bias, overconfidence, or failure to choose the best price due to suboptimal search. Readers can refer to a comprehensive survey by DellaVigna (2009). For example, Courty and Hao (2000), Eliaz and Spiegler (2008), and Grubb (2009) study monopoly screening problems when consumers are overconfident. Heidhues and Kőszegi (2008) and Spiegler (2012) show loss aversion may create kinks in demand curves, which can lead to price rigidities. Carbajal and Ely (2016) and Hahn et al. (2018) characterize price 2 Given the fixed required net revenue, the total-surplus-maximizing tariff also maximizes consumers’ surplus. 3 If the type represents income, the Pareto distribution illustrates the “80–20 law": 80 percent of income in the society is owned by 20 percent of the population. 13 Nonlinear pricing, biased consumers, and regulatory policy discrimination when a monopolist faces consumers with loss aversion and state-contingent reference points. My model is built on the literature of nonlinear pricing in Mussa and Rosen (1978) and Maskin and Riley (1984) and regulated tariff (Ramsey pricing) in Brown and Sibley (1986) and Wilson (1989). I depart from the literature by assuming consumers respond to average price instead of marginal price. The paper is closely related to three earlier articles.4 Sobel (1984) and Esponda and Pouzo (2016) aim to rationalize average-price bias. Sobel (1984) explains average-price response results from consumers thinking they face a linear price schedule with a constant unit rate. Esponda and Pouzo (2016) introduce a Berk–Nash equilibrium in which agents choose optimal strategies given beliefs and the beliefs put probability one on the misspecified set of subjective distributions over consequences that are closet to the true distribution; so, average-price response is a result of a Berk-Nash equilibrium. Instead of rationalizing average-price bias, I take the bias as an exogenous feature of consumer decision making and examine the implications. Martimort and Stole (2020) take a similar approach and study monopoly pricing that maximizes net revenue of a monopolist and the implications on the firm’s profit.5 On the other hand, I focus on regulatory pricing that maximizes total social welfare subject to a specified net r (...truncated)