Strategic Implications of Competing For Consumers with Time - PDF document

Strategic Implications of Competing For Consumers with Time Inconsistent Preferences ∗ Alexei Alexandrov † University of Rochester ‡ March 13, 2009 Abstract I examine oligopolistic competition for time inconsistent consumers. The two cases of in- vestment (health clubs) and leisure goods (credit cards) have different implications for strategy. For leisure goods the firms offer introductory rates at the fully rational consumer level, but consumers end up paying higher fixed rates later. In the limit, the markups go to zero. For investment goods there is a non-trivial cutoff of consumer naivete above which the market equi- librium is as if the consumers are rational. Below the cutoff the firms offer schedules such that consumers pay the membership fee, but do not attend. 1 Introduction Behavioral literature has grown considerably during the past ten years 1 . Yet, one of more interesting questions about not fully rational behavior – how does it affect firm competition and market structure – has not received enough attention. I take one of the least controversial assumptions about not fully rational consumer behavior, quasilinear hyperbolic discounting, and examine firms’ incentives and market outcomes in oligopolistic competition for time-inconsistent consumers. I examine two settings - goods with immediate benefits and later payments (credit cards) and goods with immediate payments and postponed benefits (gyms). The two applications that I am interested in the most in the first setting are the payday lending and the credit card industries 2 . In the second setting my work applies to personal-investment industries such as health clubs and education. ∗ Keywords: time inconsistent consumers, imperfect competition, product differentiation, credit cards. JEL Codes: D03, D14, G21, L13. † Thanks to be added. ‡ Assistant Professor of Economics and Management, email: Alexei.Alexandrov@Simon.Rochester.edu 1 See Camerer (2008) for a summary of the advances. See Ellison (2006) for the summary of the advances in Industrial Organization literature in particular. This paper fills Ellison’s ”Hyperbolic Discounting”-”Static Oligopoly” box with not trivial results. See Hendricks (2006) for a discussion. 2 According to a review of the payday lending industry by Stegman (2007), ”Most reforms of payday lending revolve around efforts to reduce serial borrowing”. 1

In the first setting (credit cards) I find that with nave consumers (the ones that do not realize they are time-inconsistent), firms offer an introductory rate which they would have offered to the fully rational discounting consumers, and a much higher fixed rate. The consumers sign up believing that they will pay off during the introductory period, but end up paying off the fixed rate in the last period. Increased competition makes the difference between the rates smaller, and in the limit it goes to zero - consumers pay marginal cost, despite being effectively locked up for the last period. If some of the consumers are sophisticated (realize that they are time inconsistent), than firms lower both rates, with the introductory rate approaching the fully rational non-discounting con- sumer rate, and the fixed rate approaching the introductory rate with nave consumers. In the limit, as all of the consumers are sophisticated, they pay the fixed rate which is the same as the fully rational discounting consumers would have paid. The second setting is the one where consumers have to pay before they get the benefit (for example gyms). Firms announce contracts, consumers first sign up for gym membership, then given the per-visit rate decide whether to visit the gym, and if they do visit, they get the benefit (health) the period after. The results are different in this case. If the consumers are sufficiently rational, the equilibrium prices are as in the fully rational equilibrium, with consumers signing up and attending in the next period – imperfect competition completely mitigates the effects of time-inconsistent behavior, even with just nave consumers in the market. However, if once the consumer gets to the attendance decision, and his discounted benefits of attendance are less than firms’ marginal cost, then the firms play a deceiving equilibrium - consumers pay the membership fee, but do not attend. Adding some sophisticated consumers to the mix does not alter the threshold above. However, below the threshold there is a region where a mixed equilibrium is played - some firms catering to sophisticated consumers and others catering to nave. The qualitative differences between the two regimes are due to the situation in the second period when time-inconsistency kicks in and the consumer chooses between either paying now or later (credit cards) or attending or not (gyms). In the case of credit cards, it is always best for the firms to push it to later – consumers are willing to pay a lot for that option (at that point in time), and the firms’ marginal costs are much smaller than the consumers’ willingness to pay for this postponement. In case of the gyms, if the firms entice the consumers not to attend, the firms do not have to pay the marginal cost, however they lose the value of the discounted benefits which they could have extracted from consumers, and sometimes the firms are better off making sure that the consumer actually attends. I assume that firms are symmetric, and that consumers have random i.i.d. preferences for each of the firms (Perloff and Salop (1985)). I assume that these random preferences are realized in the first period, and thus the consumers are homogenous by the time time-inconsistent behavior kicks in. This results in an unattractive feature of having either all consumers attend the gym or none of them. This is a trade-off for the generalized random preferences structure. In the appendix, I use the standard Salop’s circle (1979) to show that even when the consumers are not homogenous 2

at that point, the results still go through. An added complexity is an additional Salop-style kink in the demand function. Many consumers end up paying more when they sign up for low introductory offers as opposed to signing up for fixed rates. Also, the credit card industry is differentiated – consumers do not necessarily pick the credit card with the lowest interest rate, rather there is a whole list of options which might or might not be there: particular airline miles, particular discount, cash back on a particular set of purchases, a whole menu of fees for cash advances, international transactions, and so on 3 . Ausubel (1991) empirically examines profits of the credit card companies, and suggests that consumer irrationality might be one of the reasons for abnormally high profits. Payday lenders are product differentiated at least in location, adding frequent advertisements on top of that. Skiba and Tobacman (2008) structurally estimate the demand side of the payday industry, and conclude that the consumers are (at least partially) naive about their time preferences. The health club industry is well-covered in the literature, see DellaVigna and Malmendier (2006). In relation to the recent housing crisis, the same question arises for the negative amortization mortgages, with the infamous catch phrases like 999 dollars per month for a 300,000 dollar house. While this is not exactly the same as the introductory rate in credit cards, many consumers perceive it to be the same, and similar reasoning applies there 4 . The paper that is the closest to mine is Shui and Ausubel (2005), exaiming switching costs in the credit card industry, with presence of hyperbolic behavior, both theoretically and empirically, and finding that naive consumers like introductory offers because they underestimate what they will own, and sophisticated consumers like introductory offers because it provides them with a commitment device. There is a stream of literature in the optimal contract design with time- inconsistent consumers with perfectly competitive firms (some papers also look at monopolists and/or switching costs). DellaVigna and Malmendier (2004) examine optimal contract structure (for perfect competition) for investment goods (i.e. gyms) and for leisure goods (i.e. credit cards) and find that firms price the first kind below the marginal cost, and the latter above the marginal cost. I find that while there is an incentive to do this with imperfect competition, depending on the degree of competition and differentiation both of these results might not hold in oligopolistic competition. Heidhues and K¨ o szegi (2008b) are more interested in the contracts in the credit card industry in particular, and in the effects of consumer heterogeneity. Gottlieb (2008) introduces non-exclusive contracts, and explains consumer behavior in the industries like alcohol and tobacco, again under assumption of perfect competition. Incekara (2006) allows consumers to hold more than one (two) cards at the same time, with companies potentially competing on the interest rates, and finds that, despite perfect competition between the two firms, they might derive positive profits under some parameter values. Time inconsistent, in particular hyperbolic, behavior was heavily covered by economists lately, starting with the seminal Laibson (1997) article. One of the more recent empirical papers is 3 See Chapter 7 of Evans and Schmalensee (2000). 4 In this case, the interest rate is the same, but the minimum payment is only 999. If one thinks of it as consumers being too optimistic, then Manove and Padilla (1999) seems to apply more. 3