optimal dynamic marketing mix policies for frequently purchased products and services versus consumer durable goods a generalized analytic approach abstract this paper deals with the qualitative characterization of optimal pricing and advertising policies together with the optimal ratio of the advertising elasticity of demand to its price elasticity over time the problem is studied for frequently purchased products and services fps as well as consumer durable goods cdg in both monopolistic and duopolistic markets demand dynamics cost learning and discounting of future profits are taken into consideration in addition both the open loop and feedback methodologies are pursued to characterize and compare the derived optimal policies the paper uses an analytical approach to characterize the optimal dynamic policies in a general setting as is mathematically tractable followed by the analysis of more specific models to gain additional managerial insights while maintaining a certain degree of generality optimal fps marketing mix policies are shown to be different from their cdg counterparts for both monopolistic and duopolistic markets while the ratio of advertising elasticity to price elasticity appears to have been governed by similar set of rules for fps and cdg the direction of change of such ratio over time looks different from each other managerial implications and directions for future research are also discussed

can self control explain avoiding free money evidence from interest free student loans abstract this paper uses insights from behavioral economics to explain a particularly surprising borrowing phenomenon one in six undergraduate students offered interest free loans turns them down models of impulse control predict that students may optimally reject subsidized loans to avoid excessive consumption during school using the national postsecondary student aid study we investigate students take up decisions and identify a group of students for whom the loans create an especially tempting liquidity increase students who would receive the loan in cash are significantly more likely to turn it down suggesting that consumers choose to limit their liquidity in economically meaningful situations

rationalizable conjectural equilibrium between nash and rationalizability abstract static equilibria can be viewed as steady states of recurring play of a game such steady states in which players do not perfectly observe the actions of others need not be nash equilibria this paper suggests a static solution concept rationalizable conjectural equilibrium that corresponds to such steady states to present it the basic model of a normal form game is enriched by specifying the signals that players get about others actions the solution is a profile of actions such that each player s action is optimal given that it is common knowledge that all players maximize utility given their signals journal of economic literature classification number c72

weak separability and the estimation of elasticities in multistage demand systems the necessary conditions for multistage budgeting to be at least approximately justified are reviewed and the plausibility of these assumptions i e weak separability and low variability of price indices with utility level are discussed using no further assumptions simple relationships between expenditure and price elasticities in different budgeting levels are derived these results are applied to a three stage model for swedish food consumption and it is shown that the assumptions are not inappropriate restricting the analysis to the last stage of a multistage budgeting process is also shown to lead to considerable errors which could well have policy consequences

the hyperbolic consumption model calibration simulation and empirical evaluation ur preferences for the long run tend to conflict with our short run behavior when planning for the long run we intend to meet our deadlines exercise regularly and eat healthfully but in the short run we have little interest in revising manuscripts jogging on the stairmaster and skipping the chocolate souffleala mode delay of gratification is a nice long term goal but instant gratification is disconcertingly tempting this gap between long run intentions and short run actions is apparent across a wide range of behaviors including saving choices a 1997 survey found that 76 percent of respondents believe they should be saving more for retirement looking only at respondents who believed they were at an age where you should be seriously saving already the survey found that 55 percent reported being behind in their savings and only 6 percent reported being ahead farkas and johnson 1997 the report on the survey concluded t he gaps between people s atti tudes intentions and behavior are troubling and threaten increased insecurity and dissatisfaction for people when they retire americans are simply not doing what logic and their own reasoning suggests they should be doing a 1993 luntz webber merrill lynch survey found similar answers when baby boomers were asked what percentage of your annual household income do you think you should save for retirement and what percentage of your annual

dynamic advertising and pricing in an oligopology a nash equilibrium approach a general dynamic oligopolistic price advertising model is formulated and open loop nash solutions are derived as a main result a generalisation of the well known dorfman steiner theorem to heterogenous oligopoly markets is presented furthermore a detailed discussion of long run equilibrium solutions is given for an important special case of the general model formulation it is shown that the optimal advertising policies are constant over time and constitute degenerated feedback solutions

joint stochastic dynamic pricing and advertising with time dependent demand abstract this paper examines the sale of a finite number of items in a class of stochastic dynamic pricing and advertising models with time dependent demand elasticities we prove structural properties of the optimal expected profits with respect to time inventory level price impact advertising impact and different model parameters such as discount rate marginal unit costs and holding costs we find that the value of an additional item opportunity costs is decreasing in the unit costs the discount rate the holding cost rate and the number of items left to sell we also derive structural properties of optimal joint pricing and advertising strategies this way we obtain general qualitative insights in the complex interplay and the mutual dependence of optimal pricing and advertising decisions among other properties we show that a higher advertising impact leads to higher optimal prices and lower advertising rates which in turn implies a lower speed of sale the results obtained help practitioners to respond to changes in market conditions by adjusting price and advertising accordingly our results allow speeding up numerical computations of decisions as the set of possible actions can be reduced significantly our analysis implies general results for pure pricing as well as pure advertising models with time dependent demand elasticities

paying not to go to the gym how do consumers choose from a menu of contracts we analyze a novel dataset from three u s health clubs with information on both the contractual choice and the day to day attendance decisions of 7 752 members over three years the observed consumer behavior is difficult to reconcile with standard preferences and beliefs first members who choose a contract with a flat monthly fee of over 70 attend on average 4 3 times per month they pay a price per expected visit of more than 17 even though they could pay 10 per visit using a 10 visit pass on average these users forgo savings of 600 during their membership second consumers who choose a monthly contract are 17 percent more likely to stay enrolled beyond one year than users committing for a year this is surprising because monthly members pay higher fees for the option to cancel each month we also document cancellation delays and attendance expectations among other findings leading explanations for our findings are overconfidence about future self control or about future efficiency overconfident agents overestimate attendance as well as the cancellation probability of automatically renewed contracts our results suggest that making inferences from observed contract choice under the rational expectation hypothesis can lead to biases in the estimation of consumer preferences

rational addiction with learning and regret we present a theory of rational behavior in which individuals maximize a set of stable preferences over goods with unknown addictive power the theory is based on three fundamental postulates that consumption of the addictive good is not equally harmful to all that individuals possess subjective beliefs concerning this harm and that beliefs are optimally undated with information gained through consumption although individual actions are optimal and dynamically consistent addicts regret their past consumption decisions and regret their initial assessment of the potential harm of the good addict prone individuals who believe it could not happen to them are most likely to be drawn into a harmful addiction

optimal pricing and advertising in a durable good duopoly abstract this paper analyzes dynamic advertising and pricing policies in a durable good duopoly the proposed infinite horizon model while general enough to capture dynamic price and advertising interactions in a competitive setting also permits closed form solutions we use differential game theory to analyze two different demand specifications linear demand and isoelastic demand for symmetric and asymmetric competitors we find that the optimal price is constant and does not vary with cumulative sales while the optimal advertising is decreasing with cumulative sales comparative statics for the results are presented

stochastic dynamic pricing and advertising in isoelastic oligopoly models abstract in this paper we analyze stochastic dynamic pricing and advertising differential games in special oligopoly markets with constant price and advertising elasticity we consider the sale of perishable as well as durable goods and include adoption effects in the demand based on a unique stochastic feedback nash equilibrium we derive closed form solution formulas of the value functions and the optimal feedback policies of all competing firms efficient simulation techniques are used to evaluate optimally controlled sales processes over time this way the evolution of optimal controls as well as the firms profit distributions are analyzed moreover we are able to compare feedback solutions of the stochastic model with its deterministic counterpart we show that the market power of the competing firms is exactly the same as in the deterministic version of the model further we discover two fundamental effects that determine the relation between both models first the volatility in demand results in a decline of expected profits compared to the deterministic model second we find that saturation effects in demand have an opposite character we show that the second effect can be strong enough to either exactly balance or even overcompensate the first one as a result we are able to identify cases in which feedback solutions of the deterministic model provide useful approximations of solutions of the stochastic model

addiction and cue triggered decision processes we propose a model of addiction based on three premises 1 use among addicts is frequently a mistake 2 experience sensitizes an individual to environmental cues that trigger mistaken usage 3 addicts understand and manage their susceptibilities we argue that these premises find support in evidence from psychology neuroscience and clinical practice the model is tractable and generates a plausible mapping between behavior and the characteristics of the user substance and environment it accounts for a number of important patterns associated with addiction gives rise to a clear welfare standard and has novel implications for policy

dynamic duopolistic competition with sticky prices the authors study duopolistic competition in a homogeneous good through time under the assumption that its current desirability is an exponentially weighted function of accumulated past consumption this implies that the current price of the good does not decline by as much to accommodate any given level of current consumption our an alysis is conducted in terms of a differential game it is found that the equilibrium price corresponding to the open loop nash equilibriu m strategies approaches the static cournot equilibrium price while th e equilibrium price corresponding to the closed loop nash equilibrium strategies which are subgame perfect approaches a price below it copyright 1987 by the econometric society

measuring self control problems we develop a survey instrument to measure self control problems in a sample of highly educated adults this measure relates in the manner that theory predicts to liquid wealth accumulation and personality measures yet while self control problems are typically seen as resulting in overconsumption and low wealth we identify a significant group who underconsume and thereby accumulate high levels of wealth in addition self control problems are smaller in scale for older than for younger respondents those who put money aside in retirement accounts may be delaying access to a point at which self control problems are no longer important jel d12 d14

commitment and self control abstract the literature on self control problems has typically concentrated on immediate temptations this paper studies a gul and pesendorfer temptation and self control econometrica 69 2001 1403 1435 self control and the theory of consumption econometrica 72 2004 119 158 style model in which decision makers are affected by temptations that lie in the future while temptation is commonly understood to give rise to a demand for commitment it is shown that temptation by future consumption can induce its absence the model also exhibits procrastination provides an alternative to projection bias as an explanation for some experimental results and can simultaneously account for myopic and hyperopic behavior the evidence on preference reversals supports temptation by future consumption and suggests that it may not be restricted to short time horizons

the revealed preference theory of changing tastes we analyse preferences over finite decision problems in order to model decision makers with changing tastes we provide conditions on these preferences that identify the strotz model of consistent planning building on an example given by peleg and yaari 1973 we show that for problems with infinitely many choices strotz s representation of preferences may not be well defined for that case we propose a well defined approximation which is empirically indistinguishable from the strotz preference that is being approximated

learning self control this article examines how a decision maker who is only partially aware of his temptations learns about them over time in facing temptations individuals use their experience to forecast future self control problems and choose the appropriate level of commitment i demonstrate that rational learning can be perpetually partial and need not result in full sophistication the main result of this article characterizes necessary and sufficient conditions for learning to converge to full sophistication i apply this result to a consumption savings environment in which a decision maker is tempted by present bias and establish a learning theoretic justification for assuming sophistication in this setting an individual who finds himself continuously repudiating his past plans may learn to distrust his future behavior and may do something about it strotz 1955

payoff information and self confirming equilibrium abstract in a self confirming equilibrium each player correctly forecasts the actions that opponents will take along the equilibrium path but may be mistaken about the way that opponents would respond to deviations this paper develops a refinement of self confirming equilibrium in which players use information about opponents payoffs in forming beliefs about the way that opponents play off of the equilibrium path we show that this concept is robust to payoff uncertainty we also discuss its relationship to other concepts and show that it is closely related to assuming almost common certainty of payoffs in an epistemic model with independent beliefs journal of economic literature classification numbers c72 d84

consumption savings decisions with quasi geometric discounting we study the consumption savings problem of an infinitely lived rational consumer who has time inconsistent preferences in the form of quasi geometric discounting the consumer operates a weakly concave production function and must simply divide current resources into current consumption and savings there is no uncertainty a solution to the consumer s problem is a subgame perfect equilibrium of a dynamic game between the consumer s successive selves we show that this game has a continuum of equilibria in stationary markov strategies not only is the stationary point of the consumer s asset holdings indeterminate but each stationary point has a continuum of dynamic paths converging to it the savings policy rules underlying these dynamic paths are step functions

dynamic inconsistency and self control a planner doer interpretation we show that gul and pesendorfer s econometrica 69 2001 1403 representation result for preferences with temptation and self control can be reexpressed in terms of a costly intrapersonal conflict between a planner and doer as in thaler and shefrin j political econ 89 1981 392 and psychologists standard view of self control problems

choice and procrastination author s o donoghue ted rabin matthew abstract recent models of procrastination due to self control problems assume that a procrastinator considers just one option and is unaware of her self control problems we develop a model where a person chooses from a menu of options and is partially aware of her self control problems this menu model replicates earlier results and generates new ones a person might forego completing an attractive option because she plans to complete a more attractive but never to be completed option hence providing a non procrastinator additional options can induce procrastination and a person may procrastinate worse pursuing important goals than unimportant ones

the red and the black mental accounting of savings and debt in the standard economic account of consumer behavior the cost of a purchase takes the form of a reduction in future utility when expenditures that otherwise could have been made are forgone the reality of consumer hedonics is different when people make purchases they often experience an immediate pain of paying which can undermine the pleasure derived from consumption the ticking of the taxi meter for example reduces one s pleasure from the ride we propose a double entry mental accounting theory that describes the nature of these reciprocal interactions between the pleasure of consumption and the pain of paying and draws out their implications for consumer behavior and hedonics a central assumption of the model which we call prospective accounting is that consumption that has already been paid for can be enjoyed as if it were free and that the pain associated with payments made prior to consumption but not after is buffered by thoughts of the benefits that the payments will finance another important concept is coupling which refers to the degree to which consumption calls to mind thoughts of payment and vice versa some financing methods such as credit cards tend to weaken coupling whereas others such as cash payment produce tight coupling our model makes a variety of predictions that are at variance with economic formulations contrary to the standard prediction that people will finance purchases to minimize the present value of payments our model predicts strong debt aversion that they should prefer to prepay for consumption or to get paid for work after it is performed such pay before sequences confer hedonic benefits because consumption can be enjoyed without thinking about the need to pay for it in the future likewise when paying beforehand the pain of paying is mitigated by thoughts of future consumption benefits contrary to the economic prediction that consumers should prefer to pay at the margin for what they consume our model predicts that consumers will find it less painful to pay for and hence will prefer flat rate pricing schemes such as unlimited internet access at a fixed monthly price even if it involves paying more for the same usage other predictions concern spending patterns with cash charge or credit cards and preferences for the earmarking of purchases we test these predictions in a series of surveys and in a conjoint like analysis that pitted our double entry mental accounting model against a standard discounting formulation and another benchmark that did not incorporate hedonic interactions between consumption and payments our model provides a better fit of the data for 60 of the subjects the discounting formulation provides a better fit for only 29 of the subjects even when allowing for positive and negative discount rates the pain of paying we argue plays an important role in consumer self regulation but is hedonically costly from a hedonic perspective the ideal situation is one in which payments are tightly coupled to consumption so that paying evokes thoughts about the benefits being financed but consumption is decoupled from payments so that consumption does not evoke thoughts about payment from an efficiency perspective however it is important for consumers to be aware of what they are paying for consumption this creates a tension between hedonic efficiency and what we call decision efficiency various institutional arrangements such as financing of public parks through taxes or usage fees play into this tradeoff a producer developing a pricing structure for their product or service should be aware of these two conflicting objectives and should try to devise a structure that reconciles them

ramsey meets laibson in the neoclassical growth model the neoclassical growth model is modified to include a variable rate of time preference with no commitment ability and log utility the equilibrium features a constant effective rate of time preference and is observationally equivalent to the standard model the extended framework yields testable linkages between the extent of commitment ability and the rates of saving and growth the model also has welfare implications including the optimal design of institutions that facilitate household commitments steady state results are obtained for general concave utility functions and some properties of the transitional dynamics are characterized for isoelastic utility

competitive dynamic advertising a modification of the case game abstract in this paper we consider a modified version of the advertising differential game of case 1979 we derive non cooperative nash equilibria for open loop controls as well as for feedback strategies we consider finite and infinite planning horizons the feedback equilibrium is shown to be robust against stochastic disturbances of the state equation

tying odysseus to the mast evidence from a commitment savings product in the philippines we designed a commitment savings product for a philippine bank and implemented it using a randomized control methodology the savings product was intended for individuals who want to commit now to restrict access to their savings and who were sophisticated enough to engage in such a mechanism we conducted a baseline survey on 1777 existing or former clients of a bank one month later we offered the commitment product to a randomly chosen subset of 710 clients 202 28 4 percent accepted the offer and opened the account in the baseline survey we asked hypothetical time discounting questions women who exhibited a lower discount rate for future relative to current trade offs and hence potentially have a preference for commitment were indeed significantly more likely to open the commitment savings account after twelve months average savings balances increased by 81 percentage points for those clients assigned to the treatment group relative to those assigned to the control group we conclude that the savings response represents a lasting change in savings and not merely a short term response to a new product

strategic ignorance as a self disciplining device we analyse the decision of an agent with time inconsistent preferences to consume a good that exerts an externality on future welfare the extent of the externality is initially unknown but may be learned via a costless sampling procedure we show that when the agent cannot commit to future consumption and learning decisions incomplete learning may occur on a markov perfect equilibrium path of the resulting intra personal game in such a case each agent s incarnation stops learning for some values of the posterior distribution of beliefs and acts under self restricted information this conduct is interpreted as strategic ignorance all equilibria featuring this property strictly pareto dominate the complete learning equilibrium for any posterior distribution of beliefs

behavioral equilibrium in economies with adverse selection i propose a new solution concept behavioral equilibrium to study environments with players who are naive in the sense that they fail to account for the informational content of other players actions a behavioral equilibrium requires that i players have no incentives to deviate given their beliefs about the consequences of deviating ii these beliefs are consistent with the information obtained from the actual equilibrium play of all players and iii when processing this information naive players fail to account for the correlation between other players actions and their own payouncertainty i apply the framework to certain adverse selection settings and show that contrary to the received literature the adverse selection problem is exacerbated when naive players fail to account for selection more generally the main distinguishing feature of the framework is that in equilibrium beliefs about both fundamentals and strategies are jointly restricted consequently whether a bias may arise or not is determined endogenously in equilibrium jel c72 d82 a large literature presents evidence that psychological and cognitive biases aect people s be havior this evidence raises some questions what are the eects of these biases and can they persist at all in economic settings where people strategically interact with each other and have the opportunity to learn from their experience 1 in this paper i introduce a game theoretic equilibrium framework to study these questions in the context of a particular bias people s failure to take into account the informational content of other people s actions i apply the framework to a class of games that arises naturally in adverse selection settings and then show that the adverse selection

marketing and investment policies of duopolists in a growing industry abstract this article deals with the analysis of the investment price and advertising policies of two firms competing over time the problem is stated as a differential game where each firm tries to maximize its net present value the open loop equilibrium of the game defines the policies to be implemented by the competitors over the horizon the results show how the combination of competition and growth has a relevant influence on the policies of the firms