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Revealed preference approach to multiperson consumption behavior Laurens Cherchye MWC – 10/12/2009

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RP analysis of multi-person consumption 1.RP analysis of ‘rational’ individual behavior 2.RP analysis of ‘rational’ multi-person behavior 3.RP analysis and experiments

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RP analysis of multi-person consumption 1.RP analysis of ‘rational’ individual behavior: GARP

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4 RP analysis of individual consumption behavior Decision problem rational individual: maximize a (single) utility function over the individual budget set Data rationalizing utility function: A utility function such that each observed consumption bundle maximizes that function (under the respective budget constraint) when compared to all other observed consumption bundles Existence of such a function if and only if the (price- quantity) data is consistent with the Generalized Axiom of Revealed Preference (GARP)

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5 “Utility max. over budget set” iff “cost min. over better-than set” GARP: nonparametric reconstruction of ‘better- than-set’ from set of observations: Direct revealed preference relationship: bundle i is directly revealed preferred to bundle j if bundle j was attainable under prices and outlay for bundle i but not chosen RP analysis of individual consumption behavior

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6 Good 1 q1q1 q2q2 Good 2 q 1 R 0 q 2

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7 From direct revealed preference relationship to revealed preference relationship: preferences are transitive Revealed preference relationship: RP analysis of individual consumption behavior

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8 Good 1 q1q1 q2q2 Good 2 q 1 R q 3 q3q3

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9 Generalized Axiom of Revealed Preference: set of observations S satisfies GARP if and only if Test for data consistency with the model of the rational individual proceeds in two steps: (1) identify R 0 and R relations; and (2) check whether consumption bundles are cost minimizing over their revealed preferred sets RP analysis of individual consumption behavior

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10 Good 1 q1q1 q2q2 Good 2 Rejection of GARP: q 1 R q 2 and p’ 2 q 2 >p’ 2 q 1

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RP analysis of multi-person consumption 1.RP analysis of ‘rational’ individual behavior 2.RP analysis of ‘rational’ multi-person behavior: Collective consumption model of Chiappori (1988, 1992) RP characterization Extensions

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12 RP analysis of multi-person consumption Two group members (can be generalized for M members) Assumptions regarding the commodities Goods can be privately consumed, publicly or both

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13 RP analysis of multi-person consumption Assumptions regarding the individual preferences Preferences may depend on own private consumption and the public consumption

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14 RP analysis of multi-person consumption Assumptions regarding the bargaining/allocation process – Rational multi-person decisions are Pareto efficient – Or: for each q i :

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15 RP analysis of multi-person consumption Data rationalizing individual utility functions: Individual utility function such that each observed (aggregate group) consumption bundle is Pareto efficient (under the respective budget constraint) when compared to all other observed consumption bundles

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RP analysis of multi-person consumption RP characterization: – Collective rationality requires, for each individual member m, consistency with GARP condition in terms of – Or: collective rationality requires individual rationality Condition can be reformulated in integer programming (IP) terms, which allows for empirical testing

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RP analysis of multi-person consumption Extension 1: recovery – Recover individual (revealed) preference structure – Recover the ‘decision power’ of individual group members i.e. use the budget share allocated to (or ‘consumed by’) an individual as an indicator of the bargaining power of that individual Extension 2: model assumptions – Allow for externalities of privately consumed goods – ‘Noncooperative’ Nash equilibrium solution instead of ‘cooperative’ Pareto efficient solution

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RP analysis of multi-person consumption 1.RP analysis of ‘rational’ individual behavior 2.RP analysis of ‘rational’ multi-person behavior 3.RP analysis and experiments

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RP analysis and experiments RP methodology has been advocated as particularly appropriate for analyzing consumption data gathered through laboratory experiments (e.g.: Sippel, 1997; Harbaugh, Krause and Berry, 2001; Andreoni and Miller, 2002) Motivation: – RP analysis applies the theory directly to the data (‘let the data speak for themselves’) – Laboraty experiments avoid typical measurement problems associated with ‘real-life’ data

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RP analysis and experiments Analysis of multiperson groups – Study degree of group rationality in terms of different model specifications (e.g. cooperative versus noncooperative) – Study the decision/bargaining power of individual group members – Relate these results to group characteristics, individual characteristics and context factors that can be manipulated (experimentally) Analysis of individual behavior Cf. literature of ‘multiple selves’ (or individual as a group)

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1 Market Demand from Individual Demand. 2 In this section we want to think about market demand as the result of adding up demands from many individuals.

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