Optimal consumption decisions of family networks with similar felicity functions

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Optimal consumption decisions of family networks with similar felicity functions Alfredo Omar Palafox-Roca1 • Roma´n Rodrı´guez-Aguilar2 • Claudia Estrella Castillo-Ramı´rez2 Francisco Venegas-Martı´nez3



Ó Springer Science+Business Media, LLC, part of Springer Nature 2019

Abstract Family networks have increased at an accelerated pace through social networking through social networking services, online platforms, and social media clubs. This paper develops a model of an economy populated by networks of families with similar preferences (the same functional form of the felicity or utility function) but family members differ in their deep parameters (compulsion for consumption and risk tolerance), which, in turn, leads to some kind o heterogeneity among the families. In this context, the problem of felicity (utility) maximization of the average family in the network is solved. The optimal path of consumption is obtained for the average family and graphical comparative static exercises are performed. Finally, the economic welfare of the typical family in a network is calculated and comparative static experiments are carried out. This approach improves the understanding of the consumption decision making of families interacting in social networking services. Keywords Consumption decisions  Social networks  Networks of families  Average family JEL Classification C61  D91

1 Introduction The main concern of this paper is to study the inter-temporal decision problem of consumption of an average or typical family belonging to the network. It is assumed that the economy is populated by families whose members (parents and descendants) have the same functional form The authors appreciate and thank the two anonymous referees for all their valuable comments and suggestions. & Francisco Venegas-Martı´nez [email protected] Alfredo Omar Palafox-Roca [email protected] Roma´n Rodrı´guez-Aguilar [email protected] Claudia Estrella Castillo-Ramı´rez [email protected] 1

Universidad de las Ame´ricas Puebla, Cholula, Mexico

2

Universidad Panamericana, Mexico City, Mexico

3

Instituto Polite´cnico Nacional, Mexico City, Mexico

(bonding) of the felicity (utility) function but differ in their subjective discount rates and risk aversion coefficients (deep parameters). The heterogeneity in the family members comes from the subjective discount rate (anxiety or compulsion for present consumption) and the risk aversion coefficient (risk tolerance), which, in turn, leads to some kind o heterogeneity among families. More and more family networks are being formed through social networking services (public or private). To mention some of them, ‘‘FamilyLeaf’’, ‘‘FamilyWall’’, ‘‘eFamily.com’’, ‘‘JustFamily’’, ‘‘Rootsy’’, ‘‘Pinterest’’, etc. A relevant issue, from the economic point of view, regarding family networks is concerned with investigating about the inter-temporal decision making of consumption of the average (or typical) family belonging to the network. To do