Abstract
Based on insights from psychology, we argue that individual well-being has two incommensurable dimensions, gratification and flourishing. We provide a model in which the individual’s vitality is tunneled to different goals/practices. Gratification is represented by discharge of flow, while flourishing corresponds to generated power. The two dimensions are correlated in a way that depends on the characteristics of the available goals/practices, and their relationship need not be monotonic. We also extend the model to social interaction, prove existence of an equilibrium and show the possibility of ‘flourishing traps’.
Acknowledgements
We would like to thank Steffen Huck, Carmen Marchiori, Herakles Polemarchakis, and two anonymous referees for very useful comments.
Appendix
Proof of Proposition 1
In the case of two pipes we have
and
The flow through pipe k is
The hydroelectric power produced by turbine k is
The overall electric power produced by the turbines – representing the individual’s flourishing – is
Recalling (footnote 6) that
the ‘attractiveness’
of goal/practice k is monotonically increasing in its value/meaningfulness (i. e. in the corresponding pipe’s cross-section area) Ak.
The partial derivative of P2 w.r.t. α2 is
so the more attractive is goal/practice 2 deemed, the higher the power produced by turbine 2. At the same time, the partial derivative of P1 w.r.t. α2 is
so the more attractive is goal/practice 2, the lower the power produced by turbine 1. Together, the partial derivative of overall flourishing,
Since all variables are non-negative,
only when
and this is a minimum point of flourishing (overall turbines’ power) because
Reverting back to the original variables
ᅛᅛᅛᅛᅛᅛᅛᅛ ■
Proof of Proposition 2
When multiplying
will also increase by the factor β – as long as
However, once
thus decreasing by the factor β > 1 when
Proof of Social Equilibrium Existence
For each individual n and goal/practice k,
where
and her vitality flow is
where
From the definitions in the main text we also have:
so that
and
Notice, by (10) that
(since
The flourishing of individual n in goal/practice k is in turn defined by:
which is therefore bounded from above by
and below by 0.
From (6) it hence follows that
and below by 0.
Then for the compact convex domain
the continuous map
defined according to (11), (10) and (6) by
has a fixed point by Brouwer’s fixed-point theorem, which constitutes a social equilibrium.ᅛᅛᅛ ■
Proof of Proposition 3 (Existence of Flourishing Traps)
Assume a social network with n = 1, 2 symmetric individuals, where
are constant, i. e. the individuals do not influence each other’s vital flow
and where the functions
are the fourth root. Assume, for simplicity, that
Given the symmetry between the two individuals in the network, when looking for a symmetric social equilibrium we have to solve
or
which has two solutions:
with the corresponding flourishing levels
There exist values of Z1, A1, Z2 and d2 for which [10] we have
In such a social network the first social equilibrium with values
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
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Articles in the same Issue
- Research Articles
- Optimal Forestry Contract with Interdependent Costs
- Bi and Branching Strict Nash Networks in Two-way Flow Models: A Generalized Sufficient Condition
- Pay-What-You-Want in Competition
- Two Rationales for Insufficient Entry
- Students’ Social Origins and Targeted Grading
- Pricing, Signalling, and Sorting with Frictions
- On the Economic Value of Signals
- The Core in Bertrand Oligopoly TU-Games with Transferable Technologies
- Reasoning About ‘When’ Instead of ‘What’: Collusive Equilibria with Stochastic Timing in Repeated Oligopoly
- Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims
- Costly Rewards and Punishments
- Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies
- Strategic Activism in an Uncertain World
- On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy
- Optimal Incentives Under Gift Exchange
- Public Good Indices for Games with Several Levels of Approval
- Vagueness of Language: Indeterminacy under Two-Dimensional State-Uncertainty
- Winners and Losers of Universal Health Insurance: A Macroeconomic Analysis
- Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy
- Flourishing as Productive Tension: Theory and Model
- Notes
- A Note on Reference-Dependent Choice with Threshold Representation
- Regular Equilibria and Negative Welfare Implications in Delegation Games
- Unbundling Production with Decreasing Average Costs
- A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution
- Decision Making and Games with Vector Outcomes
- Capital Concentration and Wage Inequality
- Annuity Markets and Capital Accumulation