Imperfect Substitutability in Standard and Reference-Dependence Models

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Imperfect substitutability and the endowment effect

Hanemann (1991) points out in his footnote 25 that Kahneman and Tversky‟s (1979) loss aversion, observed from some reference point, differs from the standard disparity. Indeed, in the Hicksian framework, preferences over consumption bundles are independent of initial endowments. In reference to the gain and loss perspective, Thaler (1980) proposed the term endowment effect. When an agent is endowed with a good, her reference point changes, she shifts her position on the map, and the shape of her indifference curve is altered. If we adapt the standard framework to the loss aversion idea, a gain or a loss in q can be written q1 q0 and q1 q0 , with 0 . Assume agent‟s utility is affected by variations of the environmental quality level q . In this case, her utility u 0 v p , q 0 , y, which now involves a single indifference curve, changes either to u in a case of a gain or to u in case of a loss:
u v p , q 0 , y [14a]
u v p , q 0 , y [14b]
Bateman et al. (1997) define two additional measures, identified with some reference point. Regarding the first measure, the question is what additional amount of private consumption is as preferable as an increase in the environmental quality. This is the equivalent gain, equal to WTA. Regarding the second measure, the question is what loss of private consumption would be just as preferable as a decrease in the environmental quality. This is the equivalent loss, equal to WTP. When the agent is endowed, fixing a gain and a loss in [3a] and [3b] or [4a] and [4b] gives the following relationships: C or compensating gain is the maximum amount she would pay to secure the gain; E or equivalent gain is the minimum amount she would accept to sacrifice the gain;E or equivalent loss is the maximum amount she would give up to avoid the loss;C or compensating loss is the minimum amount she would accept to tolerate the loss. The summary is recapitulated in Table 1.2.

Imperfect substitutability and loss aversion

In their 1991 article, Tversky and Kahneman propose the behavioral reference-dependent theory as an alternative to the Hicksian theory of preferences. Outcomes are now valued using a value (utility) function where agents have preferences over goods relative to some reference levelrx , rq seen as the status quo. According to them, (i) all is perceived as a gain or a loss; (ii) losses are weighted more heavily than gains or agents are loss averse; and (iii) the marginal value of gains or losses exhibits diminishing sensitivity. They assume that preferences are transitive, continuous and nondecreasing (but not convex).
If rx , rq stands for the reference points for consumingx, q, the utility function changes to u u x, q, rx , rq; the demand functions take the form of xi h i p , q , y , rx , rq and xi  h i p , q , u , rx , rq; the indirect utility is now v p, q, y , rx , rq just as is the expenditure function e p , q, y , rx , rq. These new functions are discontinuous at the reference point (Putler 1992). Fig. 1.3. shows a typical loss aversion curve observed within the context of welfare measurement.

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Imperfect substitutability and boundedness

Randall and Stoll (1980) demonstrate that the disparity between WTP and WTA is bounded by the ratio between the price flexibility of income and endowment. Cook and Graham (1977) assert that the compensation demanded for irreplaceable commodities, which we can assume to be imperfectly substitutable, depends on the initial level of wealth or endowment. As the probability of loss p1, WTA, dependent on the income that buys the x‟s, tends to infinity as the indifference curve is asymptotic to the vertical line at p1. This is what Amiran and Hagen (2003) also suggest in a slightly different manner: in presence of asymptomatically bounded utility functions, there exists an initial level of wealth sufficiently high to produce an infinite WTA–. Nevertheless, the substitution effect still plays a capital role, for it induces frictional trade-off between public and private goods. In terms of elasticity, the authors show that the income elasticity of the inverse compensated demand is bounded above and below by positive values independent of the amounts of public goods. In case of reference-dependent preferences, we believe that imperfect substitutability accentuates the pivoting of the indifference curve, which in turn can produce infinite compensation demanded. We replace the nonsatiation assumption by the assumption that for each level of income y, the status quo q1 is strictly preferred to the net loss of the public good q0 or uq 0 , y< uq1, y with q 0 < q1 . A double outcome arises. The first outcome lies in the convex curvature of the indifference curve. In point of fact, imperfect substitutability induces a steeper slope for higher opportunity losses (see Fig. 1.4.: grey segment and arrow 1). The second outcome results from the enlargement of the substitution effect due to aversion of net losses, yielding clockwise rotation and, accordingly, a steeper slope of the initial indifference curve (see Fig. 1.4.: black segment and arrow 2).

Table of contents :

Chapitre 0 Introduction Générale
0.1. Le préambule
0.2. L‟approche économique
0.3. Les méthodes d‟élicitation
0.4. Les enchères expérimentales
0.5. Le résumé de la thèse
0.6. Les recommandations de politique publique
0.7. Références
Chapter 1 Imperfect Substitutability in Standard and Reference-Dependence Models
1.1. Introduction
1.2. The standard model
1.3. The substitution effect
1.4. Imperfect substitutability and the endowment effect
1.5. Imperfect substitutability and loss aversion
1.6. Imperfect substitutability and boundedness
1.7. Concluding remarks
1.8. References
1.9. Appendix
Chapter 2 Private Valuation of a Public Good in Three Auction Mechanisms
2.1. Introduction
2.2. The experimental design
2.3. The results
2.4. Discussion
2.5. Concluding remarks
2.6. References
2.7. Appendix
Chapter 3 Endogenous Market-Clearing Prices and Reference Point Adaptation
3.1. Introduction
3.2. Auctions and incentive-compatibility
3.3. Interactive incentive-compatibility
3.4. The behavioral model
3.5. The empirical study
3.6. Concluding remarks
3.7. References
3.8. Appendix
Chapter 4 Competitive Private Supply of Public Goods
4.1. Introduction
4.2. The public good game
4.3. The explicit logarithmic model
4.4. Concluding remarks
4.5. References
4.6. Appendix

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