Production theory under price uncertainty for firms with disappointment aversion

Abstract

This paper studies the production theory of the competitive firm under price uncertainty by adopting four of the most well-established models of disappointment aversion. Our results show that a disappointment-averse firm will generally produce less than a risk-averse firm. Further, the disappointment-averse firm's optimal output level will surely decrease with an increase in the disappointment coefficients. Moreover, the optimal outputs among the four disappointment-averse models are not the same. As a real case example, we apply our models to determine the optimal building heights for new buildings in Punta del Este, Uruguay. In this example, our disappointment averse models' predictions are very close to the observed heights of these new projects.

Keywords:

• disappointment theory
• disappointment aversion
• risk aversion
• uncertainty
• construction industry
• optimal building height

JEL Classification:

• D21
• D24
• D81

Acknowledgments

The authors are grateful to the Editor-in-Chief, Alexandre Dolgui, the associate editor and two anonymous referees for substantive comments that have significantly improved this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Seen on web address at https://buffett.cnbc.com/annual-meetings/

2 We follow Wong (2014) to assume that the cost function is strictly convex, implying that the technology of the firm's production follows decreasing return to scale.

3 A similar price binary model has been used in Aizenman and Marion (1999), Lien (2001) and Wong (2014) to explain different economic problems. The analysis for more complex price distributions is far beyond the scope of this paper.

4 Bell (1985) and Jia, Dyer, and Butler (2001) make this assumption.

5 Readers may refer to Delquié and Cillo (2006) for the meaning and inference drawn from both $A(\cdot )$ and $B(\cdot )$.

6 Even though this prohibition, the local Government could allow new buildings above this height limit.

7 We assume that the land has been purchased before the maximisation problem, and hence, it is a fix cost and it does not affect the developer's maximisation process.

8 It is worth noticing that the base price $P_0$ does not affect the rates because it is just a scale factor.

9 All the monetary values are expressed in US dollars.

10 Although this is an integer optimisation problem, the optimal floor level should be rounded to the nearest integer.

Additional information

Funding

The authors would also like acknowledge the financial support by National Natural Science Foundation of China (11701034), National Social Science Fund of China (NSSFC-16BTJ013, NSSFC-16ZDA010), Sichuan Project of Science and Technology (2017JY0273), ANII, Universidad de Montevideo, Asia University, China Medical University Hospital, Hang Seng University of Hong Kong, the Research Grants Council of Hong Kong (Project Number 12500915) and Ministry of Science and Technology (MOST), Taiwan (Project Numbers 106-2410-H-468-002 and 107-2410-H-468-002-MY3). The second author would like to thanks comments by Maria Belen Egozcue. The third author would also like to thank Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement.