Pricing of a Risk Averse Monopoly in the Presence of Stochastic Demand
Author(s)
Kolos Csaba Ágoston
Affiliation(s)
Department of Operation Research and Actuarial Sciences, Corvinus University of Budapest, Budapest, Hungary.
Department of Operation Research and Actuarial Sciences, Corvinus University of Budapest, Budapest, Hungary.
ABSTRACT
In the paper, we investigate the pricing behavior of a risk averse monopoly. Since the focus is on the risk averse attitude of the firm, we ignore cost in our model. Demand is considered to be stochastic demand: as price decreases, the expected number of customers increases, but it has a variation. Although demand is uncertain, it relates to the aggregation method of individual demands and the individual demand has the usual form. In our framework a risk neutral (or profit maximizer) monopoly does not change the product’s price as the number of clients increases. On product markets the risk averse monopoly with DARA utility function always increases the price as the number of clients grows, but in insurance markets the implication can be the opposite: the price of insurance may decrease as the number of clients increases.
In the paper, we investigate the pricing behavior of a risk averse monopoly. Since the focus is on the risk averse attitude of the firm, we ignore cost in our model. Demand is considered to be stochastic demand: as price decreases, the expected number of customers increases, but it has a variation. Although demand is uncertain, it relates to the aggregation method of individual demands and the individual demand has the usual form. In our framework a risk neutral (or profit maximizer) monopoly does not change the product’s price as the number of clients increases. On product markets the risk averse monopoly with DARA utility function always increases the price as the number of clients grows, but in insurance markets the implication can be the opposite: the price of insurance may decrease as the number of clients increases.
Cite this paper
Ágoston, K. (2015) Pricing of a Risk Averse Monopoly in the Presence of Stochastic Demand. Theoretical Economics Letters, 5, 217-224. doi: 10.4236/tel.2015.52026.
Ágoston, K. (2015) Pricing of a Risk Averse Monopoly in the Presence of Stochastic Demand. Theoretical Economics Letters, 5, 217-224. doi: 10.4236/tel.2015.52026.
References
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[1] Schmitt, A.J., Snyder, L.V. and Shen, Z.M. (2010) Inventory Systems with Stochastic Demand and Supply: Properties and Approximations. European Journal of Operational Research, 206, 313-328. http://dx.doi.org/10.1016/j.ejor.2010.02.029 [2] Holmberg, K. and Tuy, H. (1999) A Production-Transportation Problem with Stochastic Demand and Concave Production Costs. Mathematical Programming, 85, 157-179. http://dx.doi.org/10.1007/s101070050050 [3] Barberá, S. and Pattanaik, P.K. (1986) Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings. Econometrica, 54, 707-715. http://dx.doi.org/10.2307/1911317 [4] Bandyopadhyay, T., Dasgupta, I. and Pattanaik, P.K. (2002) Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference. Journal of Economic Theory, 107, 483-489. [5] Alcantud, J.C.R. (2006) Stochastic Demand Correspondences and Their Aggregation Properties Decisions. Economics and Finance, 29, 55-69. http://dx.doi.org/10.1007/s10203-006-0060-6 [6] Hoy, M. and Robson, A.J. (1981) Insurance as a Giffen Good. Economics Letters, 8, 47-51. http://dx.doi.org/10.1016/0165-1765(81)90091-4 [7] Stiglitz, J.E. (1977) Monopoly, Non-Linear Pricing and Imperfect Information: The Insurance Market Review of Economic Studies. Review of Economic Studies, 44, 407-430. http://dx.doi.org/10.2307/2296899 [8] Kliger, D. and Levikson, B. (1998) Pricing Insurance Contracts—An Economic Viewpoint. Mathematics and Economics, 22, 243-249. http://dx.doi.org/10.1016/S0167-6687(98)00002-X [9] Raviv, A. (1979) The Design of an Optimal Insurance Policy. American Economic Review, 69, 84-96. [10] Zhou, C. and Wu, C. (2008) Optimal Insurance under the Insurer’s Risk Constraint. Mathematics and Economics, 42, 992-999. http://dx.doi.org/10.1016/j.insmatheco.2007.11.005 [11] Gollier, C. (1999) The Economics of Risk and Time. GREMAQ and IDEI, University of Toulouse, Toulouse. [12] Mosin, J. (1968) Aspects of Rational Insurance Purchasing. Journal of Political Economy, 76, 553-568. http://dx.doi.org/10.1086/259427