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RISKY PRODUCTION WITH EX‐ANTE PRICES UNDER MONOPOLY ANALYTICAL AND SIMULATION RESULTS
Author(s) -
Driver Ciaran,
Lambert Peter,
Vial Stéphane
Publication year - 1993
Publication title -
bulletin of economic research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.227
H-Index - 29
eISSN - 1467-8586
pISSN - 0307-3378
DOI - 10.1111/j.1467-8586.1993.tb00556.x
Subject(s) - economics , certainty , multiplicative function , demand curve , price elasticity of demand , econometrics , monopoly , ex ante , robustness (evolution) , mathematical economics , microeconomics , mathematics , mathematical analysis , biochemistry , chemistry , geometry , gene , macroeconomics
This paper concerns the case of a monopolist facing multiplicative uncertainty in demand. Karlin and Carr (1962), henceforth KC, show that, when price and production are both chosen ex ante , the uncertainty price exceeds the certainty price. They also give a sufficient condition under which the firm locates above the certainty demand curve, but they do not consider the effect on the output level. In this note we replicate the KC results and then go further. In the special case that the price elasticity of certainty demand is constant, and the probability distribution for the uncertainty parameter in the demand function is uniform, output is unambiguously lower under uncertainty, and KC's condition for the firm to locate above the certainty demand curve can be strengthened to one that is both necessary and sufficient. The robustness of these results is tested under less stringent assumptions on demand, abandoning symmetry for a lognormal distribution of the uncertainty parameter. Simulation confirms that the results hold up, and also determines the effects upon the firm's decisions of an increase in demand uncertainty.