TITLE:
Multiplicative Normal Noise and Nonconcavity in the Value of Information
AUTHORS:
Stefan Behringer
KEYWORDS:
Value of Information, Inverse Problems, Bayesian Learning, Monopoly, Multiplicative Noise, Nonconcavity
JOURNAL NAME:
Theoretical Economics Letters,
Vol.11 No.1,
February
25,
2021
ABSTRACT: This paper investigates a Bayesian inverse problem
of a price setting monopolist facing a random demand. In contrast to previous
investigations an unknown true market potential of demand is distorted by two
independent Gaussian errors, a zero-mean additive and a unity-mean
multiplicative one. The multi-period game allows for learning from realized
market demands (signals). Interestingly increasing the level of noise of a
multiplicative error in this dynamic setting can actually improve the Value of
Information of signals to the firm, a result that cannot hold for a single
additive error or in a static context.