On the Economic Value of Signals

Abstract

Abstract We provide sufficient conditions for the economic value of a signal to be a convex function, either locally or globally, of the input required to produce the signal. We also provide conditions under which this input can be interpreted as a measure of the information contained in this signal. We demonstrate that, under certain conditions, information is a very peculiar good that can—globally—show increasing marginal utility. In contrast to the earlier approach used to obtain the classic results on the local lack of concavity of the value of information, our approach allows permits the investigation of concavity (or lack) of the function representing the value of information, without imposing any conditions of differentiability on this function. Our approach also allows us to show that the marginal value of information can be zero even at an informative signal. Finally, we discuss some of the difficulties that can arise in designing price discrimination schemes for selling signals with various levels of quality.