Adding a stage of signal acquisition to the expected utility model shows that Bayesian updating results in a well defined law of demand for financial information when asset return distributions are conjugate priors to signals such as in the gamma-Poisson case. Signals have a positive marginal utility value that falls in their number if and only if investors are risk averse, asset markets large, and variance-mean ratios of asset returns high in fully revealing rational expectations equilibrium. Expected asset price increases in the number of signals so that expected excess return drops. The diminishing excess return prevents Bayesian investors from unbounded information demand even if signals are costless, unless the riskfree asset is removed. Signals mutually benefit homogeneous investors because revealing asset price permits updating so that a Pareto criterion judges competitive equilibrium as not sufficiently informative. However, asset price responses make incentives for signal acquisition dependent on portfolios so that welfare and distributional consequences become intricately linked when investors are heterogeneous.