  This paper delves into financial markets that incorporate a novel form of
heterogeneity among investors, specifically in terms of their beliefs regarding
the reliability of signals in the business cycle economy model, which may be
biased. Unlike most papers in this field, we not only analyze the equilibrium
but also examine welfare using objective measures while investors aim to
maximize their utility based on subjective measures. Furthermore, we introduce
passive investors and use their utility as a benchmark, thereby revealing the
phenomenon of double loss sometimes. In the analysis, we examine two effects:
the distortion effect on total welfare and the advantage effect of information
and highlight their key factors of influence, with a particular emphasis on the
proportion of investors. We also demonstrate that manipulating investors'
estimation towards the economy can be a way to improve utility and identify an
inner connection between welfare and survival.
