cost. Specifically, a signal of quality qt carries a cost in terms of utility of C (q2).
Therefore, the ex ante level of utility net of information acquisition costs is given
by
u = At + log(Et (1 + xt+ι) - (1 - ¾2)σ2t + 1 ) - c(q2).
Economic agents given their priors must decide on the quality of signals they
receive. Technically, economic agents must balance the loss in terms of utility
resulting from insufficient consumption smoothing with the loss in terms of
utility resulting from information purchase, i.e., they select the quality qt so as
to the level of utility is the largest. The first order condition for an interior
solution is given by
(1 + EtXt+1) _ 1 2
(31)
σ2:+ = <- qt
The right hand side is monotone decreasing in q2 The left hand side depends
on the ratio of the life time expected income to its variability. The solution is
characterized by several intuitive features. First of all, the higher the underlying
uncertainty the larger the precision of signals purchased. Similarly, if the under-
lying uncertainty is low then only very uninformative signals are purchased and
expectations are backward looking. Moreover, the higher the expected value of
x2+1 the lower the precision of signals. This is due to the fact that with concave
utility a loss in terms of utility resulting from an error of a given magnitude
falls with the level of consumption. In other words, at low levels of consump-
tion a given level of disequilibrium along the intertemporal margin has a larger
impact in terms of utility than the same level of disequilibrium at a high level
of consumption. This property implies that at times when economic agents
expect favorable conditions in the future, i.e., when they save little, i.e., times
of expansions, they will also choose to be less informed. As a consequence the
property implies that economic agents tolerate a higher level of intertemporal
errors when they are optimistic about the future than they do when they are
pessimistic about the future. Naturally, this implies that recessions should be
on average shorter than expansions.
In this section the paper adheres to the assumption that all agents use the
same priors. The decision making process of consumers starts with the decision
on the quality of signals. Given the prior agents choose the quality according
to the optimality condition (31). Then a specific signal is generated for each
consumer. Naturally, not all consumers receive the same signal. Let νt be the
signal for xt+ι received by consumer i. Recall that consumer i uses the signal
to form the posterior distribution F (xt+ι∣νt) and then chooses the optimal
level of investment in physical capital. The level of investment can be obtained
combining relationships (28) and (29) and is given by
klt+ι = - (1 - (qtν + (1 - qt) Etχt+1 )).
Note that the level of investment chosen by a specific agent is dependent on
the specific signal she obtained. However, the aggregate level of investment
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