accurate signals and in later periods of a search high signals get a low interest rate
offers and low signals get a high interest rate offers. This is the standard result we
observe in most of the related literature.
Note that the higher the market information quality, the further is from one and
PH
the shorter the expected search time for all individuals. This happens because case I of
the separating equilibria occurs sooner and the true type is revealed to the market
faster. In other words, the safe borrowers are getting H in the earlier periods with higher
probability and risky borrowers that get L in the initial periods will soon lose hope they
will be able to deceive a lender. On the other hand, low market quality signals may look
like credit crunches, or accentuate them, as search time increases for all borrowers.
A set of graphs that can be found in the appendix illustrate the equilibrium cases
described above. The graphs consider the different cases that can occurfor a given
S S
92(02-01) and a given r, as P changes, forX=H and Y=L; or vice versa.
S PX,ht PY,ht
In conclusion, the profit functions for a lender are:
Given a risky borrower=
p(risk) Early (taken as safe) = phr [g2(k + 01) + (1 -g2)(k- 02) 1]
Later = g2(k+ 02) +(1-2)(k- 02) 1
Given a safe borrower=
p(safe) = gl(k + 01) + (1 g)(k 01) 1
A table of results can be found in the Appendix. The table includes the expected
profits for all agents and the fraction of loans assigned in each possible equilibrium case
after the first searching period.