would specialize in whatever they do best and we would observe two separate markets
with their respective set of interest rates.
With specialization I do not mean a lender focusing in the riskiest borrowers and
another in the less risky borrowers, but rather specialization in separate markets such
as international vs. domestic borrowers, borrowers from particular industries, or in loans
for particular purposes15.
Proposition 2: The equilibrium when (1-2) does not hold and the signals do NOT
have the same accuracy is the following: The lender with an informational advantage
will implement the policy r*(H) = rj(L), r,*(L) = r(L). The competitor will implement
r*-r0(H)
the policy rj*(L) = ri(L), r*(H) = r*for r* such that = Pr(S = LISi = H)16
When (1-2) does not hold, the lender with an informational advantage can afford to
make loans to fewer good borrowers. The competitor, by having less information, is
forced to compete more aggressively by charging the lowest interest rate in the market
to those for whom it observes a high signal. This observation might help to explain why
bigger lending companies can charge higher interest rates, if you are willing to assume
they are information advantaged. Note that the existence of this equilibrium depends on
a high probability that the competitor gets a low signal when the lender with the most
accurate signal observes high. This is closely related to the probability that good
borrowers get categorized correctly only by the lender with the advantage; these are the
15 An analysis on the evidence of specialization in the market and other possible explanations for its existence is
done by Carey, Post and Sharpe (1998).
16 If PiH > Pjh but pi > pil, the equilibrium is the same in the sense that it is determined by the second and fourth
highest interest rate in (1-1) proposition 1 and by the two highest in proposition 2. i.e. Under this scenario the
order of (1-1) is different, but the second and fourth highest interest rate constitute the equilibrium when (1-2)
holds in the same fashion as described here. The analogous statement is true when (1-2) does not hold. Since the
proof is so similar to the one given for this proposition, it is omitted fromthe paper.