# Abstract

We study a credit market using an infinite horizon model where an altruistic lender offers loans to agents for production projects that may grow over time. The lender funds the loans using a combination of external debt and subsidies. The optimal way for the lender to subsidize the credit relationships depends on the probability of project growth. When growth is less likely, it is best to commit to ongoing subsidies. However, for a range of growth probabilities, ongoing subsidization may not be credible and this can have negative efficiency implications.

# Acknowledgements

The author would like to thank two anonymous referees for their very helpful comments and suggestions. Any remaining errors are author’s alone.

# Appendix

*Proof of Lemma 3*. First note that the two partial derivatives of

*Proof of Lemma 4*. With income

Consider the subsidies

First, consider the case where

Second, consider

*Proof of Proposition 1*. In 4 we confirmed that if

(i.) First, consider the case where

(ii.) Second, consider

In this case, for the *binding* at *not binding* at

Before we proceed further, we must confirm that both sides of this inequality are positive.

(*a*.) For the left-hand side, A3 ensures that

(*b*.) The right-hand side is positive if

Since we know

which holds due to A3.

Consequently, we can now claim that the inequality in eq. (11) holds if

*Proof of Corollary 1*.Under the

First, consider the case where

It is sufficient to show that

Second, consider the case where

Since

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**Published Online:**2017-8-11

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