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Retained Earnings, Interest Rates and Lending Relationship

  • Ariadna Dumitrescu EMAIL logo
Veröffentlicht/Copyright: 21. Juni 2018
The B.E. Journal of Theoretical Economics
Aus der Zeitschrift The B.E. Journal of Theoretical Economics Band 19 Heft 1

Abstract

This paper provides a moral hazard characterization of the effects of lending relationship on cost of funds. I develop a model that studies the problem of financial contracting between a bank and an entrepreneur and isolates the effect of the lending relationship on the interest rates. The main result is that a bank-entrepreneur relationship has a positive effect on the interest rates, the optimal contract specifying a decreasing sequence of interest rates. The possibility of the entrepreneur to use partially his retained earnings improves the terms of the contract between entrepreneur and lender by reducing the difference between the two interest rates.

Keywords: long-term lending relationship; moral hazard; interest rates

Appendix

Sketch of the proof of Lemma 1 and 2. In order to solve the maximization problem I need to write explicitly the incentive constraints. Thus, the problem maximization problem corresponding to the incentive constraint (IC)2 has two possible solutions: e2=α2 if α2≤1 and e2=1 if α2≥1.

Similarly, the maximization problem corresponding to the incentive constraint (IC)1 has two possible solutions: e1=α1(1−x)+e2α2−e22/2 if α1(1−x)+e2α2−e22/2<1 and e1=1 if α1(1−x)+e2α2−e22/2≥1.

Using these first order conditions I solve the initial problem in the four cases that result from above:

Case 1. e1=e2=1, α2≥1andα1(1−x)+α2≥3/2.

Case 2. e1=1, e2=α2, α2≤1, α1(1−x)+α22≥1.

Case 3. e1=α1(1−x)+α2−1/2≤1, e2=1, α2≥1.

Case 4. e1=α1(1−x)+α22, e2=α2, α2≤1, α1(1−x)+α22/2<1.

I obtain that if R>1−w12+54, e1=e2=1 is the optimal solution (Lemma 1).

If R≤1−w12+54, we need to compare the cases 2, 3 and 4. It results that the optimal solution is the one that originates from Case 4.

The solution in Case 4 is determined from a set of possible cases obtained when solving the Kuhn-Tucker problem. In order to solve this problem I replace the incentive constraints with the conditions specified in Case 4. Finally, I obtain that the solution of the problem is 0≤e1,e2≤1 such that it solves the system of eq (1) and the optimal payoff of the entrepreneur are α1=0, α2=e2 (Lemma 2).

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Published Online: 2018-06-21

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Articles
  2. Privatizing Multi-subsidiary Public Firm in Location Model
  3. Efficient Combinatorial Allocations: Individual Rationality versus Stability
  4. On Decay Centrality
  5. Sequential Auctions with Decreasing Reserve Prices
  6. The core of a strategic game
  7. Targeted Advertising on Competing Platforms
  8. Representation in Multi-Issue Delegated Bargaining
  9. Endogenous Mergers in Markets with Vertically Differentiated Products
  10. Standards of Proof and Civil Litigation: A Game-Theoretic Analysis
  11. Retained Earnings, Interest Rates and Lending Relationship
  12. Uniform Price Auctions with Asymmetric Bidders
  13. Conformity and Influence
  14. Sellouts, Beliefs, and Bandwagon Behavior
  15. Notes
  16. Eco-Firms and the Sequential Adoption of Environmental Corporate Social Responsibility in the Managerial Delegation
  17. Vertical Contract and Competition Intensity in Hotelling’s Model
  18. Constrained Allocation of Projects to Heterogeneous Workers with Preferences over Peers
  19. Irrelevance of the Strategic Variable in the Case of Relative Performance Maximization
  20. Critical Efficiencies as Upward Pricing Pressure with Feedback Effects
  21. On the Openness of Unique Pure-Strategy Nash Equilibrium
  22. Forecast Dispersion in Finite-Player Forecasting Games
https://doi.org/10.1515/bejte-2017-0002
Schlagwörter für diesen Artikel
long-term lending relationship; moral hazard; interest rates

Artikel in diesem Heft

  1. Articles
  2. Privatizing Multi-subsidiary Public Firm in Location Model
  3. Efficient Combinatorial Allocations: Individual Rationality versus Stability
  4. On Decay Centrality
  5. Sequential Auctions with Decreasing Reserve Prices
  6. The core of a strategic game
  7. Targeted Advertising on Competing Platforms
  8. Representation in Multi-Issue Delegated Bargaining
  9. Endogenous Mergers in Markets with Vertically Differentiated Products
  10. Standards of Proof and Civil Litigation: A Game-Theoretic Analysis
  11. Retained Earnings, Interest Rates and Lending Relationship
  12. Uniform Price Auctions with Asymmetric Bidders
  13. Conformity and Influence
  14. Sellouts, Beliefs, and Bandwagon Behavior
  15. Notes
  16. Eco-Firms and the Sequential Adoption of Environmental Corporate Social Responsibility in the Managerial Delegation
  17. Vertical Contract and Competition Intensity in Hotelling’s Model
  18. Constrained Allocation of Projects to Heterogeneous Workers with Preferences over Peers
  19. Irrelevance of the Strategic Variable in the Case of Relative Performance Maximization
  20. Critical Efficiencies as Upward Pricing Pressure with Feedback Effects
  21. On the Openness of Unique Pure-Strategy Nash Equilibrium
  22. Forecast Dispersion in Finite-Player Forecasting Games
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