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Complex dynamics in the market for loans

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Abstract

This paper demonstrates that endogenous fluctuations are possible in the market for loans. In the context of a three-period overlapping generations economy, the deposit rates offered to lenders are found to exhibit complex dynamics when financial intermediaries mediate borrowing and lending. Constant relative risk aversion of savers is found to generate a first-order nonlinear equation in the deposit rates. Concavity and convexity assumptions of production and savings functions are found to generate a type of dynamic relationship between the loan rates that is well known in the literature for generating complex dynamics. While the main analysis is conducted with general functions, an example is provided to support the theory presented.

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Notes

  1. See the literature on financial intermediation for similar environmental assumptions.

  2. These solutions also satisfy the second-order condition.

  3. The production function’s representation implies that the endowment and intermediate goods have distinct impacts on output. This representation ensures that entrepreneurs need the savings of both young and middle-aged lenders.

  4. These values have been chosen for illustrative purposes. Other values can be used to study the dynamic behavior. We wish to concentrate on the possibility of chaos appearing in these types of frameworks, and the exactness of the parameter values is not aimed.

  5. Graphs 3 through 6 were generated using the Julia software library’s DynamicalSystems package (Datseris (2018)).

  6. If this condition is not met, the current deposit rate will depend on both the immediate past and immediate future deposits rates and thereby generate a higher-order (possibly second-order) nonlinear difference equations in the deposit rates. This remains a topic for future analysis.

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  1. Department of Economics, Oakland University, Rochester, MI, 48309, USA

    Nivedita Mukherji

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  1. Nivedita Mukherji
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Mukherji, N. Complex dynamics in the market for loans. Decisions Econ Finan 45, 83–99 (2022). https://doi.org/10.1007/s10203-021-00341-y

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