Interpreting the Interest-Cost Assumption in a Credit-Constrained Entrepreneur Model
Summary
The document examines an interpretation of the Evans–Jovanovic model of entrepreneurship under borrowing constraints. In the stated setup, an entrepreneur chooses capital to maximize production income plus the return on wealth not invested in the business, subject to a limit linking capital to initial wealth. The questioner notes that the resulting interest term appears to charge the entrepreneur for financing while leaving principal repayment outside the period’s income equation.
The central issue is whether this setup should be understood as renting capital or as borrowing with interest-only payments, and why economic models may use that simplification. The text provides the model equations and defines its variables, but it does not include an answer, derivation, or evidence about the intended economic interpretation. It therefore identifies a modeling ambiguity rather than resolving how repayment timing, loan maturity, or the broader model’s assumptions should be treated.
Key ideas
- The model maximizes production returns plus interest on wealth not committed to business capital.
- A borrowing constraint limits chosen capital in relation to initial wealth.
- The question highlights that the income expression includes an interest cost without an explicit principal repayment.
- The document asks whether this represents rented capital or interest-only borrowing but provides no resolution.
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Full text
# A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints
# A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints
[I already posted this question on the math forum of stackexchange and I was advised that I should post this question here]
In Evans and Jovanovic (1989) you will find a model for entrepreneurs with credit constraints. The part that is important for my question follows. Here it is the production function and the income equation that one should maximize:
$$\begin{aligned} y &= \theta k^{\alpha}\\ I &= y + r(z - k)\\ \max(\theta k^{\alpha} + r(z - k)) &\text{such that } k \leq \lambda z \end{aligned}$$
Where ${\lambda}\ge1$ and it is a measure of constraints. For the rest of the notation: $y$ are the earnings of the individual from production; $I$ is income; $k$ is capital; $\theta$ is a skill measurement; $r$ it is the interest rate; $z$ is the initial wealth of the individual or household that he, or the household, lends too; $\alpha$ is a technology parameter. If you are interested in more details of the model, here it is a link: Evans and Jovanovic (1989).
So here comes my doubt. This model is about putting credit constraints for a hypothetical entrepreneur. The entrepreneur borrows $k$ in such situation but only pays the interests: $rk$; for example, in each period we could be analyzing (I mean hypothetically, I did not give a time frame for the equation), he only pays the interests of what he borrowed i.e. he does not pay a principal on what he borrowed plus interests, only interests are deducted from his income. The individual seems to rent capital rather than borrow it in a more familiar way. So I'll ask you: does this interpretation makes sense? If so, is there a larger reason for economic modeling making this kind of implicit assumption?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.