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; $r$ is a interest rate; $z$ is the initial wealth of the individual or household that he lends; $\alpha$ 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?
In a multiple period model with many suppliers of capital (investors), there is no difference in getting capital from one supplier or other. So every period you could borrow capital, return it next period, and then borrow again from same or another set of investors. From the perspective of the borrower, this is no different from keeping the capital/principal and paying interest every period. That is, long-term financing is equivalent to rolling over short-term financing. Practically, long-term financing reduces transaction costs but over time, one party may want to renegotiate. This can however be resolved by just renegotiating interest rate each year.
So in essence, as long as the market for capital is competitive, there is no advantage in considering a series of one period capital loans over a single long-term loan. However, a general setup would allow the amount of capital and the interest rate to change each period.