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[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?

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Most corporate loans and bonds are non-amortizing. Why would imposing a condition that the loan must amortize be useful? – user6900 Jan 5 '14 at 0:56
@Andy, I've seen this model being applied for micro-finance or micro lending, in which what you pay back to your lender it is a principal plus interests -- right? And I do too think that this type of assumption is frequent in economic modeling and I wanted to know why. – John Doe Jan 5 '14 at 14:19
There is a mistake in the sign in your representation of the problem. It is y+R(z-k), where R=1+r – Luca May 4 at 9:25
Luca, I agree with your first correction. But the paper that I mentioned states $r$ as the interest rate. Why is that so? Your second correction makes the interpretation more straightforward, but that is not what the paper seems to say. – John Doe May 10 at 20:54

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