Although the concept is widely discussed in the economic literatures, it is less likely to observe lenders willing to lend up to the natural borrowing limit.
Financing law school tuition fee in the United States fits into the illustrative purpose perfectly.
In order for law students to finish the degree, they have to borrow money from the bank and pay it back after becoming a lawyer.
They will only lend reasonable amount money so that they could receive back from the students without too much risk.
The natural borrowing limit is one type of restriction imposed on the consumer utility maximization problem in the economics.
In making an optimal consumption decision, she has to conform to the budget constraint she faces.
In other words, she cannot consume more than the net of the income, amount of money she borrows, and debt repayment.
To rule out such situation and Ponzi schemes, and to make above consumers problem more interesting, there has to be a borrowing limit.
This limit comes from the common sense requirement that it has to be feasible for the consumer to repay his debt in every possible realization of the future.
[3] The way that the borrowing limit is imposed on the consumer utility maximization problem is very important in the economic research, since, it affects the stream of consumption, and thus welfare of the agent.
However, consumer can smooth the consumption almost surely under the natural borrowing limit, even under the incomplete market assumption.
Readers who are familiar with economics will get better understanding by reading below example of the utility maximization problem.
[citation needed] Think of a standard infinite horizon consumer utility maximization problem of the economic agent, having stochastic income stream
Let's assume, the agent can only buy risk-free bond (incomplete market assumption),
that imposes the natural borrowing limit on the consumer maximization problem, substitute
However, it is easy to argue that the natural borrowing limit will never bind when assuming Inada condition of the instantaneous utility function.
In such case, the agent cannot consume at all for the rest of the period, since she has to use all her income to pay back her debt.
The agent will end up having negative infinity lifetime utility due to the zero consumption for the rest of her life.
[4] In their study, they showed that a competitive loan market suffers from the credit rationing problem.
Furthermore, Williamson (1987)[6] showed that the credit rationing arises if lenders suffer from monitoring costs.
Cooley and Quadrini (2001)[7] showed that the evolution and the distribution of the firm size and ages implied by their economic model mimic the real world data closely.
A specific type of friction under their concern was premium associated with increasing equity and costly defaulting on debt.
Furthermore, Angelini and Generale (2005) elaborated Cooley and Quadrini's result by developing direct ways to measure the financial constraints that firms face.
By using an equilibrium business cycle model, Bianchi and Mendoza (2010)[8] showed that economic agents facing collateral constraint borrow too much and the economy suffers from larger magnitude financial crises than it would have suffered under the social planner's economy.