**Access to Credit: Part I**

This blog is part one of a two part series. It will go over some of the theory of credit market inefficiencies and further set the groundwork for The Digital Reserve. The second blog in the series will add more theory about information asymmetry and how that affects potential lending through The Digital Reserve. This blog starts with a very big question:

Are there potentially good borrowers who want credit, but do not have access to it?

After addressing this issue we narrow in our focus on credit rationing, a phenomena where demand far exceeds supply of credit, to identify where exactly The Digital Reserve fits into the credit ecosystem.

**Access to Credit:**

Figure 1 shows that there are two types of people who do not use credit — those who have access, but don’t use it either because they don’t need it or for cultural/religious reasons which do not permit usage, and those who may need it, but cannot access it.

The four reasons mentioned above on why people may not have access to credit have slight overlaps, but are unique.

**Low income**may prevent access to credit even in a market with adequate supply. They may simply be unable to pay the interest at a reasonable market interest rate. The market interest rate is simply the cost of borrowing determined by supply and demand of the market. These people may still benefit from credit and we will focus on this group in later posts.**Expensive credit**may prevent good borrowers from accessing credit, if the cost of borrowing goes beyond the market rate. As we will address later, in the second part of this series, theory suggests that with higher interest rates the likelihood of lending to a riskier borrower increases.**Discrimination**is self explanatory in how it prevents access to credit, redlining is one of the most common forms.- The final reason is
**credit rationing**, which means the supply of credit is far below the demand for credit at the market interest rate and the lender will not increase the interest rate because they cannot maximize profit beyond the set interest rate. We will focus in more detail on the theory of credit rationing below since it has the largest impact on the supply of affordable credit.

**Credit Rationing:**

Credit rationing is one of the largest problems for access to credit and it arises from information asymmetries in the credit market, the borrower and lender have different information about the risk of the borrower. Below is the current theory of credit rationing, and in the next part of our series we will discuss information asymmetries more closely.

Assuming a perfectly competitive market, where price = marginal costs, the lenders potential profits are:

Where E(π) = Expected profits, r = interest rate and MC = marginal costs. If we assume away perfect repayment we have:

Where p = probability of repayment. Model (2) is a linear function depending on the probability. The lower the probability of repayment the lower the expected profits. We know that the probability of repayment is contingent on many factors including the interest rate itself. The higher the interest rate, the less likely a borrower will be able to repay the loan. According to the theory of credit rationing, lenders will not lend beyond a certain interest rate because it will no longer be profitable, so we must change our model to become non-linear, to model a relationship with diminishing returns. We will make the probability of repayment a function of interest and other borrower specific characteristics which is shown below:

Where p(r) is the probability of repayment as a function of the interest rate and b is a vector of borrower specific characteristics that affect the probability of repayment. We can now update our model to the following:

Model (4) is the same as (3) using the substitution of the function and model (5) is an expansion of (4). To find the maximum interest rate (r*) offered by the lender, we will take the derivative of model (5) (don’t worry about the calculus) to find:

so the maximum lender interest is:

And the lender will supply the loan so long as the expected profit is greater than zero:

The models and graph above show a clear shortage in supply of credit at the optimal interest rate, leaving many borrowers in need of credit without access. One solution for ending credit rationing is creating strong property rights so that borrowers have adequate collateral for loans. Given the difficulty of solving this problem, we need to, in the short run, find ways of increasing the supply of credit to disadvantaged groups with uncollateralized debts. Microfinance institutions and other informal institutions aim to fix this problem through means such as family borrowing, rotating credit and savings associations, payday loans etc. However, many of these come with higher transaction costs as well as higher interest rates.

This is where The Digital Reserve comes in. The Digital Reserve’s lending model works on a borrower interest selection model. While this model at first glance may seem counter-intuitive, we will see in the next blog (PART 2) that the model works well within the framework of some empirical results of research conducted on information asymmetries within the credit market in developing nations.

Author: Troy W — Entrepreneur , Public Policy and Statistics grad student, interested in research and applications of Blockchain.