Why charge higher interest rates to poorer customers?

Consumer loans/credit charge different rates depending on the individual's risk. In particular, it charges more to poorer individuals. Whilst this seems to make sense from a risk perspective, there is some circularity involved. This is, "the more an individual has to pay, the more risk there is s/he doesn't pay".

In other words, higher interest rates increases the risk of the loan, which means higher interest rates are charged, which increases the risk of the loan, which... etc.

is this studied by economic/finance theory? Can someone explain me the circularity and provide some intuition? It's like if standard theory looks at a linear demand and supply curve, but it seems the supply curve is exponential (more cost increases the risk which increases the cost which increases the risk...).

• You answer yourself in the first half of your third sentence. – ThisIsNoZaku Nov 11 at 17:16
• @ThisIsNoZaku Please read the question. The apparent circularity is the reason why I cast doubt on that explanation. – Danny_R Nov 11 at 18:41
• It's possible for an infinite quantity of numbers to have a finite sum. – ThisIsNoZaku Nov 11 at 20:01
• @ThisIsNoZaku If you think you have an answer, please write it. – Danny_R Nov 11 at 22:10
• “In other words, higher interest rates increases the risk of the loan” I believe it works the other way around, the riskier the loan the higher the interest rate. That is why we base interest rates relative to the “risk free” government bond. The residual interest rate after accounting for that of the government bond would be considered the risk premium – Brennan Nov 12 at 0:01

Rather you can think about this as a version of a multiplier. For example, consider standard concept of money multiplier. In fractional reserve system if a central bank issues 100€ and reserve ratio is 10% then the original 100€ gets deposited 10€ is kept and 90€ lent which is then again deposited ad infinitum. So you might get puzzled here and think that the original 100€ creates infinite money but that would be incorrect as sum of infinite addition can be still finite. In this case even with infinite banks the original 100€ would crate only max $$100(1/0.10)=1000€$$.
How this applies here? Well here again even though higher interest rate makes person poorer and hence riskier leading to even higher interest rate it does not necessary make the person twice as riskier. Assuming for simplicity proportional relationship between riskiness and interest rate (relaxing this would not change the intuition) as long as the total effect of this increase measured as a fraction is less then 1 then the problem will converge to some final interest rate $$r$$ at which it would be possible to lend money to the poor person. If the fraction would be above 1 the series would be divergent meaning the optimum interest rate would be infinity and in that case bank would simply not lend money to this poor person.