The Selection Problem: Why Small Loans Are Unavailable Rather Than Expensive

A household needs $400. Mainstream lenders will not make that loan at any price — not at 12%, not at 36%. The household ends up at a pawn shop, a title lender, or the rent-to-own store. The standard explanations are that these borrowers are too risky, or that they are being exploited. Both are incomplete, and neither predicts the pattern well. The binding constraint is that the cost of resolving uncertainty is fixed per application while revenue scales with loan size — which creates a size below which no lawful rate covers the cost of deciding. Above that threshold lenders price. Below it they refuse. This report works the arithmetic, derives what the model predicts, and argues that it explains the evidence better than the alternatives.

The question the standard account can't answer

Two explanations dominate discussion of the small-dollar credit gap.

The risk account: these borrowers default too often, so mainstream lenders avoid them. The exploitation account: high-cost lenders target vulnerable populations who lack alternatives.

Both contain truth. Neither answers the question that should be obvious: if the problem is risk, why don't lenders simply charge more? Credit markets price risk routinely across enormous ranges. A lender willing to lend at 8% to one borrower and 29% to another is already demonstrating that risk is a pricing input, not a barrier. If a $400 borrower defaults at 20%, a rate exists that compensates for it. Lenders do not offer that rate. They decline to participate.

The exploitation account has the mirror problem. If high-cost lenders earn extraordinary returns from this population, entry should compete those returns away — and the segment has seen substantial entry, from storefronts to online lenders to the earned wage access products of the last decade. Prices have not converged toward mainstream levels. Something is holding a floor under cost that competition does not erode.

Our claim is that both accounts miss the mechanism because both focus on the risk of the loan while the constraint operates on the cost of the decision. Once you separate those, the pattern resolves — including several features the standard accounts treat as anomalies.

If risk were the barrier, lenders would charge more. They don't — they decline. That behavior is the evidence that something other than risk is binding.

The model

A lender's profit on a single loan:

π = (r × L × t) − (λ × L) − F − (s × t) − (c × L)

Where L is loan size, r the annual rate, t the term in years, λ the expected loss rate, F the fixed cost of origination, s the annual servicing cost, and c the cost of capital.

The structure matters more than the notation. Four of these terms scale with loan size. Two do not.

• Scales with L: interest revenue, credit losses, cost of capital.
• Does not scale with L: origination cost F, and servicing cost s — which is largely a function of the number of payments processed, statements sent, and calls handled, not of the amount.

What is in F? Bureau inquiry, decisioning, identity verification, income verification where performed, fraud screening, disclosure generation, adverse action processing for the declines that never fund, compliance overhead, and the cost of funding the loan operationally. The verification and decisioning economics we've described elsewhere are precisely this cost, and note the item that is easy to miss: the cost of applications you decline is borne by the applications you approve. A lender approving one in four applicants pays four times the per-application screening cost on every funded loan.

Now solve for the rate that makes π = 0:

r* = λ/t + c + (F + s×t) / (L × t)

The final term is the whole argument. The break-even rate contains a component proportional to 1/L. As loan size falls, the rate required to cover fixed costs rises hyperbolically — not linearly, not gradually, but toward infinity as L approaches zero.

Which yields the central result: for any binding rate ceiling, there exists a loan size below which no lawful rate produces a viable loan. Not an unprofitable loan — an impossible one. And the threshold is determined by F, not by λ.

The arithmetic

Stylized but realistic parameters. Assume origination cost F = $75 (bureau, decisioning, verification, compliance, and allocated cost of declined applications), servicing s = $60 per year, cost of capital c = 8%, one-year term.

Loan size	Fixed cost as % of principal	Break-even rate at 10% loss	Break-even at 20% loss
$300	45%	63%	73%
$500	27%	45%	55%
$1,000	13.5%	31.5%	41.5%
$2,500	5.4%	23.4%	33.4%
$10,000	1.35%	19.4%	29.4%
$25,000	0.54%	18.5%	28.5%

Read down the third column. At $25,000, a lender facing a 10% loss rate breaks even around 18.5% — comfortably inside most state ceilings, and a viable business. At $300, the same lender facing the same 10% loss rate needs 63%.

The risk is identical across every row. The required rate varies by a factor of more than three. That is the entire finding, and it is arithmetic rather than opinion.

Now impose a 36% ceiling — a common benchmark in state law and the standard for military lending. The $2,500 loan works at either loss rate. The $1,000 loan works at 10% losses and fails at 20%. The $500 and $300 loans fail at every loss rate, including zero. Set λ = 0 in the model and the $300 loan still needs 8% + $135/$300 = 53%. A lender who could underwrite perfectly, with no defaults whatsoever, still could not make that loan at 36%.

This is the sentence that should reframe the debate: the small-dollar gap is not primarily about default. A lender with a crystal ball and zero losses could not serve it under a 36% cap.

Why lenders ration instead of pricing

The model explains a behavior that puzzles observers: lenders in this segment set minimum loan amounts rather than offering small loans at high prices.

If pricing were the mechanism, you'd expect a smooth distribution of loan sizes with rates rising as amounts fall. What you observe instead is bunching at a floor — a lender advertising "loans from $2,000" who will not lend $800 at any rate. That is the signature of a fixed-cost constraint, not a risk constraint, and it is the single most visible piece of evidence for this account.

Three further behaviors follow, each conventionally explained some other way:

Upselling small applicants to larger loans. Frequently read as predatory — and it is a real harm when the borrower didn't need the larger amount. The model says it is also the rational response to a constraint: the lender cannot serve the requested amount, and the nearest serviceable product is larger. Both readings are true simultaneously, which is why the practice is genuinely hard to regulate. Prohibiting the upsell does not create the small loan; it removes the transaction.

Fee structures rather than interest. A flat fee is the natural instrument for recovering a fixed cost, which is precisely what a fee is. The persistent industry preference for fee-based pricing on small products — and the equally persistent regulatory preference for expressing everything as APR — is a disagreement about whether the fixed cost should be visible as such. APR was designed to make loans comparable across sizes, and it does that badly when a large share of the cost doesn't scale with size. This is the same measurement problem our earned wage access analysis encountered from the other direction: a $3.18 fee annualizing to 109.5% is arithmetically correct and economically misleading about what is being charged for.

Extreme underwriting minimalism. Payday lending's characteristic feature — almost no underwriting — is usually described as recklessness. The model says it is the only viable response to the constraint. If F is what kills the loan, drive F toward zero. Verify employment and a bank account, skip the bureau pull, skip income verification, accept the resulting loss rate, and price for it. That is a coherent business model given the constraint, and it explains why "just underwrite them better" is not the costless improvement it appears — better underwriting raises F, which raises the break-even rate, which is the problem being solved.

What this says about rate caps

Here the model earns its keep, because it resolves an empirical literature that looks contradictory.

Studies of interest rate ceilings reach opposing conclusions with roughly equal frequency: some find caps reduce prices with modest supply effects, others find they eliminate credit availability. The model predicts both, and predicts which you'll observe from a single parameter.

	Large loans	Small loans
Fixed cost share of revenue	Small	Dominant
Break-even rate	Well below typical ceilings	Frequently above any lawful ceiling
Effect of a cap	Compresses margin; supply largely persists	Eliminates viability at every rate; supply exits
What researchers observe	"Caps lower prices"	"Caps destroy access"

Both literatures are correct about different segments. A study of installment loans averaging $3,000 and a study of $400 advances will disagree permanently, and the disagreement is not about method.

We should state our position plainly, since even-handedness here would be evasion. A rate cap set below the fixed-cost break-even for a loan size does not make that credit affordable. It removes it. The Connecticut episode our earned wage access report documented is a clean instance — providers exited, and surveyed users reported going without, borrowing from family, or using credit cards.

The honest counterargument, which we take seriously: removal may still be welfare-improving. If the credit being removed leaves borrowers worse off on average — through rollover cycles, escalating fees, or the collateral loss our lease-purchase analysis describes — then eliminating supply is a feature. That is a coherent position and the evidence on borrower outcomes is genuinely mixed. What is not defensible is the intermediate claim that a cap will make the same credit available more cheaply. The arithmetic forecloses it. Advocates for caps should argue that the credit shouldn't exist, which is an argument they can make honestly, rather than that it will get cheaper.

What fills the gap, and why its cost structure differs

The products that serve the sub-threshold region share a feature: they replace expensive screening with something cheaper. That is the unifying logic, and it explains the product set better than any account based on borrower vulnerability.

Product	How it avoids the fixed cost	What the borrower pays instead
Pawn	Collateral eliminates underwriting entirely — no bureau, no income, no identity risk	Loss of the item; very high effective rates
Auto title	Collateral substitutes for assessment	Vehicle loss, which is frequently income loss
Payday	Minimal verification; recovery via account access	High fees; overdraft cascade risk
Rent-to-own	Retained ownership removes credit risk — the goods are the security	Two to three times retail; no equity accrual
Earned wage access	Payroll verification is nearly free; repayment intercepted at source	Per-transaction fees; recurring use
Overdraft	Existing relationship — screening cost already sunk	Flat fees on tiny amounts, per our overdraft analysis

Two observations from reading down that middle column.

Every one is an information-cost solution, not a risk solution. Collateral doesn't reduce borrower risk — it makes assessing the borrower unnecessary. Payroll integration doesn't make the worker more creditworthy — it makes verification free. These products exist because they found a way around F, and their prices reflect what that workaround costs the borrower.

The overdraft row is the most instructive. A bank charging a flat fee on a small overdraft is the cheapest possible screening — the customer is already onboarded, the relationship already exists, and the marginal cost of the decision is near zero. That the resulting product is nonetheless expensive in APR terms tells you the fee is recovering something other than screening: it is recovering the value of a service being priced against a captive relationship. Which is the case where the exploitation account is strongest, and it's worth conceding that the fixed-cost model doesn't explain overdraft pricing well. A model that explained everything would be suspicious.

Why some interventions work and others don't

If the constraint is F, then interventions sort cleanly into those that reduce it and those that don't. This is the model's most useful output.

Interventions that relax the binding constraint:

• Cheaper verification. Consented payroll and bank data reduce origination cost directly — which is why the data access fight matters far more for small-dollar availability than for any other segment. Note what the model implies about the fee question in that rulemaking: if data access acquires a per-call price, it raises F, which raises the minimum viable loan size. The population harmed is precisely the one the access right was meant to help.
• Portable credit information, reducing duplicated assessment across lenders.
• Standardized compliance, since a fifty-state patchwork multiplies fixed cost — the fragmentation our licensing analysis documents is, in this model, a direct tax on small loans specifically.
• Relationship-based lending, where prior data makes marginal assessment nearly free — which is exactly why credit unions can offer small-dollar products that standalone lenders cannot, and why the renewal economics we've described are so favorable.
• Automation, which reduces F and s together.

Interventions that address the non-binding constraint:

• Loss guarantees and risk-sharing. These reduce λ. Return to the arithmetic: at $300, setting λ to zero still leaves a 53% break-even. A guarantee cannot fix a problem that persists at zero losses. This is the most important practical implication in the report, and it explains why well-intentioned guarantee programs aimed at small-dollar access repeatedly underperform expectations.
• Rate caps, discussed above.
• Exhortation to lend responsibly, which does not change any parameter.

The general principle: subsidize information, not risk. A dollar spent making assessment cheaper expands access at every risk level and every loan size simultaneously. A dollar spent absorbing losses expands access only where losses were the constraint — which, at small sizes, they are not.

The strongest objections

"Fixed costs are a choice, not a constant." The best objection. Lenders choose how much to spend on assessment, so F is endogenous — a lender could underwrite more cheaply and accept higher losses. True, and payday lending is exactly that solution. But the choice set is bounded below by compliance: disclosure, adverse action, identity verification, and recordkeeping are not optional, and they constitute a floor under F that no business model can go beneath. The model's claim is about that floor, and the floor is set by regulation rather than by lender preference. Which is uncomfortable, because it means consumer protection requirements raise the minimum viable loan size — a real tradeoff that deserves acknowledgment rather than denial.

"This excuses high-cost lending." It explains part of it and excuses none of it. The model accounts for why small loans carry high rates; it does not account for rollover-dependent business models, for products whose revenue depends on repeat distress, or for the overdraft pricing discussed above. A useful test: does the price track the cost structure, or does it track the borrower's lack of alternatives? Where a product's economics improve when the borrower's situation worsens, the fixed-cost account has stopped applying and something else is operating.

"Discrimination explains the gap better." These are not competing. Fixed costs determine where the threshold sits; they say nothing about whether borrowers on the same side of it are treated equally. The evidence on differential treatment at identical risk is a separate matter and the fixed-cost model neither supports nor rebuts it. What the model does add is a caution: an observed disparity in access to small loans may reflect a size threshold rather than differential treatment, and distinguishing the two requires comparing at constant loan size — which fair lending analysis does not always do.

Predictions and what would falsify this

Our house view, stated so it can be wrong:

1. Minimum loan amounts should cluster rather than distributing smoothly toward zero, and the cluster should sit near the break-even threshold implied by prevailing rate ceilings. Observable in any lender's product terms today.
2. Rate cap exit should be concentrated at small sizes. Following a cap, the distribution of surviving loans should shift upward in size, with disappearance at the bottom rather than uniform contraction.
3. Falling verification cost should lower the minimum viable size even with risk appetite unchanged. As consented data access spreads, expect minimum loan amounts to fall — and if they don't, the model is in trouble.
4. Relationship lenders should serve smaller sizes than standalone lenders at equivalent risk, because their marginal F is lower. Credit union small-dollar programs are the natural test.
5. Loss guarantees should fail to expand small-dollar supply while succeeding at larger sizes. This is the cleanest falsification test: if a guarantee program materially expands sub-$1,000 lending, the fixed-cost account is wrong.
6. Compliance additions should raise minimum loan sizes, which is the prediction we least want to be true and would most want tested honestly.

The fifth is the sharpest. If someone runs a well-designed loss-guarantee program at small loan sizes and access expands substantially, this analysis is wrong and should be discarded. We think it won't, because the arithmetic at zero losses says it can't.

The broader conclusion is unglamorous and, we'd argue, more actionable than the debate it replaces. The small-dollar credit gap is frequently treated as a moral problem about who deserves credit and at what price. It is substantially an engineering problem about the cost of making a decision. Which is good news, because engineering problems yield to investment in a way moral disagreements do not — and because the specific investment required, cheaper and more portable information about borrowers, is already underway and being litigated over on other grounds entirely.

Frequently asked questions

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This report presents an analytical model and the authors' interpretation; it is not legal, financial, or investment advice. Parameters used in the worked examples are stylized illustrations chosen to demonstrate the mechanism and do not describe any specific lender's cost structure. The predictions identified as testable should be treated as hypotheses rather than findings.