Chapter 17
The Price of Externalization: Platform Fees

17.1 The implication tested

The claim of the previous section — that the price of externalization is a transfer of ${\varphi }_{\mathit{𝑏𝑎𝑟𝑔}}$ — can be tested directly. Following the discipline of Part III, the implication was fixed before the survey.

Registered implication: a platform’s fee rate increases monotonically in the number of terms the platform absorbs.

The alternative is stated explicitly: fee rates are set by market power rather than by the functions absorbed. That is, the very decomposition of Chapter 6 into ${\varphi }_{\mathit{𝑝𝑟𝑜𝑑}}$ and ${\varphi }_{\mathit{𝑏𝑎𝑟𝑔}}$ is at issue.

Two comparisons were specified in advance for identification.

(1)

Same function, different scale. If the rates are close, the function account holds; if they differ greatly, the market-power account does.

(2)

Differences in rate within one operator. Whether there is a difference the function account cannot explain.

This survey falls under none of the obstacles of Section 13.2: the price lists are public, and neither per-firm data nor confidentiality is involved.

17.2 Result: a ladder of rates

Effective rates were computed for a $50 transaction. Where payment processing is charged separately, 2.9%$+$$0.30 is added.

The same ordering is shown in Figure 17.1.

The ladder is broadly monotone. Stripe absorbs payment only, at a flat 3.6% for domestic cards, debit, wallets and convenience-store payment. The merchant-of-record providers Paddle and Lemon Squeezy charge 5%$+$50¢ and collect and remit sales tax in more than 200 jurisdictions. The increment from Stripe to a merchant of record can be read as the price of $T_{\mathit{𝑖𝑛𝑠𝑡}}$. For an individual selling into Europe, the alternative is registering for VAT in each country or paying an accountant monthly, so a price of 1.4–2.4 points is consistent with a return to function.

17.3 A natural experiment within one platform

This is the most important observation. Gumroad’s 30% Discover fee applies only when the customer arrived through Gumroad’s marketplace; purchases through one’s own link or an external route are charged the standard 10%. Discover can also be switched off.

The same platform, the same market power, the same other functions. The only difference is whether $T_{\mathit{𝑎𝑐𝑞}}$ was supplied.

$$\text{price of }{T}_{\mathit{𝑎𝑐𝑞}}=20.0\text{points}$$

(17.1)

The market-power account cannot explain this difference: one and the same firm charges the same customer different rates according only to whether it performed the acquisition. Equation (17.1) is the strongest evidence for the implication.

Moreover the standalone price of $T_{\mathit{𝑎𝑐𝑞}}$, 20 points, exceeds the sum of all the other items (about 11 points, from 3.6% to 14.5%). Customer acquisition is the most expensive item to externalize. The judgment in family 6-4 that $T_{\mathit{𝑎𝑐𝑞}}$ is the dominant component is supported in direction.

17.4 A counterexample: price discrimination by size

At the same time, a case the function account cannot explain was obtained.

The App Store Small Business Program cuts the fee from 30% to 15% for developers earning under one million dollars a year. Paid apps, in-app purchases and subscriptions are all covered.

The functions supplied are exactly the same and only the rate differs, by a factor of two. A 15-point difference cannot be a return to function; it is price discrimination by size.

The circumstances of its introduction are also suggestive. The programme was announced in 2020, when antitrust actions by the US Department of Justice and the European Commission coincided with the dispute with Epic Games. Pressure from the institutional layer moved the rate.

17.5 Verdict

In the decomposition of (6.1), the level of platform fees can therefore be written

$${\varphi }_{\text{fee}}=\underset{20.0\text{pt}}{\underbrace{{\varphi }_{\mathit{𝑝𝑟𝑜𝑑}}}}+\underset{15.0\text{pt}}{\underbrace{{\varphi }_{\mathit{𝑏𝑎𝑟𝑔}}}}$$

(17.2)

the first from the within-platform comparison on Gumroad and the second from the App Store’s two size tiers. This is the only case in this text where two of the three components were separated numerically for a single transaction.

17.5.1 The risk component: untested

For the second term of (17.3), an implication follows from Proposition 2.9.

As Remark 2.10 states, the limit of (2.11) bottoms out at $\rho {\sigma }^2$. An intermediary can pool away risks that are independent within an industry but cannot remove the part correlated through a common factor.

Proposition 2.9 assumes $\rho$ does not depend on $n$ (Remark 2.11). If an intermediary takes on industries with higher correlation as it adds merchants, $\rho$ rises and the effect appears more strongly than stated here. Dropping the assumption does not change the sign.

Registered implication: differences in payment-processing rates across industries correspond not to the mean chargeback rate $\mu$ of the industry but to the within-industry correlation $\rho$. An industry with a merely high mean can pass the cost through, whereas an industry structured so that the whole of it deteriorates at once requires an additional premium.

This splits the explanation “the rate is high because the risk is high” in two. Whether the high rates for information products or travel are due to an average incident rate or to the whole industry deteriorating together has different implications for the design of $\mathrm{\Phi }$: the former can be passed through in price, the latter cannot.

Testability is constrained as set out in Remark 17.3.

In the three-way decomposition of Chapter 6, a fee contains both ${\varphi }_{\mathit{𝑝𝑟𝑜𝑑}}$ (the functions actually performed) and ${\varphi }_{\mathit{𝑏𝑎𝑟𝑔}}$ (transfer), and Gumroad’s design gave the means of separating them.

This is consistent with the durability claim of Section 6.3: the part deriving from market power is eroded by the institutional layer. The App Store’s cut from 30% to 15% was a product of regulatory pressure, whereas the part deriving from function (Gumroad’s 20 points for acquisition) has not been eroded.

17.6 Practical implications

Prices now enter the launch strategy of Chapter 8.

Each term of (8.11) now carries a price. Only acquisition is an order of magnitude more expensive: $T_{\mathit{𝑎𝑐𝑞}}$ alone at 20 points exceeds the sum of all other items (about 11 points). The guidance follows that $T_{\mathit{𝑎𝑐𝑞}}$ is often better done in-house. Placing the “publish and build credit” stage first in the transition across families in the previous chapter was an investment of time in doing $T_{\mathit{𝑐𝑟𝑒𝑑𝑖𝑡}}$ and $T_{\mathit{𝑎𝑐𝑞}}$ oneself. Against a price of 20 points, that investment of time is readily justified.

17.7 Limits of the measurement

The rates cover only major platforms in Japan and the United States, and no population was declared. By the discipline of Section 12.9 this is a comparison of cases, not an estimate. The within-platform comparison on Gumroad is an identification that does not depend on the population, however, and that part alone is robust.

Effective rates also depend on transaction size. Because of the fixed components (50¢, 30¢), the effective rate of merchant-of-record models rises at low transaction values. The table is computed at $50.

17.8 How the institutional layer acts

Section 6.3 stated that the ${\varphi }_{\mathit{𝑏𝑎𝑟𝑔}}$ deriving from market power is eroded by the institutional layer. This section checks how it acts, in four cases.

Capping a rate is rare, and the trend is towards abolition. Securities commissions were liberalized above 1bn yen in 1994, above 50m in 1998, and entirely in October 1999. The United States did the same in 1975 and the United Kingdom in 1986.

In property brokerage the cap can be seen to bind. The July 2024 amendment raised the cap for properties up to 8m yen from 180,000 to 300,000 yen, and the stated background was that 247 municipalities — 14% of the total — had no licensed brokerage at all, and that the business was not viable at the existing commission. Supply disappeared because the cap was too low, which is direct evidence that the cap binds.

17.9 Assessing feasibility of further investigation

The result of applying the taxonomy of Section 13.2 to the other questions of this chapter is recorded here.

17.9.1 Runner-up: decomposing ${\lambda }_{\mathit{𝑛𝑜𝑣𝑒𝑙}}$

${\lambda }_{\mathit{𝑛𝑜𝑣𝑒𝑙}}$ can be decomposed, and its components map onto the layers of Section 6.3.

Public data exist for three of the four, and an implication follows.

Registered implication: the fewer the dependencies in a configuration, the smaller ${\lambda }_{\mathit{𝑑𝑒𝑝}}$ and the longer unmanned operation can run.

This bears directly on design decisions: if unmanned operation is the aim, few dependencies should be preferred to rich functionality. Connecting a measurement of $\lambda$ to cessation events must be built oneself, however, and that is where the work concentrates.

17.9.2 Questions abandoned

Direct measurement of the unmanned operating period lacks a population frame for this chapter’s objects. No list of solo-developed services exists, and collecting those that stopped after the fact reproduces the conditioning on survival of Section 12.2 exactly.

The abandonment is specific to the objects, however. In the “inside” partition of Chapter 10, the protocol record is itself the population, and duration and cessation rates can be measured on the full population (Section 18.3). What cannot be measured is solo-developed services, not the unmanned operating period as such.

Transitions between families are similar. Cases that transitioned can be collected, but cases that did not and cases that failed cannot be observed, so nothing can be said about the effectiveness of the route.

The rate of unmannedness itself is an ill-posed proposition. Defining what fraction of $\delta$ is automated requires a unit for $\delta$, and none exists. The defect has the same form as that of the measurability hypothesis in Section 15.3.5.0.

17.10 Limits of this chapter

(1)

${\lambda }_{\mathit{𝑛𝑜𝑣𝑒𝑙}}$ was not measured. Estimating the unmanned operating period depends on that value, and there is no basis for it.

(2)

Chapter 17 is a comparison of cases with no declared population. Apart from the within-platform identification, it must not be treated as an estimate.

(3)

The implication registered in this chapter states the same relation as one registered in Chapter 10. This was not noticed at the time of registration. The test of $\mathrm{\Phi }$1 rejected it (Section 18.2). It was not tested on this chapter’s objects.

(4)

${\lambda }_{\mathit{𝑛𝑜𝑣𝑒𝑙}}$ was not decomposed into its four components. What Section 18.3 measured is the rate of response, not a breakdown by component.