Product × Finance × AI: Financial Products in the Age of AIPart Three AI: how much an agent can do on people's behalf中文
Chapter 19

The amplification factorHow much an AI agent actually saves people

Data as of October 2026

The original meaning of "agent" is someone who acts for another. Handing a task to an AI agent is the same relationship as hiring someone to do a job, seeing a doctor or giving money to a fund manager: what is handed over is the right to act, and the result appears only afterwards, under asymmetric information. Whether the relationship is worth it is measured in the principal's own time. On that measure, every setting that has been tested in a rigorous randomized controlled trial shows an observed amplification factor of only about 1.0–1.2×, far below the theoretical range. The gap does not come from models being too slow. It comes from three places: the scope in which the agent applies is limited, checking the result takes time, and errors have to be reworked.

1. An agent is, originally, someone who acts for another

The original meaning of "agent" is someone who acts on behalf of another. When one party hands a matter to another to handle and grants the corresponding authority, a principal–agent relationship is formed: the party handing over the matter is the principal, and the party handling it is the agent. Ross (1973) posed this as a general economic problem, and Jensen and Meckling (1976) used it to analyse the relationship between shareholders and managers.

The principal–agent relationship is one of the most basic forms of human cooperation. Employer and employee, patient and doctor, client and lawyer, investor and fund manager, voter and representative: all involve one person acting for another. Human cooperation has two other basic forms. One is exchange: buying and selling something that already exists, which ends at delivery, with a result that can be verified on the spot. The other is joint production: several people completing something together, where the difficulty lies in measuring each person's contribution (Alchian and Demsetz, 1972). What sets the principal–agent relationship apart from both is that what is handed over is the right to act, and the result appears only afterwards, under asymmetric information. A user handing a task to an AI agent belongs to this form: what the user hands over is not a finished thing but something to be done on the user's behalf.

Three basic forms of human cooperation

Pick a form to see what is handed over, when the result can be verified and where the difficulty lies. A user handing a task to an AI agent belongs to the third.

The difficulty of joint production is from Alchian and Demsetz (1972); the principal–agent relationship is from Ross (1973) and Jensen and Meckling (1976).

2. The structure of the principal–agent problem

The principal–agent problem has two roots. The first is asymmetric information: the principal cannot fully observe the agent's ability and conduct. The second is conflicting goals: the two parties' aims and interests are not fully aligned. Together they produce two classic problems. Before the handover, the principal cannot see the other party's ability clearly and may choose the wrong one; this is called adverse selection. After the handover, the principal cannot see the other party's conduct, and the agent may shirk or serve itself; this is called moral hazard. The price the principal pays for this is called agency costs, which Jensen and Meckling divide into three parts: the principal's monitoring expenditure, the bonding expenditure the agent incurs to win the principal's confidence, and the residual loss that still cannot be removed.

The remedies fall into three groups. First, raise observability, so that the principal can verify what the agent did and on what basis. Second, bring about incentive compatibility, so that the agent's self-interested behaviour also serves the principal's interest. Third, cap losses and make responsibility clear, for example with a limit enforced by the system: it does not narrow the first two gaps, it only caps the loss. AI agents face the same two roots. The principal can hardly see the limits of an agent's ability or the actual basis of its actions directly, and the agent acts according to its training objective and the provider's rules, which may not match what the principal intends at this moment.

The structure of the principal–agent problem

Two roots produce two kinds of problem, and the principal pays agency costs for them. Pick a type of remedy to see what it targets.

PrincipalHands over task and authority
Hands over the task, grants authority
Asymmetric informationAbility and conduct are hard to seeConflicting goalsInterests are not fully aligned
Performs and reports
AgentActs for the principal
Before the handoverAdverse selectionAbility is hard to see, so the wrong party may be chosen
After the handoverMoral hazardConduct cannot be seen, so the agent may shirk or serve itself
Agency costs MonitoringThe principal verifies what was done BondingBorne by the agent to win confidence Residual lossThe part that still cannot be removed

The three-part division of agency costs is from Jensen and Meckling (1976); the three types of remedy are the author's grouping. The lengths of the cost bars are illustrative only.

3. A definition: whose time is saved

When a renovation crew redoes a kitchen and the workers spend ten days on it, the homeowner does not save ten days: the homeowner still has to explain what is wanted, inspect the work along the way, and arrange rework when problems turn up. Whether it is worth having someone do the job is measured by how much the homeowner's own input falls, not by how fast the workers are. The same holds for AI agents. This chapter defines the amplification factor as:

The principal's input to do the task aloneThe input the principal still spends after handing it to an agent

The denominator has three parts: explaining the task, checking the result and reworking errors. How long the agent itself runs does not count towards the denominator. The figures common in promotion do the opposite: they compare a person's working time with the agent's running time.

Two measures, fifty times apart

The same report: written yourself, it takes 8 hours; handed to an agent, the agent runs for 2 minutes, but the principal still has to explain, check and rework.

Do it yourself
480 minutes
Hand to agent
Agent runs 2 minutesExplaining the task 15 minutesChecking 60 minutesRework 30 minutes

Illustrative figures. The vendor's measure compares a person's working time with the agent's running time; this book's measure compares the principal's input to do the task alone with the input the principal still spends after handing it to an agent.

4. Is it worth doing: how much is saved over a year

The amplification factor answers only how much is saved each time. Whether a task is worth handing over also depends on how many times a year it occurs, and on whether handing it over makes possible something that could not be done before. Put the three together and you get the annual value of delegation:

Annual value of delegation = opportunity cost per occurrence × (1 − 1 ÷ amplification factor) × occurrences per year + capability extension + better results

The first term is time saved. At an amplification factor of 2×, half of each occurrence is saved; at 5×, 80%; at 50×, 98%. Beyond about 5×, a higher factor barely changes the share saved, and the saving is determined mainly by the input per occurrence and the number of occurrences. The second term is capability extension: what an ordinary individual could not do before and can do once the task is handed over, such as continuously reviewing large amounts of information, or carrying out an analysis that needs specialist skills. The third term is better results: the part done better than one would do it oneself.

This calculation carries an implicit premise: the agent's output is as good as what the principal would have produced. It is therefore a nominal value; how much of it is realized depends on whether the result can be checked and how severe the consequences of an error are.

How much is saved over a year

Adjust the time to do the task yourself once, how many times a year it occurs and the amplification factor, and see the time saved in a year. The curve is the share saved each time: beyond about 5×, it barely rises.

Saved in a year

Time saved in a year = time to do the task yourself once × (1 − 1 ÷ amplification factor) × occurrences per year; capability extension and better results are not shown. The times and frequencies of the three examples are illustrative. The daily portfolio check counts trading days.

5. How much it could amplify in theory

First assume that the agent completes the task fully and correctly every time, and that the principal only has to explain and check. Under this ideal condition, a theoretical range can be estimated type by type: the input to do the task oneself has a range, the input after handing it to an agent has a range, and pairing the ends gives the lower and upper bounds of the factor.

How the theoretical range is calculated

Take a medium-sized development ticket as the example, and assume the agent never errs and the principal only has to explain and check.

Do it yourself Half a day to 3 days Hand to agent Brief + review + confirm Low: 240 ÷ 120 = 2× High: 1440 ÷ 40 = 36×
The horizontal axis is the principal's input in minutes, on a log scale. The lower bound pairs the least input to do the task yourself with the most input after handing it to an agent; the upper bound does the reverse. The theoretical ranges of other types of delegation are estimated the same way.

Estimated the same way, the theoretical ranges of common types of delegation lie mostly between 2× and several tens of times. These figures are upper bounds; they assume that the agent never errs and that the principal only spot-checks.

6. How much is observed

In the past two years, randomized controlled trials of delegation have appeared in four fields, programming, clinical notes, customer service and security alerts: the task is actually handed to an agent, and the total input of the principal or team is then measured. Apart from security alerts, the observed factors are all about 1.0–1.2×. Studies in which a person leads and AI assists find similar results. Measured in working time, surveys of employed people in the United States and Denmark show that those who use generative AI report saving about 3%–5% of their working hours; counting those who do not use it, all employed people in the United States saved only about 1.4% of working hours.

Theoretical ranges and published measurements

Log scale. Tap any row to see the source study.

Tap any row to see the source study and how it was measured.
Theoretical ranges are estimated as "the principal's input to do the task alone ÷ the principal's input when the agent performs fully and correctly". Among the measurements, solid dots are randomized controlled trials of delegation, hollow dots are studies in which a person leads and AI assists (used as a proxy), and diamonds are vendor self-reports or model self-estimates (which leave out the principal's checking).

Vendor self-reports and models' own estimates mostly run at 3–20×, several times to an order of magnitude above the observed figures, and the reason is precisely the difference in measure: they compare only the agent's running time. The one case that falls within the theoretical range, security-alert triage, is a single, batch-processed task, and about 80% of the gain comes from the agent automatically closing reports that are plainly harmless, a kind of judgement whose correctness is easy to verify afterwards.

7. Where the gap comes from

After a task is handed to an agent, the principal's input consists of three pieces:

  1. The part the agent cannot do is still done by the principal. In Taobao's customer service, the agent applied to only 5.8% of sessions; ambient clinical-note tools were used in only about 30% of visits (Lukac et al., 2025, preprint data).
  2. The cost of checking. In OpenAI's GDPval evaluation, an expert took on average 109 minutes to review one piece of model output, about a quarter of the time needed to do it oneself. This alone caps the amplification factor at about 3.7×.
  3. Rework after errors. Leading legal research tools gave wrong or unsupported answers on 17%–33% of queries; of the agent-written code submissions that were eventually merged, about 45% still received additional human edits before merging (Watanabe et al., 2025). The strongest current models can complete, with 80% confidence, tasks of about 1–3 hours, while a single development ticket often takes half a day to three days.

Breaking down the amplification factor

Take the input to do a task yourself as 100, adjust three factors, and see how much the principal still has to put in.

The share of the work that can be handed to the agent; the rest is still done yourself
Time to explain the task and check the output, as a share of the time to do it yourself
The probability the agent gets it right the first time; when it is wrong, the principal must redo the work
Amplification factor
—
Do it yourself
Hand to agent
Agent not applicable, still done yourselfExplaining and checkingRedoing after errors
Principal's input = (1 − applicable share) + applicable share × [checking cost + (1 − success rate)]; the amplification factor is its reciprocal. For simplicity, the model assumes the principal redoes the work from scratch after an error; in practice rework may be less, or more if the error is found late. Of the presets, "Vendor demo" and "Expert checks every item" correspond to the measures cited in the text; "Real deployment" uses illustrative values drawn from the studies in the text, not measurements from any single study; "Programmatically verifiable" illustrates tasks such as code migration, whose results can be checked automatically by compilation and tests, so the checking cost is low and the applicable share is wide.

Broken down this way, the conclusion is direct: making the agent generate faster barely changes the result; what really determines the factor is the cost of checking and reliability. Code migration is a counter-example: its results can be verified by compilation and automated tests, and the 2–14× that companies report falls broadly in the lower half of the theoretical range. This is exactly the monitoring expenditure among agency costs: the harder an agent is to monitor, the less delegation saves.

8. Implications for product design

Each mechanism in this chapter corresponds to one design requirement.

Chapter summary: six requirements for designing agent products

Each corresponds to one mechanism in this chapter.

Principal–agentTreat agency costs as a design object

Let the principal see what was done, align the agent's interest with the principal's, and cap losses with hard limits.

MeasureMeasure value by the principal's input

Ask how much less time the principal spent and how much checking it took, not how fast the agent finished.

Annual valueStart with tasks that are frequent and costly each time

Beyond about 5×, how much is saved depends mainly on the input per occurrence and the number of occurrences; capability extension is counted separately.

BreakdownCut checking costs before chasing generation speed

Give the basis and sources, flag key assumptions, highlight what changed, and automate whatever checks can be automated.

VerifiabilityStart with tasks whose results can be verified

Hand the agent first the tasks where the cost of error is manageable; keep human confirmation for those that are hard to verify or whose errors are irreversible.

Scope of applicationFirst widen the scope the agent can take on in full

When the agent covers only a small part of the work, the rest is still done by the principal, and the overall factor stays low.

Scope and limitations

References