Raising Your Hourly Rate Does Not Make You Free, Because Both Halves of the Division Have Limits

Divide income by the hours worked and one value comes out: how much money each hour generated. That is the hourly rate. It lets you compare at a glance how heavy each job is, so as an instrument of management it is well made. The moment you install that figure as a target, however, time is fixed in the position of the denominator. In a division whose denominator is fixed, there are only two ways to make the answer larger. Enlarge the numerator, or shrink the denominator.

What gets offered as ways of raising it runs to seven: establishing a specialism, improving skill, becoming efficient, automating, subcontracting, standardising, starting earlier. All seven fall into one of those two. So the ratio does rise. And after it has risen, income remains proportional to the hours worked. The gradient of the proportion changed; that the relation is a proportion is not broken by any of the seven.

Three things can be settled here. Why the state of affairs at month end does not change even though you pushed efficiency through. Why the figure does not rise in proportion even though your skill did. And why the work of making something once that then goes out repeatedly never gets started. All three come out of the shape of the division rather than out of a quantity of will.

Some things cannot be settled. What share of turnover should come from income that arrives without your hands moving — that level is not given here. With different fixed costs and different living conditions, the same share means something entirely different. Nor is it decided here whether to stop the work of raising the ratio right now. In a phase where income has not reached the level that supports living, improving the ratio is the fastest-acting response there is. Nor does this cover the state in which the working itself is up against the limit of your physical stamina. That is not a problem of how to read a measure; it is a state in which the volume of work has to come down first.

And the centre of the damage does not lie where this measure produces a bad number. It lies where the measure keeps producing a correct one. In a month spent making something that goes out repeatedly, only the denominator grows while the numerator does not, so that work is displayed by the measure as the least worthwhile option available. It is not rejected; it never rises into consideration. Which is why the sequence “I will start once there is room” never reaches the day of execution.

What follows begins with how the measure decides its own range, then places the difference between an hourly rate and an hourly wage. On that basis it sorts which half of the division the list of methods touches, looks separately at the floor under the denominator and the ceiling over the numerator, and traces the sequence by which a risen ratio goes into job count. It ends with the response of adding one figure rather than discarding the measure.

A Measure Decides What Is Not Measured by Deciding What Is

At the moment you decide what to measure, the region that becomes invisible is decided along with it. This is not a defect peculiar to hourly rates; it is a property of measuring as such.

What an hourly rate measures is the money that arose per unit of time. Take this month’s turnover and divide it by the hours used to produce that turnover. Job A works out at eight thousand an hour, job B at three thousand. Once that comparison is available, judgement gets faster. As a measure it is well built.

The problem lies on the unmeasured side. Turnover that arose without your hands moving has nowhere to sit inside this measure. Its denominator is zero. Since you cannot divide by zero, turnover of that kind falls outside the totals. What falls out is not displayed, and what is not displayed does not become material for judgement.

And when the measure becomes a target, this property bites one degree harder. While it is measuring where you stand, the measure is a description of the present. The moment you install it — “this term I will bring the hourly rate up to ten thousand” — conduct rearranges itself in the direction that improves the value. Conduct that raises it is adopted; conduct that does not is not.

That rearrangement has been treated in management research for a long time. In 1956 Valentine Ridgway set out how systems that measure performance numerically produce unintended distortions in the conduct of those being measured (Ridgway, 1956, Administrative Science Quarterly, 1(2), 240–247). At the centre of it is the observation that installing a single measure leaves the work not contained in that measure systematically thin.

The point of the observation is not ill will on the measuring side. It is that replacing a measured value with a target moves the unmeasured region into the region you do not work on. The numbers stay accurate, and conduct changes to fit their shape.

Apply that to the work of making something once that then goes out repeatedly. While you are making it, turnover is zero and only time goes down. The hourly rate for that period comes out at zero or close to it. On the measure, in other words, it is displayed as the least worthwhile option available.

Had it been rejected deliberately, the reason for the rejection could be reopened. If it merely sits near the bottom of the display, the occasion for reopening never arrives. Not dropped, but never on the table in the first place. Those two look identical from outside, and what happens inside them is entirely different. The first leaves a record of a judgement; the second leaves none.

An Hourly Rate and an Hourly Wage Are Different Quantities in a Similar Shape

An hourly wage is an amount settled in advance; an hourly rate is a ratio that comes out afterwards. That difference decides the difference in how each one can be moved.

An hourly wage is an amount agreed in advance as consideration under a contract of employment. Work an hour and that amount arises; whether you finish early or late, the amount per unit does not move. To move it you have to change the agreement itself.

An hourly rate is the income of a given period divided by the time invested to earn it. It is not settled in advance; it comes out of a calculation at month end. So the same job gives a higher figure if it finishes early and a lower one if there is rework. Where an hourly-rate arrangement is spoken of, what is actually fixed in the contract is a wage or a day rate, and the hourly rate is a ratio worked back from it.

How you calculate follows from the same difference. Everything that moved for the sake of that income goes into the denominator. Meetings, travel, quoting, invoicing. Put only the production work in the denominator and the ratio comes out higher than the reality. People puzzle over how to handle fractions of an hour, but for the purpose of watching a ratio, rounding up or down matters far less than leaving something out.

Only two quantities are in this definition. Money and time. Consider what is not. Whether that income will arise again next month. What remains after the job ends. Where the next enquiry comes from. None of the three is inside the definition.

Their absence follows from the design. An hourly rate cuts out a period and measures efficiency within it. Cutting out a period means properties that span periods cannot be measured.

Look at a comparison that arises constantly in practice. Job A finishes quickly and pays acceptably. Job B takes trouble for a thin fee. Follow the measure and you increase A and reduce B. But it happens that continuing enquiries are born out of B while A ends as a one-off. Or that the material made for B becomes the prototype of the next product. That difference never appears in a comparison of ratios, so it does not become material for judgement.

There is also no distinction between kinds of time invested. Time used to get an enquiry done and time used to build the route by which enquiries arrive are both simply “time” on this measure. The former makes this month’s turnover; the latter does not. So the more time goes to the latter, the lower the ratio.

That the distinction is absent is not itself a design error in the measure. An hour is an hour wherever it goes. The slippage arises only in this: the ratio keeps no record of what that hour left behind. A quantity that is not recorded cannot be retrieved later.

All Seven Methods on Offer Touch the Inside of the Division

Sort the seven and they divide into shrinking the denominator and enlarging the numerator. Not one of them touches the outside of the division.

Shrinking the denominator: efficiency, automation, subcontracting, standardisation, starting earlier. Produce the same result with less of your own time. Enlarging the numerator: establishing a specialism and improving skill. Receive a higher amount for the same time. Both make the ratio larger.

This is not a criticism. Given that they are offered as ways of raising an hourly rate, touching one half of the division is what you would expect. A method that improves a measure by touching that measure’s own components is logically sound. What is worth establishing is the range over which the list holds.

All seven genuinely work. Become efficient and time goes down; establish a specialism and the amount goes up; take-home pay increases. Denying that is contrary to fact. But consider the state that remains after all seven have been worked through. The denominator is down as far as it goes and the numerator is up as far as it goes. What decides income then?

It is still decided in proportion to the hours worked. The coefficient got bigger. That the relation is a proportion is nowhere broken. So the question left after executing the seven has the same shape as the question before. Work more and you earn more. While that relation holds, turnover in a month where the work stops is thin.

Here is one option that the list does not contain. The option of handing something over in a form that does not require your time each time it is handed.

Its absence from the list is not an oversight by whoever wrote the list. It is that taking that option makes the hourly rate itself uncomputable. Turnover whose denominator is zero cannot be handled by this framework. So while the question is “how do I raise my hourly rate”, it cannot enter the field of candidate answers.

The way the question is put has already decided the range of the answer. What lies outside is not rejected as incorrect; it is never printed on the answer sheet at all.

Even among the seven, how they work differs. Methods that shrink the denominator take effect in the month you start them; methods that raise the numerator take time to arrive. So the denominator side gets chosen first, and the denominator side, holding a part that no tool or sequence can cut, hits its floor first. Because of the order, you begin with the methods that reach their floor soonest.

And when the floor is reached, what gets doubted next is not the methods. It is the person who executed the seven. The list does not state the range over which it holds, so the only place left to put the reason for the loss of effect is the quantity of one’s own effort. That is where the damage begins.

The Denominator Side Keeps a Floor

Time that can be cut has a bottom. Its position differs from person to person; that there is one does not.

Strip out wasteful steps, get the tools together, put the sequence in order. This far, it comes down steadily. Then past a certain point, what can be cut runs out. What remains is the time to hear what the other party is dealing with, the time to understand the situation, the time to think about how to handle it. That part does not get shorter with better tools. The more the periphery is cut, the larger the share held by what cannot be.

The account of why that part remains sits on the economics side. It is a distinction between a region where the operation called productivity reaches and a region where it cannot in principle. That distinction, and the consequence for costs that follows from it, are treated in why raising productivity does not leave you with free time. Only the conclusion is needed here. The denominator does not go to zero.

Among the methods for shrinking the denominator, subcontracting looks like the only one that can break through this floor, because results arrive without your time being used.

But subcontracting takes your time in another form. Finding whom to hand it to, conveying the requirements, checking what comes back, asking for corrections. This time is not easily booked to the job’s own working hours, and it certainly occurs. It also grows in proportion as volume grows.

What subcontracting reduces is working time, not judging time. And judging time can only be housed inside yourself. So subcontracting lowers the floor under the denominator and leaves the floor itself in place.

Subcontracting also has a property that pushes the denominator back up. As volume grows the number of people you hand to grows, and as that grows you need the grain of what you convey to be consistent. You make material to make it consistent, set standards for checking, and correct mismatches of understanding. The larger the scale, the larger this cost.

Check it with numbers. Take a month of a hundred and sixty working hours and put twenty of them into building routes. With turnover unchanged, the denominator goes from a hundred and forty to a hundred and sixty and the ratio drops by roughly a tenth. On the measure, those twenty hours are booked as a loss. Whether the route got thicker is nowhere in that calculation.

And when an enquiry arrives from that route the following month, the ratio does not distinguish where it came from. Where an enquiry came from appears in neither the numerator nor the denominator. The side that was invested looks like a loss, and the side that was recovered is booked anonymously. Put those two together and route-building is displayed on the measure, permanently, as work that does not pay.

The Numerator Side Has a Different Ceiling

The numerator can be raised. How far, though, is settled in advance on the side of that field’s standard level.

Raising the numerator means receiving a higher amount for the same time. Establish a specialism, improve skill, move into a field with a higher going rate. That does happen. But look at how the amount is decided and the constraints on raising it become visible.

The level of the numerator is decided on the side of what it costs to make that working capacity available again, not as a result of dividing up the profit generated. How that works is treated in getting out of labour-intensive form, so only the one point that bears directly on the numerator is taken here.

That point is this: the relearning needed to keep up is included in the consideration from the outset. Continuing to learn is already counted in as a premise, so having caught up is not an addition on top. What has an effect is the deduction for not having caught up.

From here, one phenomenon can be explained: skill rises and income does not rise in proportion. The numerator moves only when the standard level of that field itself has moved. The fact that you improved more than others does not touch the standard.

There is also a side effect: raising the numerator increases the denominator. In fields with higher rates, the preparation demanded per job gets heavier. Prior research, working up the proposal, the grain of reporting. These go into the denominator. Raise the numerator and the denominator rises too. As a ratio it does improve, but the improvement comes out smaller than the estimate made by looking at the numerator alone.

Here is the awkward property of this measure. The numerator and the denominator are not independent. Move one and the other moves. So improvement in the ratio advances more slowly than expected.

The numerator side also has a constraint coming from the buyer. Plenty of people feel that the volume of working time invested decides the price — three days’ work must be worth more than one day’s. But the buyer’s willingness to pay is not looking at how many days it took you. It looks only at what happens to them by having it. That something taking ten times as long to make does not sell for ten times as much is not because buyers are in bad faith. The volume put in and the worth to the other party are simply different quantities.

Lay the two together and the character of the numerator becomes clear. The numerator can be raised, and it does rise. But what rose is the level on the standard’s side; the form in which you receive has not changed. While the form is the same, the numerator has a ceiling coming down from the standard.

The Sequence by Which a Risen Ratio Goes into Job Count

What efficiency produces is not free time but capacity to take work. Capacity, if empty, gets filled.

Watch what happens one step at a time. Say efficiency halves the time per job. In principle you can then choose between halving your working hours and doubling the number of jobs in the same hours. In practice it tends to be the latter.

Explaining that as a problem of will is not accurate. Look at the conditions of the choice and the latter is what gets selected.

First, inside a form where income is tied to hours worked, filling empty capacity is always rational. Fill it and turnover rises; leave it and turnover falls. Judge job by job and filling tends to win. Second, you do not decide when enquiries arrive. So capacity has to be kept clear in order to accept them when they come, and capacity kept clear gets filled when they do. Third, right after a rate rise, the grounds for declining are at their weakest, because the enquiry arriving is on better terms than before.

With those three in place, the room created by efficiency gets filled as fast as it is created.

I lived through the same thing during the period when music was my work. What I was making was the kind of composition whose terms are settled beforehand. The more I put the process in order, the shorter the time per piece became, and the number of pieces I took grew by exactly that much. The measure improved and the state of affairs at month end did not change. However much the ratio improves, if the time in the denominator is full, the absolute quantity does not move.

At the time I took this as a matter of drawing my lines too loosely.

It is not a matter of drawing lines. The occasion for judging whether to fill the capacity never actually arrived. At the point an enquiry came, no grounds for declining were in view. It is not looseness of judgement, but absence of the occasion for it.

Choosing not to fill empty capacity is possible. There are people who have reduced their hours without increasing their job count. That choice, though, comes coupled with a decision to accept a fall in turnover. So without slack on the living side, it cannot be executed.

That is what saying it is not a matter of will means. Not that you cannot choose, but that the conditions for choosing are somewhere else. Decide “I will draw my lines more strictly” without meeting those conditions and you are back in the same place next month.

The range over which this sequence holds extends as far as a state where enquiries arrive continuously. In a phase where the enquiries themselves are lacking, empty capacity does not get filled and room is produced in excess. The task then is not the destination of capacity but the route by which enquiries arrive.

This Can Look Like an Argument for Discarding a Useful Measure

Measuring and installing as a target are different acts. Only the second is treated here.

Running a business without knowing how much money your work generates per hour means judging without material. Knowing the ratio per job tells you where time is being absorbed and gives grounds for pricing. This is not an argument that measuring should stop.

While you are only measuring, an hourly rate is a description of where you stand. A description does not govern conduct. On finding that some job’s ratio is low, you can reduce that job, or continue it if it carries worth of another kind. Judgement sits outside the measure. Install it as a target and this relation inverts. Conduct rearranges itself in the direction that improves the measure, and judgement moves inside it.

It cannot be said that installing it as a target is always an error. At a stage that has not yet reached the level a life runs on, raising the ratio acts fastest, and installing it as a target is appropriate in that phase. The work of changing the form cannot even be begun unless living is already covered.

What is being stated is which of the two comes first. Improving the ratio does not, by itself, become a terminus. After it has been improved to the end, the proportional relation remains as it was. So the work of breaking the proportion has to begin in parallel while the ratio is being improved. And that parallel is hard precisely because the hourly rate keeps displaying the work to be begun in parallel at the bottom of the list.

This objection has a variant worth answering. That once the ratio is high enough, room will appear in due course and the work of changing the form can be begun then.

When the ratio rises, empty capacity gets filled. Once filled, no room appears. So the sequence “start once there is room” keeps postponing the moment of starting, unless it contains the conditions under which room appears.

There is only one such condition. Deciding in advance not to fill the empty capacity. That is not obtained automatically by improving the ratio; it has to be decided independently of the ratio. As a sequence, then, it means deciding the destination of the improvement in advance rather than waiting for the ratio to improve.

There is another variant: that people with high ratios do visibly look free. Sometimes they are. But whether that freedom comes from the ratio or from turnover that arises with their hands stopped cannot be told apart from outside. The same shape of life comes out of two different structures. So when taking someone else’s state as a model, what you look at is the composition of their turnover rather than their ratio.

What Spans Periods Is Placed Outside the Measurement

An hourly rate measures flow, and what accumulates is the balance. The side being measured and the side that accumulates are separate.

What the measure does not cover comes to three. Turnover that arose without your hands moving. The effect this month’s work leaves on the months after. Whether the route by which enquiries arrive got thicker. What the three have in common is that they span periods. A measure that cuts out a period cannot cover them.

The same explains why the unease about next month does not go when income rises. The cause is not the smallness of the amount but being inside a form where this month’s result does not carry over into next. So it does not go when the amount rises. What rose is this month’s flow, not the balance that has accumulated.

And this measure has no mechanism for telling you that a limit is approaching. A ratio can be computed however full your hours are. Twenty hours a week or sixty, it comes out in the same shape. Watching the value alone, you cannot tell that you are near the limit. You find out when you reach it.

The number being measured keeps improving while the state of affairs deteriorates. That combination holds because the measure sees only part of the state.

One more thing is outside. The concentration of dependence. Whether eight tenths of turnover comes from one client or is split across five, the ratio computes the same way. From the side of the ratio the two come out as the same value. What happens in a month where one client stops, though, is entirely different.

And spreading it does not change the ratio either. Spreading lowers the simultaneity of dependence and leaves untouched the form of moving on receipt of enquiries. In this case the measure’s failure to respond is correct behaviour. Since the form has not changed, a measure of the inside of the form not moving is what you would expect.

Something can be read backwards from this. A response that left the hourly rate unmoved has probably not touched the form. That is usable as a test. After changing something, if neither the ratio nor the turnover that arises with your hands stopped has moved, then what moved was only an arrangement inside the form.

The test comes with a limit attached. The work of changing the form moves neither number in the month you begin it. While you are making the thing, only the denominator grows and the second number is still zero. So the month right after starting looks the same as not having touched the form at all. They separate once what was made actually starts going out.

Which is why the test cannot be used on a single month. It is usable as a comparison after the same response has continued for several months. Applied to a single month, it misreads the month of starting as not working.

Put a Second Number Alongside

The response is not to discard the hourly rate. It is to hold one more number that measures what spans periods.

Discard it and material is lost. The ratio is useful for grasping where you stand. What gets added is a number covering the region the ratio is structurally unable to see.

The simplest form is to split this month’s turnover in two. What arose because your hands moved, and what arose without them moving. Record the amount of the second and its share, every month.

In most cases the second is zero at first. A zero is not a mark of being behind. Knowing that it is zero is what matters. While the hourly rate was the only thing being watched, the very fact of its being zero was not displayed anywhere.

An hourly rate cannot handle turnover whose denominator is zero. So whether such turnover has come into being has to be seen somewhere other than in the hourly rate. And the second has one property the hourly rate lacks. Installed as a target, it does not strengthen the proportional relation. Make the hourly rate the target and conduct that puts time in the denominator gets selected. Make turnover-without-hands the target and conduct that takes time out of the denominator gets selected.

This number carries a cost. The second number barely moves at first. Some months the same zero as last year lines up. Recording a number that does not move looks pointless. And because the fact that it does not move meets your eye every month, in the early period the record itself feels heavy.

Yet the fact that it does not move is precisely the information not displayed while the hourly rate was watched alone. An hourly rate fluctuates monthly, so it looks as though something is moving. Only with the second alongside does it become visible that what moves is the flow and the balance does not. Line up a year and the contrast is sharper still: one column goes up and down, the other stays flat.

Why does raising an hourly rate not make you free? Because what is being raised is the coefficient of the proportion, not the proportion. While time sits in the denominator, however far the coefficient goes up, turnover in a month where the hands stop is thin.

And the work of raising the ratio was not wasted either. A risen ratio is the funds that buy the time to make the second number. With a low ratio, the twenty hours for route-building cannot be taken at all. So the sequence is not abandoning improvement of the ratio in order to move to form, but deciding in advance where the improvement goes. The question of which column you want to move can only be asked once the two stand side by side.

How the first form and the second differ concretely, and where the material for the second is taken from, are broken down in what to know before earning on your own: the ceiling on selling time. The mechanism by which efficiency gets absorbed into job count is treated in why raising productivity does not leave you with free time, and where the level of the amount is decided is in before negotiating a rate rise, know how the amount is decided. The hourly rate is a tool on the measuring side of the ceiling on income and how figures get decided. The structure being measured is taken apart in getting out of labour-intensive form.