Economies of Scale and Scope Compared, and Where Scale Stops

Scale is one product spread over more units. Scope is one plant spread over more customers or more products. Anjani Stationers Private Limited's fixed cost is Rs 29.60 a register at 2,50,000 and exactly Rs 18.50 at its rated 4,00,000, so filling the works is worth Rs 11.10 a register. Beyond 4,00,000 the base steps up instead of spreading further.

Two words share a root and are treated as one idea by almost everybody who uses them. Scale and scope are not one idea. The two divide by different things, they arrive from different directions, and a business can be swimming in one and have none at all of the other. The two come apart under arithmetic that can be checked line by line, on one published cost base divided twice.

Anjani Stationers Private Limited, an invented manufacturer, makes a hard-bound register of 200 printed sides. Its published year runs 2,50,000 registers at Rs 108.00 each, or Rs 2,70,00,000/- of revenue; contribution of Rs 46.20 a register, or Rs 1,15,50,000/- in total; a fixed baseThe block of cost a business carries at much the same size in a slow year and a rushed one. Rent, salaries, insurance and supervision sit inside it. One register fewer shrinks none of them. of Rs 74,00,000/-; and, at the foot of it all, Rs 16.60 of operating profit a register, or Rs 41,50,000/- for the year. Every one of those per-unit figures multiplies back to its published total exactly, and multiplying back is the only thing that entitles a per-unit figure to exist at all. Rs 46.20 less Rs 29.60 is Rs 16.60, a subtraction anybody can repeat. Chitra Binding Works Private Limited, a second invented business, is a separate binding plant. The plant binds registers for Anjani Stationers and for other customers too, and its published profit for the year is Rs 10,00,000/-.

What does the arithmetic rest on?

Three things. Everything downstream is only as good as these three are, so they are worth naming before any dividing starts.

First, an arithmetic fact: a cost that does not move with volume gets smaller for each unit as volume rises, and on paper it does that forever. There is nothing clever in it. Rs 74,00,000/- divided by a bigger number is a smaller number, and it carries on being a smaller number no matter how big the divisor gets. The endless division is why the idea feels so satisfying and why it is so easy to over-believe. Arithmetic never runs out of room.

Second, a physical fact: a works has a rated output set by its slowest stage, and past that output the business does not make more units on the same base. It buys another shift, another line, another building, another supervisor. The base is no longer the base. So the curve the arithmetic draws is real up to the ceiling and imaginary beyond it, and almost every serious mistake made on this subject comes from running the first fact past the second one. Almost the whole subject is the collision between the two facts.

Third, a denominator that is not the same kind of thing in the two cases. The difference in the denominator is exactly why the two words get muddled. Scale divides by more units of one product. Scope divides among more customers or more products sharing one asset. Scale and scope have the word economies in common and nothing else. Anjani Stationers carries a clean example of the first in its own accounts. Chitra Binding Works carries a clean example of the second in somebody else's.

What is an economy of scale?

The costs that do not move when one more is made, the marginal unitThe next single unit, the one just past whatever has already been made. Asking what it adds to cost, and what it adds to income, is a different question from asking what an average unit carries. as a costing sheet would call it, are divided by the number made. The division is the whole of it. Anjani Stationers has a fixed base of Rs 74,00,000/- and it made 2,50,000 registers, so each register carries Rs 29.60 of that base. An economy of scale is a division and nothing more mysterious than that, and the only thing that changes is the divisor.

Notice what does not change. The paper inside each register costs what it costs. The carriage on each register costs what it costs. The binding of each register costs what it costs. Paper, carriage and binding are variable costsCosts that arrive with each extra unit and leave with each unit not made. Materials, piece-rate labour and carriage behave this way, so the total moves with volume while the amount for one unit sits still., and making more registers does not make any of them cheaper for one register. Only the share of the unmoving block moves, and it moves because the block is being cut into more parts.

The same thing appears at a scale anybody can stand next to. A food stall hands over a monthly Rs 600/- for its pitch. The pitch costs the same whether the stall sells sixty plates in the month or a hundred and twenty. Across sixty plates the pitch is Rs 10/- a plate. Across a hundred and twenty it is Rs 5/- a plate. The potatoes cost exactly the same either way, in both months, for every single plate. Nobody negotiated anything, nobody bought better, and the stall holder has not become a shrewder purchaser overnight. The rent was simply divided by a bigger number.

What is an economy of scope, and why is it a different thing?

Now hold the volume still and change something else. An economy of scope is one asset spread sideways: across more customers, or across more products, rather than stretched further along one product. The asset is shared rather than filled.

Scale changes how many of the same thing; scope changes how many different things, or how many different buyers. The two share a word and nothing else, and a business can be full of one and have none whatever of the other. A business full of one and empty of the other is not a rare edge case but the ordinary situation, and Anjani Stationers itself turns out to be one.

One test keeps them apart. Look at the denominator. If it is more of the same thing, that is scale. If it is more different things, or more different buyers, sharing one asset, that is scope.

The everyday version is an oven. A bakery buys one oven and bakes bread in it every morning. If it bakes more bread in the same oven, that is scale: the same product, more units, the oven divided further. Now it starts baking pizza in the same oven every evening. The oven cost has not changed by a rupee, the morning bread has not increased by a single loaf, and yet a second product is now carrying part of the same oven. The evening pizza is scope. Notice that the second use needed something specific to be possible: the oven had to have an evening free. The same free evening decides whether scope is available at all, and the rated output of a works is the same condition in another form.

What does scale look like in Anjani Stationers' own figures?

The works is ratedThe output a plant is designed to produce in a period when every stage runs at the speed it was built for. The rated output is a design figure, set by whichever stage is slowest. at 4,00,000 registers a year and it made 2,50,000, which is utilisationActual output as a share of the rated output. Utilisation says how much of the designed capability of a plant the year actually used. How the figure is built and checked is set out under capacity utilisation. of 62.50 per cent. So run the same division at the rated figure. Rs 74,00,000/- divided by 4,00,000 registers is exactly Rs 18.50 a register.

The gap is Rs 11.10 a register and not one paisa of it comes from buying anything more cheaply. No supplier was squeezed, no material was substituted and no wage was cut. The identical Rs 74,00,000/- was simply cut into 4,00,000 parts instead of 2,50,000. Both divisions are exact, and both multiply back to the published base to the paisa, so the working stands in place of a result to be taken on trust.

Now the sentence a careless writer gets backwards. Reaching 4,00,000 would mean running faster, not running longer. Anjani Stationers already ran all 4,000 of its line-hoursThe hours a production line is actually staffed and running in the period. Multiplied by the rate achieved in an hour they give the output, so hours and rate are two separate levers and not one., and it ran them at 62.5 registers an hour against a rated 100. The idle capability is idle rate, not idle time. The shifts were all worked, so the business could not get to 4,00,000 by adding shifts or working later. How the rated figure and the utilisation percentage are put together and checked is covered separately under Capacity Utilisation: How to Compute It and What It Hides.

What exactly is the Rs 11.10 a register worth?

On 4,00,000 registers, Rs 11.10 each comes to Rs 44,40,000/-. The Rs 44,40,000/- is where most writing on this subject quietly goes wrong, so it is worth arriving at the long way round rather than by a multiplication that hides what it is.

The long way runs like this. Charging 4,00,000 registers at the rate the business currently incurs, Rs 29.60 each, would load Rs 1,18,40,000/- of fixed cost onto them. The base is not Rs 1,18,40,000/-. The base is Rs 74,00,000/-, and it stays Rs 74,00,000/-. The difference between the two, Rs 44,40,000/-, is overheadThe pool of costs a business carries to be in business at all, rather than to make any particular unit. Rent, supervision, insurance and administration are the usual residents. that never has to be added at 4,00,000 registers. The Rs 44,40,000/- is not money arriving but money that was never required.

A spread fixed cost is not a sale. Nothing established so far shows that the extra 1,50,000 registers could be made, that anybody would buy them, or that they would be bought at Rs 108.00 or at any other figure. All that has happened is a division. The effect of filling the works on revenue, on margin and on the return on capital is covered separately under Throughput: The Rate the System Actually Produces.

Can that Rs 11.10 be handed to the volume the business actually made?

No, and the reason is exact rather than long. The Rs 18.50 rate exists at 4,00,000 registers and at no other output. So the Rs 11.10 gap between it and Rs 29.60 belongs to 4,00,000 registers and to no other volume. Multiplying Rs 11.10 by the 2,50,000 the business actually made produces a figure that describes nothing that happened and nothing that could have happened at that volume. At 2,50,000 registers, Anjani Stationers incurred Rs 29.60 a register and saved precisely nothing.

A per-unit saving belongs to the volume that produced it and to no other volume. That is why the Rs 44,40,000/- never appears in a sentence without 4,00,000 sitting in the same sentence, and why any note that quotes it on its own deserves suspicion.

The everyday version arrives every time a group hires a coach. A coach costs Rs 8,000/- and the fare falls to Rs 200/- a head if forty people travel. Twenty five people actually book. Their fare is Rs 320/- a head. The Rs 120/- difference never existed at the number who travelled, so it is not a saving they lost, missed or gave up. The lower fare belonged to a coachful of forty, and there were twenty five.

Where does the curve stop, and what happens past the end of it?

Anjani Stationers' works is rated at 4,00,000 registers. Ask 4,00,001 of it and the same Rs 74,00,000/- does not stretch to cover them. The business needs another line, another building, more supervision, another layer of people to run all of it. Beyond rated capacity the fixed base steps up rather than spreading further, so the unit cost line does not carry on downwards. It jumps, and only then begins falling again from a higher level, and the business reaches a rate below Rs 18.50 only after it has filled the new capacity as well.

A unit cost curve drawn falling forever is a line the business cannot walk along. The ceiling is where the arithmetic stops describing anything, so the ceiling belongs beside the arithmetic and never in a footnote.

No figure exists for the size of that step. Anjani Stationers publishes nothing on what another line would cost, and a plausible-looking figure invented to fill the hole would be worse than the hole: it would be a number written from memory, sitting in a table, being multiplied by somebody six months from now.

A tuition teacher shows the shape of it in one room. She teaches four students in her front room for an hour. A fifth student arrives and costs her nothing at all: the same room, the same hour, the same explanation, and her cost for each student simply falls. The fifth student is the curve. The sixth student does not fit. Now she needs a second room, a second evening and eventually a second teacher, and her cost for each student jumps upwards before it starts falling again. Her curve did not carry on falling; it stepped, and the step arrived at a particular student.

What does scope look like in these same two businesses?

Turn to Chitra Binding Works. Its published profit for the year is Rs 10,00,000/-. Of that, Rs 3,00,000/- is the profit arising on the binding it does for Anjani Stationers, and Rs 7,00,000/- is the profit arising on the binding it does for everybody else. Seven over ten is 70.00 per cent, so 70.00 per cent of what that plant earns comes from outside the two businesses in this case.

Read that as a picture rather than as a ratio. There is one plant. One set of machines, one shed, one lot of people who know how to bind. Registers from Anjani Stationers go through it, and so does other people's work, and the same machines do both. The plant is being shared sideways, precisely as the oven is shared when it bakes pizza in the evening. The binding plant is paid for mostly by people who are not Anjani Stationers, and that is what scope looks like when it is real.

Notice how carefully the 70.00 per cent has to be said, and notice what it does not establish. The figure does not say how many other customers there are, and no such figure is published. The figure does not say how full the plant is, and fullness is a different measurement entirely. And the figure says nothing about who holds Chitra Binding Works or how one set of accounts is combined with another. Combining accounts belongs to financial accounting.

So which of the two is Anjani Stationers actually getting?

The honest answer is the less flattering one, and it is worth sitting with. On scale, Anjani Stationers has room it has not taken. At 62.50 per cent utilisation it is carrying Rs 29.60 a register of a base that would work out at Rs 18.50 if the works were full, and the difference is not a failure of purchasing or a failure of costing. The difference is simply the arithmetic of a works that is running at 62.5 registers an hour against a rated 100.

On scope, the shared plant in the picture is Chitra Binding Works, and most of what that plant earns arises on work that has nothing to do with Anjani Stationers. The shared plant is unmistakably scope for the plant. Whether it amounts to scope for Anjani Stationers is a different and much less comfortable question. Settling it would need figures for what Anjani Stationers pays for its binding and what it would pay elsewhere, and no such figures are published.

A business can have the shape of an advantage and not be getting it, and the shape is not the thing. Whether to fill the works is a decision, and a decision needs things arithmetic cannot supply.

Does a lower unit cost make a cost advantage?

No, and everything about the two rates stands or falls on this point rather than on any of the arithmetic. Rs 29.60 and Rs 18.50 are Anjani Stationers measured against itself at two volumes. One of those volumes happened and the other did not. No rival's unit cost is published and none has been assumed, so nothing has been compared with a competitor.

An advantage is a gap against somebody, and a cost compared with the same business's other volume is not one. The habit worth building is small and it is the whole discipline: state what every figure is measured against, every single time it is written down. Rs 18.50 against Rs 29.60 is Anjani Stationers against Anjani Stationers. Stated that way, the sentence stays true anywhere it is quoted.

Whether a cost gap counts as an advantage at all, and what would stop a rival closing it, is worked out separately under The Sources of Competitive Advantage, and Whether Any of Them Lasts.

Why do scale and scope get confused, and what does the confusion cost?

Both of them make a unit cost fall and both of them get called economies, so the word does the thinking, nobody checks the denominator, and the two get confused. A wrong label would be harmless if the label were the only consequence. It is not.

Here is the consequence, and it is expensive. A business that believes it has scope when what it actually has is scale expects a new product to arrive cheap. The business reasons that the plant is already paid for, so a second product can ride on the same asset for very little, and it prices the new product on that assumption. Then it discovers that the plant was already full, and that the second product needs its own room on the line, its own setup, its own supervision. Scope needs spare room in the shared asset, and a full asset has none to share.

The full asset brings scope back to the ceiling that ended scale. The rated output that ends the scale curve is the same rated output that decides whether scope is available at all. An asset running at 62.50 per cent has room for both conversations. An asset running at its rated output has room for neither, and the bakery whose oven is already busy every evening cannot take on pizza at any price, however good the arithmetic looks on paper. AbsorptionCharging a block of cost against the units produced in a period. Each unit then carries a share of the block, the share is a calculation choice rather than a payment, and the money left the business regardless of how it was charged. is a calculation. Spare room is a physical fact, and only one of the two can be arranged in a spreadsheet.

How does a practitioner test an economies claim?

A lender reads these four in a particular order and for a particular reason. A falling unit cost with no ceiling stated is a projection that has quietly assumed a new line without pricing it, so the first thing a credit officer looks for in a projection where the unit cost falls year after year is the rated output. An equity analyst uses the same four questions differently. A business running at 62.50 per cent of its rated output has a very different set of possibilities from one already running at the rated figure, and neither of those possibilities is visible in a margin, so the second question, at what volume, is where most of the value in the answer sits. And a household does the same arithmetic without naming it, every time somebody works out whether the second-hand van is worth buying for a business that has work for it three days a week.

Where does this arithmetic go wrong in careful hands?

Which questions does the arithmetic leave open?