📈 Economies of Scale

Definition, measurement and the basis of economies of scale
Limits of scale and diseconomies of scale
Sources: purchasing, managerial, financial, marketing, technological
Internal versus external economies of scale
Determinants: physical, statistical, transactional, capacity balancing, division of labour, managerial, learning and growth
Capital cost, operating cost, byproducts and exporters
Economies of scale versus returns to scale
History of economic analysis: Smith, Mill, Marx, Marshall, Sraffa, Cournot's dilemma

💡 Core Idea

In microeconomics, economies of scale are the cost advantages that enterprises obtain due to their scale of operation, and are typically measured by the amount of output produced per unit of cost (production cost).

A decrease in cost per unit of output enables an increase in scale: increased production with lowered cost.
When average costs decline as output increases, economies of scale occur.
The basis may be technical, statistical, organizational, or related to the degree of market control.
They arise at various levels: a production line, a plant or an entire enterprise.
Some have a physical or engineering basis, such as the capital cost of manufacturing facilities and friction loss of transportation and industrial equipment.
The concept dates back to Adam Smith and the idea of obtaining larger production returns through the use of division of labor.
Diseconomies of scale are the opposite.

Formal condition

Economies of scale exist whenever the total cost of producing two quantities of a product $X$ is lower when a single firm rather than two separate firms produces it:

$TC((Q_1+Q_2)X) < TC(Q_1X) + TC(Q_2X)$

🚧 Limits of Economies of Scale

Economies of scale often have limits, such as passing the optimum design point where costs per additional unit begin to increase.

Exceeding the nearby raw material supply, such as wood in the lumber, pulp and paper industry.
For raw materials with a low cost per unit weight, saturating the regional market, so products must be shipped uneconomic distances.
Using energy less efficiently.
A higher defect rate.

Commodities versus specialty grades

Large producers are usually efficient at long runs of a product grade (a commodity) and find it costly to switch grades frequently.
They therefore avoid specialty grades even though those have higher margins.
Smaller (usually older) facilities often remain viable by changing from commodity-grade production to specialty products.

What is not an economy of scale

When a plant is used below its optimal capacity, a higher degree of utilization lowers total average cost of production.
Nicholas Georgescu-Roegen (1966) and Nicholas Kaldor (1972) both argue that these economies should not be treated as economies of scale.

🧭 Overview

The simple meaning of economies of scale is doing things more efficiently with increasing size.

Common sources

Source	How it lowers cost
Purchasing	Bulk buying of materials through long-term contracts
Managerial	Increasing the specialization of managers
Financial	Lower interest charges on bank borrowing and access to a greater range of financial instruments
Marketing	Spreading the cost of advertising over a greater range of output in media markets
Technological	Taking advantage of returns to scale in the production function

Each factor reduces the long run average costs (LRAC) by shifting the short-run average total cost (SRATC) curve down and to the right.

Why it matters

It may explain patterns in international trade and in the number of firms in a given market.
It helps explain why companies grow large in some industries.
It is a justification for free trade policies, since some economies of scale require a larger market than a single country offers.
- Example: it would not be efficient for Liechtenstein to have its own carmaker if it sold only to its local market. A lone carmaker may be profitable, but even more so if it exported cars to global markets.
It also plays a role in a natural monopoly.

Internal versus external

Type	Description
Internal	Costs of production fall when the number of firms in the industry drops, but the remaining firms increase their production to match previous levels
External	Costs drop due to the introduction of more firms, allowing more efficient use of specialized services and machinery

🔍 Determinants of Economies of Scale

Physical and engineering basis: economies of increased dimension

The square-cube law: the surface of a vessel increases by the square of the dimensions while the volume increases by the cube.
- Direct effect on the capital cost of buildings, factories, pipelines, ships and airplanes.
In structural engineering, the strength of beams increases with the cube of the thickness.
Drag loss of vehicles like aircraft or ships generally increases less than proportionally with cargo volume, so larger vehicles usually use less fuel per ton of cargo at a given speed.
Heat loss from industrial processes varies per unit of volume for pipes, tanks and other vessels in a way somewhat similar to the square-cube law. A larger plant can reduce average variable cost thanks to energy savings from lower dispersion of heat.

A common misinterpretation

Economies of increased dimension are often misinterpreted because of confusion between indivisibility and the three-dimensionality of space.
Three-dimensional production elements, such as pipes and ovens, are technically indivisible once installed and operating.
But economies from increased size do not depend on indivisibility; they depend exclusively on the three-dimensionality of space.
Indivisibility only implies economies from the balancing of productive capacities, or increasing returns in the utilisation of a single plant. The latter has nothing to do with economies of scale, which are by definition linked to the use of a larger plant.

Economies in holding stocks and reserves

Returns to scale linked to statistical factors.
The greater the number of resources involved, the smaller, in proportion, the quantity of reserves needed to cope with unforeseen contingencies (for instance machine spare parts, inventories, circulating capital).

Transaction economies

One reason firms appear is to reduce transaction costs.
A larger scale gives greater bargaining power over input prices, so purchasing raw materials and intermediate goods is cheaper than for companies ordering smaller amounts.
These are called pecuniary economies: nothing changes from the "physical" point of view of the returns to scale.
Supply contracts entail fixed costs, which lead to decreasing average costs as production scale increases. This is useful in the study of corporate finance.

Economies from balancing of production capacity

A larger scale can mean a more efficient use of the capacities of the individual phases of the production process.
If inputs are indivisible and complementary, a small scale may suffer idle times or underutilization of some sub-processes.
A higher production scale can make the different capacities compatible.
Reducing machinery idle times is crucial when machinery is costly.

Division of labour and superior techniques

A larger scale allows a more efficient division of labour.
The economies derive from faster production, specialized personnel and more efficient techniques.
More division of labour inevitably changes the quality of inputs and outputs.

Managerial economics

Many administrative and organizational activities are mostly cognitive and largely independent of the scale of production.
As company size and division of labour grow, organizational management can be more effective and accounting and control techniques can be perfected.
The procedures and routines that proved best can be reproduced by managers at different times and places.

Learning and growth economies

These underlie dynamic economies of scale, associated with the process of growth of scale rather than the size of scale per se.

Type	Idea
Learning economies	Learning by doing improves ability to perform and promotes incremental innovations with progressively lower average costs. Directly proportional to cumulative production (the experience curve).
Growth economies	Arise when a company gains an added benefit by expanding, due to an underused resource or competence, or to specific market positions giving a differential advantage in expanding. They disappear once the expansion process is completed.

Example of a growth economy: a company owning a supermarket chain opens a new supermarket and the price of the land it owns around it rises. Selling that land to operators who want to open shops nearby yields a profit from the revaluation of building land.

Capital and operating cost

Overall costs of capital projects are subject to economies of scale.
Crude estimate, the point six to the power rule: if the capital cost of a given sized piece of equipment is known, changing the size changes the capital cost by the 0.6 power of the capacity ratio.
Installing a larger capacity electrical wire or pipe typically takes an insignificant amount of extra labor, and possibly not much more material.
The cost per unit of capacity of many types of equipment (electric motors, centrifugal pumps, diesel and gasoline engines) decreases as size increases, and efficiency increases with size.

Crew size and other operating costs for ships, trains and airplanes

Operating crew (pilots, co-pilots, navigators; not passenger service personnel) does not increase in direct proportion to capacity.
Many aircraft models were significantly lengthened or "stretched" to increase payload.
Many manufacturing facilities, especially for bulk materials like chemicals, refined petroleum products, cement and paper, have labor requirements not greatly influenced by plant capacity.
- Labor needs of automated processes tend to depend on the complexity of the operation rather than the production rate.
- Facilities often have nearly the same number of processing steps and pieces of equipment regardless of capacity.

Economical use of byproducts

Karl Marx noted that large scale manufacturing allows economical use of products that would otherwise be waste.
He cited the chemical industry, which together with petrochemicals remains highly dependent on turning residual reactant streams into salable products.
In pulp and paper, it is economical to burn bark and fine wood particles to produce process steam and to recover spent pulping chemicals for reuse.

Economies of scale and the size of exporter

Large and more productive firms typically generate enough net revenues abroad to cover the fixed costs of exporting.
With trade liberalization, resources are reallocated toward the more productive firm, which raises average productivity within the industry.
Firms differ in labor productivity and product quality, so more efficient firms are more likely to earn more net income abroad and become exporters.
Total economies of scale depend on the exporter's frequency and size: large-scale companies are more likely to have a lower cost per unit than small-scale ones, and high trade frequency companies reduce their cost per unit compared with low-trade frequency ones.

⚖️ Economies of Scale and Returns to Scale

The two are related and easily confused.

	Economies of scale	Returns to scale
Concerns	A firm's costs (average production cost versus scale)	The relationship between inputs and outputs in a long-run (all inputs variable) production function
Terms	Affected by variations in input prices	"Physical" terms

Returns to scale

Constant returns: increasing all inputs by some proportion raises output by the same proportion.
Decreasing returns: doubling inputs yields less than double the output.
Increasing returns: doubling inputs yields more than double the output.
For a homogeneous production function, returns to scale are given by the degree of homogeneity:
- constant returns: first degree homogeneous;
- increasing returns: degree greater than one;
- decreasing returns: degree less than one.

Perfect competition in input markets

If the firm is a perfect competitor in all input markets (input prices are unaffected by its purchases), then at a particular output level:

it has economies of scale if and only if it has increasing returns to scale;
it has diseconomies of scale if and only if it has decreasing returns to scale;
it has neither if it has constant returns to scale.

With perfect competition in the output market too, long-run equilibrium has all firms operating at the minimum point of their long-run average cost curves, the borderline between economies and diseconomies of scale.

Imperfect competition in input markets

If there are increasing returns in some output range but the firm is so big in an input market that buying more drives up the input's unit cost, it could have diseconomies of scale in that range.
Conversely, if the firm gets bulk discounts, it could have economies of scale even with decreasing returns in production.

Summary of the distinction

If input prices stay the same as quantities purchased increase, increasing returns to scale and economies of scale are equivalent.
If input prices vary with quantity purchased, the two must be distinguished.
Economies of scale is the more general concept, since it includes changes in input prices as scale changes.

Reverse auctions

The literature assumed that, because of competitive reverse auctions, suppliers seek higher volumes to maintain or increase total revenue, and buyers benefit from lower transaction costs and economies of scale from larger volumes.
Studies indicate procurement volume must be high enough to give profits that attract suppliers, and savings that cover buyers' additional costs.
Shalev and Asbjornse studied 139 reverse auctions in the public sector and found that higher auction volume did not lead to better auction success. Volume did not correlate with competition or the number of bidders.
Caveats: their data covered a wide range of products with widely varying competition, and further research should test purchasing the same product at small and high volumes. Keeping competitive factors constant, increasing volume may further increase competition.

📚 Economies of Scale in the History of Economic Analysis

Classical economists

Adam Smith, Wealth of Nations (1776), First Book: the first systematic analysis of the advantages of the division of labour generating economies of scale, in both a static and dynamic sense. Smith is generally considered the founder of political economy as an autonomous discipline.
John Stuart Mill, Chapter IX of the First Book of his Principles, referring to Charles Babbage (On the economics of machines and manufactories), widely analyses the relationships between increasing returns and scale of production inside the production unit.

Marx and distributional consequences

In Das Kapital (1867), Marx, referring to Babbage, concluded that economies of scale are one factor underlying the ever-increasing concentration of capital.
Under capitalism, the technical conditions of work are continuously revolutionized to raise surplus by improving the productive force of work.
Cooperation of many workers economizes the means of production and raises productivity through more division of labour. Larger machinery saves construction, installation and operation costs.
Exploiting economies of scale means ever-increasing production, requiring constant expansion of the market. If the market does not expand as fast, overproduction crises can occur.
Two tendencies connected to economies of scale: growing concentration and economic crises due to overproduction.
In his 1844 Economic and Philosophic Manuscripts, Marx observes that economies of scale have historically been associated with increasing concentration of private wealth and used to justify it. Concentrated private ownership of large-scale enterprises is a historically contingent fact, not essential to their nature.
On agriculture, Marx calls the arguments for concentrated land ownership sophistical, since defenders identified the advantages of large-scale agriculture with large-scale landed property.
Instead, Marx recommends that economies of scale be realized by associations.

Marshall

Alfred Marshall notes that Cournot and others considered internal economies without noticing that their premises imply that whichever firm first gets a good start will obtain a monopoly of the whole business of its trade.
Marshall believes factors limit the trend toward monopoly:
1. the death of the founder and the difficulty successors may have in inheriting entrepreneurial skills;
2. the difficulty of reaching new markets;
3. the growing difficulty of adapting to changes in demand and to new production techniques;
4. the effects of external economies, tied to the scale of an entire sector rather than one production unit.

Sraffa's critique

Piero Sraffa observes that Marshall, to justify the law of increasing returns without conflicting with free competition, highlighted the advantages of external economies from an increase in production of an entire sector.
Sraffa: "those economies which are external from the point of view of the individual firm, but internal as regards the industry in its aggregate, constitute precisely the class which is most seldom to be met with."
Such external economies are not called forth by small increases in production, as marginalist price theory requires, so they cannot play an important role in equilibrium theory of individual industries, which is based on marginal changes in quantities.
Sraffa concludes that if perfect competition is maintained, economies of scale should be excluded. He suggested abandoning free competition to study firms with their own particular market, which stimulated studies on imperfect competition in Cambridge.
Later he followed a different path, publishing Production of commodities by means of commodities (1966), which determines relative prices assuming no changes in output, so no question of variation or constancy of returns arises.

Rule of six-tenths

In 1947, DuPont engineer Roger Williams Jr. (1930-2005) published a rule of thumb that costs of chemical process are roughly proportional to the tonnage to the power of about 0.6.
It was widely adopted in other engineering industries and terrestrial mining, sometimes (e.g., in electrical power generation) with modified exponents.

Cournot's dilemma: economies of scale and the tendency towards monopoly

Many industrial sectors have numerous companies of different sizes and organizational structures despite significant economies of scale. This contradiction between empirical evidence and the logical incompatibility of economies of scale with competition is the Cournot dilemma.
Mario Morroni: the dilemma seems unsolvable if only the effects of economies of scale on the dimension of scale are considered.
Expanding the analysis to the development of knowledge and the organization of transactions shows that economies of scale do not always lead to monopoly: competitive advantages from a firm's capabilities and from managing transactions with suppliers and customers can counterbalance those of scale.
Heterogeneity of firm size and form can be explained by:
- product quality and production flexibility;
- contractual methods and learning opportunities;
- differentiated customer preferences about quality;
- assistance before and after the sale.
Very different organizational forms can co-exist in one sector: flexible production on a large scale, small-scale flexible production, mass production, industrial production on rigid technologies with flexible organizational systems, and traditional artisan production.
Scale considerations are important but not sufficient to explain company size and market structure; capabilities and transaction cost management must also be considered.

🌐 External Economies of Scale

External economies tend to be more prevalent than internal ones.
The entry of new firms benefits all existing competitors, creating greater competition and reducing the average cost for all firms, whereas internal economies benefit only the individual firm.
Advantages include:
- expansion of the industry;
- benefits to most or all firms within the industry;
- possible rapid growth of local governments.

🧩 Sources of Economies of Scale (Summary)

Purchasing: buying inputs in bulk or from special wholesalers lowers average costs.
Managerial: improving the management structure, for example hiring better skilled or more experienced managers from the industry, can lower average costs.
Technological: technological advancements change production processes and reduce the cost per unit. Tim Hindle argues that the rollout of the internet "has completely reshaped the assumptions underlying economies of scale".

Economies of Scale: Business Study Notes