The experience curve (not to be confused with learning curve) is a graphical representation of the phenomenon explained in the mid-1960s by Bruce D. Henderson, founder of the Boston Consulting Group. It refers to the effect that firms learn from doing, which means that the higher the cumulative volume of production (X), the lower the direct cost per new unit produced (C). Therefore, the experience curve will be convex and have a downward slope, as shown in the adjacent diagram.

There is a simple rationalisation behind all this: there is a reduction in the average cost of production of a particular product, as a consequence of an increase in the firm’s experience.  The time and cost of producing a unit of output will be reduced, as learning economies, economies of scale, economies of scope, etc. appear due to the cumulative output increase and other process related growth. The difference between learning curves and experience curves is that learning curves only consider time of production (only in terms of labour costs), while experience curve is a broader phenomenon related to the total output of any function such as manufacturing, marketing, or distribution. The ex­perience curve is defined by the following function: 

C_n = C₁X^-a

where:

C₁ = direct cost of first unit of production
C_n = direct cost of n^th unit of production
X = cumulative volume of production
a = experience rate (%)

The experience rate corresponds to the elasticity of cost with regard to output. In other words, the rate at which direct costs decrease (in percentage points) when output increases (also in percentage points).

Some important implications arise from this curve. If direct costs decrease as the cumulative output increases, this will mean that firms that have been producing more and for a longer period, will have lower direct costs per unit and thus dominate the market.

We must consider what happens when two firms compete with the same product and the same experience curve (blue curve, EC). In the diagram on the left, we have a starting situation where two firms compete. Firm B has been in that market for a longer time (or has produced more volume during the same period of time), therefore its direct costs are lower than A’s. If price equals the direct costs of A, firm B will have profits while firm A will just survive. It must be noted that B could decrease its price, which will force firm A to lower its price, thus incurring in losses. Firm A will ultimately leave this market.

However, if A and B maintain a price level at which firm A can endure, direct costs for A will decrease at a higher rate than B, because of the steeper slope for lower cumulative volumes of production. Therefore, the longer A stays in the market, the lower the profits for B, as it is drawn in the diagram on the right, where the difference between direct costs (from C’_A to C’_B) is smaller. Game theory and the analysis of oligopolies tell us that, since B is able to anticipate all these scenarios, firm B will try to banish firm A from the market.

As mentioned before, experience curves is a wider phenomenon than learning curves because they consider not only labour productivity, but also technology, distribution, etc. This difference allows for different experience curves to coexist. Let’s consider two more scenarios, considering open economies.

In the first scenario shown in the adjacent diagram, firm A enters firm B’s market with a different, steeper experience curve. This may happen when firm A is able to learn and get more experience out of the same increase in volume. A few examples include firm A’s workforce being able to learn quicker because it’s highly qualified, or because firm A’s factory allows for quicker modifications. Under these circumstances, even if firm A enters the market with higher direct costs than B (C_A > C_B), it will ultimately catch up with firm B. Actually, after a certain volume, firm A would get more experience and will have lower direct costs than firm B (C’_A < C’_B), even with lower cumulative volume.

In the second scenario, shown in the next diagram, firm C enters firm B’s market with an exclusive technology, which translates into a lower experience curve (let’s assume for the sake of simplicity that this innovative technology cannot be copied or transferred). Then, because of its lower experience curve, firm C will be able to get the same level of direct costs than B with lower cumulative volume. Initially, firm C will have higher direct costs than firm B (C_C > C_B). However, after a while, C will have reached a volume at which it has the same level of direct costs as B. After this point of inflection, firm C will produce each unit with lower direct costs than firm B (C’_C < C’_B).

These two scenarios are usually considered as good examples of the infant industry argument, since trade protectionismin these situations is welcomed. The rationale behind this is quite obvious: if we consider that all these firms (A, B and C) compete in an infant industry, which in these scenarios would be that existing in the home country of B, it is reasonable to limit the extent at which firms such as A and C can act in B’s country. If firm B isn’t kept alone for the time required to gain some experience, national industry in B’s country would not exist, and it would all be controlled by foreign and more powerful firms (A and C). This is usually the case in third world countries, in which infant industries must be protected, in order to help their economic growth.
Even though the term experience curve is usually merged in economics and business management literature with the term learning curve, there are a few differences between the two. These differences are summarized in the following grid:

The learning curve (not to be confused with experience curve) is a graphical representation of the phenomenon explained by Theodore P. Wright in his “Factors Affecting the Cost of Airplanes”, 1936. It refers to the effect that learning had on labour productivity in the aircraft industry, which translates into a relation between the cumulative number of units produced (X) and the average time (or labour cost) per unit (Y), which resulted in a convex downward slope, as seen in the adjacent diagram.

There is a simple rationalisation behind all this: the more units produced by a given worker, the less time this same worker will need to produce the following units, because he will learn how to do it faster and better. Therefore, when a firm has higher cumulative volume of production, its time (or labour cost) per unit will be lower. Wright’s learning curve model is defined by the following function:

where:    Y = average time (or labour cost) per unit

a = time (or labour cost) per unit

X = cumulative volume of production

b = learning rate (%)

Some important implications arise from this curve. If the time (or labour cost) per unit decreases as the cumulative output increases, this will mean that firms that have been producing more and for a longer period, will have lower average time per unit and thus dominate the market.

We must consider what happens when two firms compete with the same product. Since the learning curve considers only time per unit, and we consider that they spend the same amount of time per unit for a given unit when each firm’s cumulative volume of production is at the same level, both firms will have the same learning curve (green curve, LC). In the diagram on the left, we have a starting situation where two firms compete. Firm B has been in that market for a longer time (or has produced more volume during the same period of time), therefore its average time (or labour cost) per unit is lower than A’s. If price equals the average cost of A, firm B will have profits while firm A will just survive. It must be noted that B could decrease its price, which will force firm A to lower its price, thus incurring in losses. Firm A will ultimately leave this market.

However, if A and B maintain a price level at which firm A can endure, time per unit for A will decrease at a higher rate than B, because of the steeper slope for lower cumulative volumes of production. Therefore, the longer A stays in the market, the lower the profits for B, as it is drawn in the diagram on the right, where the difference between average times (from Y’_A to Y’_B) is smaller. Game theory and the analysis of oligopolies tell us that, since B is able to anticipate all these scenarios, firm B will try to banish firm A from the market.

The obvious critique to all this is that, if learning curves were so obvious and could be anticipated as easily, we would live in a world consumed by monopolies. Older firms would keep banishing potential competitors from markets until entry barriers became so great that no other firm would try to enter this market.

Even though the term learning curve is usually merged in economics and business management literature with the term experience curve, there are a few differences between the two. These differences are summarized in the following grid:

Economies of learning derive from the know-howpicked up through experience. The main difference between this and economies of scale or economies of scope is the fact that it is not correlated to production levels in the same way: it does not depend on producing more quantity or a wider portfolio, but from becoming a true specialist in a certain field, by producing a greater cumulative amount of the same product. However, this differs from economies of scale because economies of learning do not stop at a certain level, they keep on improving efficiency.

A classic example of this which is often cited is Japan’s market leadership from the 1980s in technology intensive goods such as TVs and audio equipment. The know how from economies of learning often spreads from a company with employees, leading to clusters of knowledge-rich companies often situated in a relatively small area.

There are many ways in which this learning helps drive down cost: by boosting efficiency and reducing waste in production, by R&D synergies and productivity, by better management which helps coordinate and balance the different functions and by speeding up the productive process. When learning reflects only in labour productivity, it’s analysed with a learning curve. When learning applies to the whole firm, all its processes, it’s analysed with an experience curve.

The concept of economy of learning is actually morphing into that of a ‘learning economy’, one in which efficiency and growth is driven by training and specialisation resulting in profitable, high added value goods and services.

The concept of economy of scope is very similar to that of economies of scale. When we talk about economies of scope, we mean that average costs are reduced by introducing another product into our portfolio that can share some of the infrastructure or know-how, thus reducing overall average cost per product. It is essentially the same concept as economies of scale, but based on producing more than one product instead of producing more of the same one.

This can happen for various reasons. Firstly, because fixed costs do not increase proportionally with production but rather in stages, we can introduce a second production line that benefits from the common infrastructure whilst reducing average cost per unit.

We can also see a reduction in average variable costs. Employees can benefit from shared know how or from a certain skill set that can be transferred to a much wider range of products, raising productivity across the board. In this way, labour need not increase proportionally with production output, as it is the case for economies of scale. What we can also see here are skills being transferred from one production range to another, resulting in synergies that are unique to economies of scope instead of economies of scale.

In the adjacent figure we see the case of two multi-product firms. The fact that the lower production possibility frontier (PPF) is concave rather than a straight line means that firm B will enjoy economies of scope, and be able to produce two goods for a lower average cost than when producing only one. Therefore, economies of scope exist if, for two goods, we have:

C(x₁,x₂) < C(x₁,0) + C(0,x₂)

This economic phenomenon occurs when increasing output is translated into a decline of the firm´s average cost of production. Alfred Marshall was the first economist to distinguish economies of scale depending on their origin:

-Internal economies of scale occur when something inside the firm makes the average cost of production lower:

• Purchasing: buying raw materials in large quantities or big bulks brings better prices and discounts which allow average cost to be reduced.
• Specialisation: covering all areas of management and work can be very difficult, however when operating on a large scale, workers can specialize in the activities in which they are best and more productive.
• Flexibility:  a more efficient production process can be achieved by managers when scale means that different arrangement of the inputs can be made. Better capital can be purchased by firms that have more money, increasing the quality of their products and/or reducing cost of production.

-External economies of scale occur when something outside the business, but inside its industry, makes average cost of production lower. As the industry of the firm grows, more support may come from the suppliers’ side: more variety, more quality, more quantity, etc. Government may give extra aid if it considers that the industry has some special interest.

On the other hand, diseconomies of scale may appear due to the excessive scale of a firm. Diseconomies of scale occur when average cost per unit increases due to excessive size of production.

The main reasons for diseconomies of scale to appear are:

• Demotivation issues: in firms with many workers, standing out becomes harder. Each individual may find himself as meaningless, and therefore cause him to stop working as hard as he would with fewer workers.
• Communication: the communication process of larger firms becomes slower as information has to pass through more and more layers. Information can even become distorted either accidentally or deliberately. The longer it takes managers to make decisions, and these to be known by workers, the less efficient the firm becomes.

Subadditivity is an important concept because it is often used to justify imperfect competition, the classic nemesis of neo-classicists. The only real way to justify less than perfect competition is the kind of sector which lends itself to natural monopolies. Natural monopolies are those where barriers to entry are so high that it is worth making the investment only once, and where one producer will operate more efficiently than two. Traditionally, natural monopolies are state-run, generally in energy or communication sectors, although current trends are leaning towards privatisation.

When a large investment is required in order to begin production, these costs must naturally be passed on to the consumer. What differentiates natural monopolies is that generally, once the investment is made, marginal costs are infinitely small. In these cases, if there is only one company in the market, prices for consumers may actually be lower than if there are rivals, because of the way average costs drop with additional users.

So what exactly is the difference between subadditivity and economies of scale? Subadditivity is a more generic concept which encompasses economies of scale. We say subadditivity exists when:

That is, when the costs function (including initial investment) for the sum of all units at a given level of production is actually smaller than the sum of the various cost functions (given multiple companies) at the same given level. If we look at the diagram, we can see the traditional long run costs functions for two companies. We only consider economies of scale when additional units provide a lower average cost, but costs per unit begin to rise after a certain level. Subadditivity simply means that it is cheaper to produce the same production level when only company one is producing, and that the same production level is more expensive when company two joins the market.

 

This is why subadditivity is considered a necessary but insufficient conditionfor a natural monopoly to be considered optimal, whereas if economies of scale exist, this is a sufficient but not necessary condition for a natural monopoly to be sustainable. The cyan demand curve, within the economy of scale region, indicates a viable natural monopoly. The red line would indicate a non sustainable natural monopoly. The black line indicates the frontier of a profit generating monopoly (which would attract competitors) and the green line indicates a viable duopoly.

In the long run, no cost is fixed. We can determine our production level and adjust plant sizes, investment in capital and labour accordingly. As we can see in the diagrams below, this gives us unlimited options. Depending on the scale we choose to implement, each level of production will be associated to new, short run cost curves. When we exhaust the infrastructure these provide us, we can upgrade to a new production level and so forth. The actual long run cost curve is made up of all of these individual scenarios, built up year after year.

If we look at average costs, the curve these draw is also the build up of the individual short run curves. These form a U shape, as we can see in the diagram. When average cost is decreasing with each additional investment, we are enjoying economies of scale, but not yet working at maximum efficiency. We reach this maximum efficiency at the minimum point, before the average cost per unit begins growing again.

Marginal costs only really make sense in the long run for each individual level of production. At optimal levels of production for each level, they intersect the long run average cost curve where this meets the short run average cost curve. This is what determines our optimal level of production. In summary, at our optimal level of production:

AC_SR = AC_LR = MC_SR = MC_LR

which is known as Le Châtelier’s principle.

The other important lesson to take away from this is the fact that, when we reach the optimal point where efficiency is at its best, average and marginal costs are the same, as happened in the short run (see detailed graph below these lines). At this point, the slope of the tangent line, that is, the derivative, of the short run total cost (TC_SR) is equal to zero, which is consequent with the fact that we are operating at maximum efficiency. What we can also glean from the graph is the fact that TC_SR and TC_LR are tangent where short run average cost (AC_SR) and AC_LR also meet, which is not necessarily an optimum. In fact, the only time where these junctions do suppose an optimum is in case 2.

This economic phenomenon occurs when increasing output is translated into a decline of the firm´s average cost of production. Alfred Marshall was the first economist to distinguish economies of scale depending on their origin:

-Internal economies of scale occur when something inside the firm makes the average cost of production lower:

• Purchasing: buying raw materials in large quantities or big bulks brings better prices and discounts which allow average cost to be reduced.
• Specialisation: covering all areas of management and work can be very difficult, however when operating on a large scale, workers can specialize in the activities in which they are best and more productive.
• Flexibility:  a more efficient production process can be achieved by managers when scale means that different arrangement of the inputs can be made. Better capital can be purchased by firms that have more money, increasing the quality of their products and/or reducing cost of production.

-External economies of scale occur when something outside the business, but inside its industry, makes average cost of production lower. As the industry of the firm grows, more support may come from the suppliers’ side: more variety, more quality, more quantity, etc. Government may give extra aid if it considers that the industry has some special interest.

On the other hand, diseconomies of scale may appear due to the excessive scale of a firm. Diseconomies of scale occur when average cost per unit increases due to excessive size of production.

The main reasons for diseconomies of scale to appear are:

• Demotivation issues: in firms with many workers, standing out becomes harder. Each individual may find himself as meaningless, and therefore cause him to stop working as hard as he would with fewer workers.
• Communication: the communication process of larger firms becomes slower as information has to pass through more and more layers. Information can even become distorted either accidentally or deliberately. The longer it takes managers to make decisions, and these to be known by workers, the less efficient the firm becomes.

Different levels of production have different cost levels. It is generally assumed that higher levels of production help drive down cost (by reducing fixed costs per unit, by lowering the price of raw materials and intermediate goods through increased bargaining power…). However, this is not necessarily the case when an increase in production leads to a jump in fixed costs that cannot be fully absorbed by the increase in production (purchasing a new, larger factory or a heavy investment in infra utilised machinery). To find out whether increasing production will increase efficiency (whether the increase in production will be greater than the increase in cost), we can measure elasticity.  

This is the same as measuring the result of dividing the % change in output by the % change in input. When considering the diagram seen in the short run cost analysis entry, along phase one, when efficiency is increasing with production, μ > 1. When we reach the point of inflection, μ = 1, and when we begin to have diminishing returns to scale, output begins to grow slower than inputs, and μ < 1, which is in phase III.

The law of returns to scale explains how output behaves in response to a proportional and simultaneous variation of inputs. Increasing all inputs by equal proportions and at the same time, will increase the scale of production. Returns to scale differ from one case to another because of the technology used or the goods being produce. Therefore, it is closely related to economies of scale happening within the business’ production process.

The relation by which output increases compared to the increase in inputs is the return to scale. We can measure the elasticity of these returns to scale in the following way:

That is, the sum of the partial derivatives of production with regards to each factors multiplied by the proportion each input makes up of the whole.

Depending in the proportion by which output increases compared to inputs, there are three different kinds of returns to scale:

-Increasing returns to scale (µ>1): when total output increases more than proportionately (green);

-Constant returns to scale (µ=1): when total output increases proportionately (blue);

-Decreasing returns to scale (µ<1): when total output increases less than proportionately (red).

When dealing with Cobb-Douglas functions, we can also determine which returns of scale are present, since α+β=µ.