Isn't she a beauty?
Airbus A380. Click to embiggen in a new tab.

I love IRS. Not the “Internal Revenue Service” but “increasing returns to scale”.

Understanding the economic concept of “returns to scale” is useful for understanding the tremendous increase in the production of wealth in our modern world.

A bit of vocabulary first. The stuff that goes into production are called “factors of production.” The vocabulary is the same as in basic arithmetic where the product is derived from factors — for instance, the factors 2 and 3 when multiplied yield the product 6.

When you increase the factors, the product increases. That is, the “scale” or the size of the operation increases and therefore the product increases. If the increase in production is proportionate to the increase in the factors, then we have “constant returns to scale.” For example, if by doubling the factors the amount of production doubles, then we have constant returns to scale. If by doubling factors produces less than double the product then we have decreasing returns to scale. And we have increasing returns to scale if increasing the factors results in more than proportionate increase in the product. (See note 1 for algebraic formulation of returns to scale). The existence of  increasing returns to scale gives rise to much of the wealth and prosperity we enjoy.

Increasing returns implies that as the volume of production increases, the per unit cost decreases. The average cost of making one chip (the electronic variety or the potato variety) is extremely high (of the order of billions of dollars, in the case of silicon chips) but when 2 billion chips are made, the average cost decreases to mere pennies. Why? Because of high fixed costs and low marginal costs.

To produce silicon chips, you have to first build a fabrication factory aka a fab — which sets you back a few billion dollars. You have to spend a truckload of money before you even produce one chip. But once you have paid the fixed cost, you get down to churning out chips at a very low marginal cost — which brings down the average cost.

Of course, you have to have a market which demands millions of those chips. That means the size of the market makes it possible for someone to incur the high fixed cost. With 7+ billion people, the market for operating systems (for computers, phones) is large enough for people to invest billions in developing them. The same goes for practically everything, from cars to commercial jetliners.

In the case of things like jetliners, the cost of production decreases as the number of units produced increases. The first plane rolling off the assembly line costs more in time and money than the 1000th plane.[2] That is because putting together complex machines requires skills, and skills have to be learned through practice. As more planes get built, the workforce gets more skilled, the supply chain gets more efficient, etc. We call this process “learning by doing.”

We use lots of stuff. The reason we can afford most of that stuff is because of increasing returns to scale. In a world of only 1 million people, there would be no cars, computers or commercial jetliners; in a world of 7,831 million people, the market can produce a few billion distinct products, some of which would be impossible without increasing returns to scale.

All hail IRS.


Cobb-Douglas production function

[1] Production functions are useful algebraic formulations that are used to specify the factors of production. The Cobb-Douglas production function, developed in 1927, fits production quite nicely. (Click on the image above to embiggen in a new tab.) We note that the value of the exponents a and b determine the returns to scale. If a+b is <1, then we have decreasing returns; if =1, then we have constant returns to scale; if >1, then we have increasing returns to scale.

I leave it to the interested reader to check the algebra. And if you like algebra (we economists just love that stuff), then read the wiki article on the Cobb-Douglas production function.

Historical note: that production function was developed by Charles Cobb (1875 – 1949), an American mathematician and economist, and Paul Douglas (1892 – 1976), an US Senator and Georgist economist.

[2] After introducing the 707 in 1958, Pan Am wanted a jet two and a half times its size, to reduce its seat cost by 30%. That’s IRS again — the bigger the plane, the lower per seat-mile cost. Boeing developed the 747 which entered service with Pan Am in 1970. In all, by the time production of 747s ends in 2022, Boeing would have produced 1,570 of them beauties. The Pratt & Whitney JT9D high-bypass turbofan engine was developed for the Boeing 747. Note the complementarity of production: without the 747, the JT9D would not be feasible, and without the JT9D, the 747 would not be feasible. Later variants of the 747 used GE CF6 and Rolls-Royce RB211 engines.

BONUS trivia from

Production methods have evolved enormously since the first 737 was made in 1966. The main difference is that instead of the aircraft being assembled in one spot they are now on a moving assembly line similar to that used in car production. This has the effect of accelerating production, which not only reduces the order backlog and waiting times for customers but also reduces production costs. The line moves continuously at a rate of 2 inches per minute; stopping only for worker breaks, critical production issues or between shifts. Timelines painted on the floor help workers gauge the progress of manufacturing.

When the fuselage arrives at Renton, it is fitted with wiring looms, pneumatic and air-conditioning ducting and insulation before being lifted onto the moving assembly line. Next, the tailfin is lifted into place by an overhead crane and attached. … As the aircraft moves closer to the end of the line, the cabin interior is completed – seats, lavatories, luggage bins, ceiling panels, carpets etc. The final stage is to mount the engines. According to Boeing, there are approximately 600,000 total parts on a 737NG.

The present build time is reducing from 11 days (5,500 airplane unit hours of work) towards a future target of 8 days (4,000 airplane unit hours of work). The production rate has increased from 31 aircraft a month in 2005 to 42/month in 2014 and reached 57 aircraft a month by 2019 for the 737MAX.

The 737 has since become the best-selling commercial aircraft in aviation history. Here are some statistics which illustrate its success:

  • The Boeing 737 is the best-selling commercial jetliner in history, with, as of January 2017, orders for almost 14,000 aircraft from 290 customers. Over 9,300 737s have been delivered.
  • With approximately 6,500 airplanes in service, the Boeing 737 represents a quarter of the total worldwide fleet of large commercial jets flying today.
  • On Feb. 13, 2006, Boeing delivered the 5,000th 737 to Southwest Airlines. Guinness World Records acknowledged the 737 as “the most-produced large commercial jet” in aviation history.
  • 31% (24,000) of all commercial flights are operated by the 737s.
  • More than 338 airlines in 112 countries fly the 737.
  • On average, over 2,900 737’s are in the air with nearly 500,000 passengers at any given time.
  • On average, one 737 takes off or lands every 1.5 seconds.
  • Boeing 737’s have carried more than 16.8 billion passengers; that is equivalent to every single man, woman and child flying at least twice. (2012 world population was 7 billion).
  • Boeing 737’s have flown more than 115 billion miles; equivalent to approximately 624 round trips from the earth to the sun.
  • Boeing 737’s have flown more than 180 million flights.
  • Boeing 737’s have flown more than 257.6 million flight hours; the equivalent to one airplane flying more than 29,416 years nonstop.

Author: Atanu Dey


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