The lay person setting out to learn about economics might take advice about where to start. The Whole Earth Catalogue recommends the textbook on economics by Paul Samuelson.
Pretty soon one is introduced to the "production possibility" curve. Apparently one can convert the resources used to produce butter into resources to manufacture guns and vice versa. By a combination of the two we are led to believe that the economic benefit is greater than concentrating on only guns or only butter. The graphic plot is a convex curve. If you use half the resources for guns and half the resources for butter production, you are better off than specialising in either of the two options.
This meme reappears in many economic textbooks. It seems that many authors follow the same approach as Samuelson and refine the text so as not appear to plagiarise.
The origin of the guns versus butter comes from the famous Nazi propagandist Paul Joseph Goebbels. In 1936 when the administration was under pressure for limited food availability, Goebbels told the German people that they could not have both guns and butter. This makes Samuelson's example rather unfortunate. Never mind that you have no use for grazing land if you want to make guns and you have no use for engineering workshops in maintaining a herd of cattle.
Stiglitz does not use the example of guns and butter in his exposition of the production possibility curve. He uses the example of corn and wheat. In this case cropping land can be used for growing corn or alternatively for growing wheat. I would expect that the production possibility would be a straight line (just like a budget line) since the crop would be proportional to the area sown, one crop could be traded off the other. But somehow Stiglitz manages to come up with a convex curve.
The convex curve implies that there is a higher production rate with smaller units, not any economy of scale. To test this concept we can do a worked example using real life data. Referring to the standard chemical engineering reference (Perry's Chemical Engineering Handbook) we find that empirical data shows that the ratio of plant capital costs is in the ratio of plant output capacities raised to a power. That exponent has different values for different types of plant and is almost always less than one. The exponent is typically 0.7 which means that the cost of a plant is increased by 62.5% when the output is doubled.
If we take an example where there is, for example, a supply of sodium chloride salt and a fixed quantity of capital and compute the production possibility curve for two alternative chemical plants, one making caustic soda (NaOH) and one making sodium carbonate (Na2CO3). The economy of scale exponent for caustic soda is 0.55 which results in a plant output of 28.35% capacity for a plant using half the capital available. For sodium carbonate, the exponent is 0.38 which gives a 16.14% capacity for a plant using half the capital available. This gives a production possibility curve that is distinctly concave, not convex as in the textbooks. Economies of scale justify the concentration on one product to the exclusion of the other.
If one suspends ones disbelief and delves further into the textbooks, one finds that one is presented with a curve such as a demand curve or a supply curve from which a schedule of curve points is used as if it were real data. Well, I can do that too. Taking a supply curve from the textbook that has been "shifted" and extracting a couple of points, we find that from the bottom of the curve the price must increase by a factor of ten in order for the supply to be doubled. Now this strains ones credulousness. This is an extreme dis-economy of scale. Or could it be that there is a negative fixed cost of production? One is left with the feeling that the spirit of Goebbels is alive and well in economics. Return to home page.