Even If The Workers Could Live On Air

The Maximum Rate Of Growth Around The World

Consider a model of an economy in which all commodities are produced from inputs of labor and previously produced commodities. And suppose the commodities needed as inputs in the production of commodities are described through a Leontief input-output matrix in which no commodity can be produced with (unassisted) direct labor alone. Consider the special case in which wages are zero. In a sense, this special case can be seen as a description of a futuristic economy in which all production is automated, and robots are used to produce robots.

In the theory, the input-output relations determine a finite maximum rate of profits, corresponding to the maximum eigenvalue of the Leontief matrix. This maximum rate of profits is also the maximum rate of growth that arises in the Von Neumann growth model. A composite commodity, proportional to the associated eigenvector, arises from the Leontief matrix. Along the Von Neumann ray, the output of the economy each year consists of an evenly expanding output of this standard commodity, as Piero Sraffa called it. The standard commodity, in some sense, is a generalization of "corn" in David Ricardo's corn model (which was expounded in his 1815 Essay on the Influence of a Low Price of Corn on the Profits of Stock). The commodities with positive quantities in the standard commodity are known as basic commodities, once again in Sraffa's terminology.

As this post demonstrates, this is an operational model. The graph above is based on an eigenvector decomposition of Leontief matrices. Each Leontief matrix was derived from a transaction table for a country or region. The transactions tables, in turn, are derived from the GTAP 6 Data Base, compiled by the Global Trade Analysis Project at Purdue. (I had help extracting the database and putting it in a format that I can use.) GTAP 6 data is meant to cover the year 2001. Quantities of each commodities are measured such that a unit of each commodity can be purchased with one billion dollars at prices observed when the data was taken.

The graph above and the table below show the maximum rate of profits or growth for each country or region for the snapshot yielding the data. The actual rate of profits for prices that allow for the smooth reproduction of the economy falls below the maximum, sometimes considerably, because the workers do not live on air. The larger the proportion of the net output of the economy paid out in wages, the lower the corresponding rate of profits. At any rate, prices of production fall out, given some information on the distribution of income and production conditions.

Along with calculating the maximum rate of profits, I found the standard commodity and identified which commodities are basic for each country or region. For example, the commodities produced by the following industries are basic commodities in the United States: Cereal Grains; Vegetables, Fruits, Nuts; Crops; Bovine Cattle, Sheep and Goats, Horses; Animal Products; Raw Milk; Coal; Oil; Minerals; Bovine Meat Products; Meat Products; Dairy Products; Sugar; Food Products; Beverages and Tobacco Products; Textiles; Wearing Apparel; Wood Products; Paper Products; Publishing; Petroleum, Coal Products; Chemical, Rubber, Plastic Products; Mineral Products; Ferrous Metals; Metals; Metal Products; Motor Vehicles and Parts; Transport Equipment; Electronic Equipment; Machinery and Equipment; Manufactures; Electricity; Gas Manufacture, Distribution; Water; Construction; Trade; Transport; Water Transport; Air Transport; Communication; Financial Services; Insurance; Business Services; Recreational and Other Services; and Public Administration, Defense, Education, Health. Which commodities are basic varies among countries, and I typically found a few non-basic commodities in each country.

I think this data is fairly comprehensive, and I hope that I can do further believable analyses with it.

Maximum Rate Of Growth By Country

Country	Rate of Growth (Percent)
Peru	144.8
Turkey	132.5
Rest of Southeast Asia	127.4
Albania	125.3
Uganda	122.5
Zambia	121.6
Rest of Southern Africa Development Community	120.7
Mozambique	119.3
Greece	117.8
Mexico	117.3
Argentina	116.9
Columbia	115.0
France	109.8
Sri Lanka	109.6
Chile	108.8
United States	107.1
Bangladesh	106.4
Zimbabwe	106.3
Rest of Sub-Saharan Africa	105.6
Spain	104.4
Madagascar	104.1
Rest of South Asia	104.1
Venezula	104.1
Japan	103.4
Switzerland	102.5
Italy	101.0
Botswana	98.2
United Kingdom	97.7
India	93.8
Indonesia	93.0
Rest of Free Trade Area of the Americas	92.8
Rest of EFTA	92.0
Portugal	91.4
Canada	90.7
Malta	89.3
Rest of the Caribean	88.9
Denmark	88.7
Rest of Central America	88.4
Tanzania	87.7
Rest of South America	87.1
Australia	87.1
Rest of Europe	86.2
Brazil	85.6
Sweden	85.2
Rest of North Africa	84.3
South Africa	83.5
New Zealand	82.7
Rest of Middle East	82.5
Tunisia	82.3
Taiwan	82.1
Netherlands	81.7
Finland	80.0
Poland	76.8
Germany	76.6
Latvia	75.8
Rest of South African Customs Union	75.0
Malawi	72.9
South Korea	72.9
Hungary	72.4
Austria	70.3
Luxembourg	67.6
Romania	66.6
Russia	66.2
Lithuania	66.0
Rest of East Asia	64.4
Philippines	64.2
Estonia	62.3
Thailand	61.6
Malaysia	60.5
Vietnam	60.0
Rest of Oceania	57.6
Ireland	55.2
Central America	54.3
Slovakia	54.0
China	53.8
Slovenia	53.7
Croatia	51.1
Czech Republic	47.1
Belguim	46.9
Morocco	45.9
Hong Kong	40.6
Singapore	35.0
Cypress	24.6
Rest of Former Soviet Union	12.7
Uruguay	12.4
Bulgaria	8.6
Rest of North America	4.7