Monday, August 18, 2014

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.

 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