THIS ARTICLE'S MAIN PURPOSE iS to discuss certain key problems that arise in calculating purchasing-power parities (PPPs) when making international comparisons of real product, while reviewing partially the work of Irving Kravis, Alan Heston and Robert Summers (1982). Before beginning the discussion, the author wishes to record his opinion that this work of Kravis, Heston and Summers, carried out and successively published over the past 15 years, represents one of the great contributions to applied economics. In the article that precedes this one, Kravis provides a survey of the applications of this type of data, but it must be emphasized that any such listing can do only partial justice to the scope of new applications which seem to arise almost every day. Apart from applications to various aspects of international economic policy, there is so much greater international variation in basic economic variables, such as real income and relative prices, than is usually found in typical intranational/intertemporal comparisons, that the new data inevitably represent an enormous increment in our science's general capacity for statistical experiment. Thus, the debt owed to this team of research workers, by the economics profession at large, is immeasurable. A is essentially a form of international or interregional price index, complicated, but not essentially changed, by the existence of national currencies. For example, suppose we found, by some kind of index-number calculation, that the general price level in region A was 10 percent higher than in region B of the same country. Given a common currency, the between the money circulating in the two regions is clearly 1.0, but the for region A, in comparison with region B, is 0.91, this being the number by which it is necessary to multiply a given nominal income in A to give it the same purchasing power as a corresponding income in B. It follows that the must be some average of the ratios among individual prices in the two regions. In the case of two countries with different currencies, one can speak of a commodity PPP as being the rate of exchange between the two currencies which would equalize the price of a given commodity; then the general for the two countries is some average of the PPPs. In international, as in intertemporal, comparisons, there is a duality between the problem of measuring price levels and

Managerial utility, 186. — Methods and definitions, 191. — Growth rate of demand, 193. — Imitative products, 197. — The supply of finance, 199. — The rate of profit, 200. — Completion, 202. — Interpretation, 204. — Maximizing versus satisficing, 207.

FEW WOULD DISAGREE that Adam Smith's invisible-hand theorem is the heart of the economist's Weltanschauung. Ask whether trade barriers should be lowered, the spread of multinational corporations restrained, oil prices deregulated, cartels dissolved, or more fundamentally whether a market-based capitalist system is economically superior to a state-run socialist system, and economists almost certainly will begin to answer the question by trying to apply the theorem. Every student knows that the theorem depends on the assumption of atomistic competition, which in turn assumes that the system is decentralized and that no competitor is large relatively to others. There is another crucial assumption, however, that is often ignored and usually underemphasized, namely that all competition is price competition. In reality one of the most distinctive features of capitalism-one that is most often raised in lay discussions of its merits and demerits-is the prevalence of other forms of competition, such as competition in research, development, and advertising; competition to obtain and hold monopoly; and competition for corporate growth. These various forms of competition, we shall aim to show, are not clearly analogous with the theory of price competition: more non-price competition, rather than less, is not necessarily Pareto optimal. Self-evidently, the production side of a market economy is decentralized only to a limited degree, i.e., to the level of a decision-making unit composed of more than one human. Such a unit-playing Neuron to the Invisible Hand-is typically called a firm. It is in fact a team. Rather than remaining small, firms are in practice composed of any number of individuals from a handful on to half a million. Some