Knowledge that Transforms

Abstract : In his paper 'On the Structure of Linear Models' Solow makes extensive use of some results about the characteristic roots of indecomposable nonnegative matrices which are due to Frobenius. A recent paper by Helmut Wielandt gives a drastically simplified proof of these results of Frobenius; moreover, in several places the results are sharpened. One of the purposes of writing this note is to bring this paper and its translation into English by Herstein to the attention of economists. Debreu and Herstein have succeeded in simplifying even further the proof of these results. It is pointed out here how these results are applicable in either simplifying, or obviating the need of, several of Solow's proofs.

Annual nationwide sample interview surveys provide a source of data for studying short-run changes in consumer finances. Over-all economic change or stability may be seen in relation to relative changes for subgroups of consumers. This paper presents such an analysis for consumers in different age groups. It examines shifts in distributions of economic resources and in savings patterns, and explores some of the possible relations between the former and the latter. RECENT changes in income and savings patterns of consumer units in different age groups shed new light on some aspects of the urgent question of financial security during old age. Highlighting the incidence of the postwar inflation, they also indicate to what extent both financial resources and economic behavior are correlates of age in the three years considered. Using data from the annual Surveys of Consumer Finances, we can trace the postwar shifts in income size distributions and savings among the young, middle-aged, and old.2 In this way we discover which groups benefited most and which least from rising national income. Changes in relative income positions are then related to changes in savings patterns. From this comparison of differential changes in both savings and income among the various age groups, we infer certain hypotheses about causal relationships. The possible effects on savings of some factors other than income are also considered. The reason for treating age as if it were an independent variable in a correlational analysis of consumers' monetary resources and eco