The archive.

How much mathematics should an introduction to economic modelling teach, and which tools can it afford to leave out? In this 1958 review of E. F. Beach’s Economic Models—An Exposition, Gerhard Tintner judges accessibility against technical coverage. He values Beach’s use of economic examples to make mathematical and statistical methods intelligible to readers with substantial economic knowledge but limited mathematical training. Yet he finds the explanations compressed and challenges the omission of matrices, determinants, input-output models and linear programming: these, he argues, are no harder than topics already included. This brief assessment offers a concrete view of Tintner’s pedagogical priorities, showing why an example-rich introduction can succeed while still leaving readers without useful analytical tools.

How much can a small sample tell agricultural administrators before a full census is available? In this brief 1958 review of Heinrich Strecker’s Moderne Methoden in der Agrarstatistik, Gerhard Tintner singles out a striking result: a sample covering 2% of West German agricultural enterprises produced preliminary census figures, nine-tenths of whose deviations from complete enumeration were below 10%. Tintner’s interest lies in the practical performance of statistical methods, rather than a separate examination of their theory. His favorable assessment connects this example with ongoing surveys of farm labor and agricultural production, while noting Strecker’s command of international research. The review offers a compact account of the concrete evidence on which Tintner based his confidence in agricultural sampling.

When does a statistical distribution become an economically interpretable model? In this concise 1958 review of J. Aitchison and J. A. C. Brown’s The Lognormal Distribution, Gerhard Tintner singles out the connections between income dispersion, inequality measures, and consumer demand. He values the authors’ use of Lorenz diagrams to relate lognormal variance to income concentration, and finds particular novelty in their derivation of Engel curves linking purchases to income. His assessment shows what an econometrician looks for beyond statistical fit: meaningful parameters and a model that can accommodate aggregation, prices, and household composition. Strong praise for the monograph’s methods and multilingual bibliography is tempered by a specific historical correction—the omission of H. T. Davis’s earlier work on income distribution.

A bounded growth curve can be attractive for forecasting yet awkward to estimate from observations taken at regular intervals. In this short 1958 article, Gerhard Tintner offers a precise workaround: taking reciprocals turns the logistic function into a linear relation between successive observations. Unlike an earlier method based on differential equations, his procedure avoids approximating growth rates from potentially noisy data. Swedish population figures from 1850 to 1950 provide the worked example, leading to an estimated population ceiling and a forecast for 1960. The article’s interest lies in this economical change of perspective: readers can see how a nonlinear growth model becomes tractable by matching its mathematical representation to discrete measurements, while distinguishing that computational simplification from evidence of forecast reliability.

For Gerhard Tintner, the test of an introduction to linear programming is not how thoroughly it teaches calculation, but how clearly it explains economic decisions. His 1959 review of Martin J. Beckmann’s Lineare Planungsrechnung locates its strength in the short-run production and cost problems of competitive firms, illustrated through ice-cream production and a fictitious furniture factory. Tintner distinguishes Beckmann’s emphasis on neoclassical partial equilibrium from Dorfman, Samuelson and Solow’s general-equilibrium approach. His endorsement is qualified by reservations about compressed mathematics and brief treatments of consumption and Leontief models. This compact review offers a precise account of what Tintner valued in mathematical economics: methods that illuminate familiar economic problems without making advanced mathematics a prerequisite.

When household budgets grow, does consumption expand in quantity, shift towards dearer varieties, or move into different goods altogether? Gerhard Tintner examines these alternatives through Austria’s 1954/55 urban consumption survey, distinguishing expenditure responses from changes in quantities and average prices paid. His estimates show why a simple contrast between necessities and luxuries is insufficient: rent protection and social insurance can weaken the connection between spending and household resources, while a food’s classification as “inferior” may depend on the social group examined. The report’s distinctive interest lies in its scrutiny of what such estimates warrant. Statistical uncertainty qualifies apparent differences, and forecasts depend on assumptions linking comparisons between households to changes over time. Readers can discover both concrete patterns of Austrian consumption and the limits of using household budgets to anticipate demand.

For Gerhard Tintner, mathematical economics proves its worth through contact with data and the risks of practical advice. His 1960 review of Jan Tinbergen’s Selected Papers praises precisely this combination, pointing to Tinbergen’s willingness to leave concrete policy recommendations open to later scrutiny. Yet Tintner also highlights results that unsettle easy policy assumptions: economic integration can, under specified conditions, lower real income, and increased productivity need not produce desirable outcomes. His strongest interest lies in Tinbergen’s analysis of the optimum economic regime, where formal welfare reasoning encounters ethical choices between capitalism and collectivism. This short review offers a focused account of what Tintner values in economic analysis—and where he sees its mathematical tools clarifying, rather than settling, questions of policy and institutions.

Gerhard Tintner’s brief 1960 review of Harry M. Markowitz’s Portfolio Selection focuses on a concrete trade-off: greater average return cannot be obtained from an efficient portfolio without accepting greater dispersion of returns. Tintner reads this criterion as an application of newer mathematical economics, contrasting its tools with the calculus and mechanical models of the classical tradition. His interest lies in the connection between formal reasoning and practical use: quadratic programming, computational methods, and utility theory promise an analysis that financial analysts can use. The review offers a concise account of why Tintner welcomed Markowitz’s approach, especially its combination of mathematical innovation with exposition accessible to readers lacking extensive mathematical preparation.

A rise in income can reduce demand for a good that conventional consumer theory classifies as superior—not merely by changing purchasing power, but by changing tastes. In this mathematical essay, Gerhard Tintner examines what happens when individual preferences depend on other people’s incomes and consumption. He retains utility maximization and budget constraints while replacing the assumption of socially isolated consumers with explicit relationships among their demands. The result links income responses to substitution effects and shows why market demand may reflect more than the aggregation of independent choices. Readers can discover precisely where social interdependence alters familiar demand formulas, without mistaking the framework for an empirical demonstration of how strongly those influences operate.

When do mathematical probability models warrant conclusions about economic and social data? Gerhard Tintner’s memorial survey approaches this question through Oskar Anderson’s insistence that statistical procedures answer to the populations and observations they describe. Tintner connects Anderson’s practical experience in agricultural sampling with his demands for explicit probability models and predetermined standards of accuracy. His most sustained discussion concerns the Variate Difference Method: how repeated differencing can separate trends from random variation, and why autocorrelation or short periodic fluctuations can undermine it. As a contributor to this field himself, Tintner offers appreciation tempered by technical objections. Readers can discover both the reasoning behind familiar first-difference techniques and a methodological alternative to prevailing Anglo-American approaches, grounded in Anderson’s Russian and continental statistical inheritance.

A smooth growth curve says little about the uncertainty surrounding it. In this 1963 article, Gerhard Tintner and Jati K. Sengupta construct a generalized birth-and-death process in which expected income follows a logistic path while income itself can rise, fall, or remain unchanged. Their distinctive economic premise is that the scarcest productive factors constrain output, motivating a probability distribution through the statistics of minimum values. Applied to German per-capita national income for 1851–1939, the model links a proposed long-run ceiling to a tractable estimation procedure. Readers can examine how economic assumptions become probability laws—and how historical data calibrate such a construction without independently proving its assumed ceiling or distribution of fluctuations.

An investment allocation can maximize projected income yet leave productive capacity idle, consumption sacrificed, or investment exposed to greater uncertainty. In this article, Jati K. Sengupta and Gerhard Tintner examine that tension through Dutch long-term planning and India’s Mahalanobis model. Their concern is not simply to calculate an optimum, but to ask which assumptions make it feasible and desirable: whether saving keeps pace with investment, whether production techniques can change, and whether planners value output or consumption. A numerical exercise using Indian Third Five-Year Plan constraints makes the stakes concrete, showing how a preference for lower investment risk can alter the income-maximizing allocation. Readers can discover how seemingly technical choices about coefficients and objectives shape the economic priorities embedded in a development plan.