The archive.

Profit maximization need not settle a price when a sole buyer faces a sole seller. In this theoretical note, Gerhard Tintner makes that difficulty concrete through a steel producer purchasing iron ore from a monopolist supplier. His distinctive question is when buyer control, seller control, and joint profit maximization yield the same outcome. The conditions for their agreement prove exceptional: ordinarily, static analysis establishes a bargaining range rather than a unique input price. By tracing how price-setting authority changes the result, readers can distinguish the constraints imposed by demand and production costs from the distribution of gains between the parties. Tintner’s extension to union–employer wage bargaining sharpens the stakes: on his account, bargaining power, shaped especially by political forces, determines what profit-maximizing equations leave unresolved.

Discarding observations can make a statistical test more defensible. In this 1939 mathematical note, Gerhard Tintner confronts a difficulty in time-series analysis: successive differencing may remove a smooth trend, but it also creates correlations even when the original errors are independent. His response is to select differences built from disjoint observations, allowing their variances to be compared using familiar significance tests. He applies the same selection principle to lagged products in deriving a serial-covariance distribution. The note offers a precise encounter with the trade-off between retaining information and securing a tractable sampling distribution. Readers can see how the observations chosen determine which tests become available—and why the assumptions of normality, independence and a sufficiently smooth trend matter.

What makes consumer-credit exercises useful in teaching financial mathematics? In this brief review, Gerhard Tintner assesses Charles H. Mergendahl and Le Baron R. Foster’s pamphlet as a supplement to high-school and college textbooks. He distinguishes an adequate introduction to credit concepts and calculations from the exercises themselves, which he finds thoughtfully designed, interesting and stimulating. The review offers a concise curricular judgement: its interest lies in Tintner’s emphasis on the quality of practice problems, rather than merely their number or subject matter.

Symmetry makes a many-variable probability problem unusually compact in Gerhard Tintner’s 1939 article. He studies a quadratic form in independent standard normal variables with one common coefficient for squared terms and another for cross-products. Its characteristic function separates into just two factors: one for collective movement and one for the remaining contrasts. The interest lies both in this reduction and in Tintner’s effort to turn it into a usable calculation, moving from Fourier inversion and a hypergeometric expression toward tabulated chi-square densities. Readers can trace how coefficient structure determines distributional structure, while distinguishing the robust characteristic-function result from printed density formulas whose signs, normalization, and conditions require verification before numerical use.

Can a demand curve measured across decades remain meaningful if the relationship it describes is itself changing? In this review essay on Henry Schultz’s 1938 treatise, Gerhard Tintner combines admiration for empirical demand research with a pointed challenge to its static assumptions. Dividing historical data into separate periods, he argues, yields successive snapshots without explaining how demand changes. His alternative allows both the position and slope of a demand curve to vary, ideally in response to economically meaningful factors such as population, expectations, and tastes. Equally crucial is testing whether the unexplained residuals are random before trusting statistical significance. The essay offers a concrete encounter with the tension between elegant estimation and economic change—and with Tintner’s insistence that economic theory and statistical diagnosis must develop together.

Gerhard Tintner’s brief review of S. Koller’s Graphische Tafeln zur Beurteilung statistischer Zahlen judges the book by its usefulness in statistical calculation. He identifies its nomograms—graphical aids covering several statistical distributions—and singles out the well-chosen practical examples as a help to users. The review offers a compact recommendation grounded in usability rather than theoretical novelty, showing precisely what Tintner valued in this medical statistician’s handbook.

A statistical pattern is not yet an economic explanation—and a plausible model fit is not yet a tested result. These distinctions sharpen Gerhard Tintner’s brief 1940 review of Herman Wold’s study of stationary time series. Tintner admires Wold’s mathematical framework but questions what its applications to wheat prices and Swedish living costs actually establish. His reservation is specific: without significance tests, the validity of the results cannot be assessed. The review offers a compact encounter with an economist’s demands on mathematical statistics, showing why theoretical advances in describing fluctuations still require methods of inference before they can support empirical conclusions.

A close numerical fit need not justify a statistical inference. In this 1940 article, Gerhard Tintner examines what economists can legitimately conclude from observations whose successive values depend on one another. His central tension is that the random fluctuations most amenable to existing probability methods may be less economically revealing than persistent trends and cycles. Distinguishing correlation from the “covariation” of systematic movements, he challenges the assumption that removing a trend makes conventional significance tests valid. His demand for flexible methods grounded in economic theory gives the article a concrete methodological focus: readers can discover why separating components, fitting equations, and establishing evidence are different tasks—and why success at one does not guarantee success at the others.

When does a statistical model of business cycles warrant conclusions about economic policy? In this 1941 review of J. Tinbergen’s study of the United States in 1919–1932, Gerhard Tintner admires the ambition of linking economic theory to an extensive system of estimated equations, but scrutinizes the grounds for trusting its results. His objections are concrete: time-series residuals require testing, regression coefficients may change, and expectations remain insufficiently explicit. Findings that public investment dampens fluctuations while price stabilization increases them depend on restrictive conditions, including the absence of a stock-exchange boom. The review offers a compact encounter with econometric judgment: Tintner distinguishes the achievement of constructing a comprehensive model from the reliability of its causal explanations and policy deductions.

A useful statistical textbook need not settle the theoretical problems behind its procedures. In this brief review of the second edition of Mordecai Ezekiel’s Methods of Correlation Analysis, Gerhard Tintner distinguishes genuine practical improvements from questions the discipline itself has yet to resolve. His qualified praise turns especially on the reliability of time-series forecasts: a sketchy treatment of error formulas disappoints him, but he refuses to blame Ezekiel for the absence of generally accepted solutions. Tintner also notes the edition’s reliance on Fisher’s fiducial approach rather than newer theories of estimation and hypothesis testing. The review offers a concise appraisal of what improved statistical instruction can provide—and what remains beyond its reach.

More observations do not necessarily mean more information: this difficulty gives Gerhard Tintner’s review of Harold T. Davis’s The Analysis of Economic Time Series a focus beyond its assessment of a statistical handbook. Tintner asks what mathematicians miss when economic statistics remains outside their field of attention. He distinguishes lucid exposition from genuine methodological innovation, praising Davis’s work on serial correlation while treating forecasting and business-cycle explanation as unresolved problems. Particularly revealing is his account of how dependence among observations can undermine a naïve count of degrees of freedom. The review offers a concise encounter with Tintner’s standards of judgement: mathematical ingenuity matters, but so do the limits of inference and the connection between statistical technique and economic interpretation.

A production decision commits resources now while changing what can be done later. In this article, Gerhard Tintner asks how firms should plan when future prices and productive conditions are uncertain—and when the highest expected profit need not be their preferred prospect. His distinctive move is to separate the probability distribution of possible profits from the firm's valuation of that distribution, allowing dispersion and skewness to matter alongside the mean. A two-period example, in which applying lime now improves later agricultural production, gives this abstract distinction a concrete setting. Through graphical demonstrations, readers can trace how present commitments, later adjustments, and preferences toward risk jointly determine a production plan. Tintner also treats uncertainty about probability distributions themselves, rather than assuming that the relevant odds are always known.