Gerhard Tintner — Risk and Uncertainty

Gerhard Tintner’s conference contribution, originally published in 1977 and republished in 2012, examines the conditions under which demand and supply depend on relative prices rather than their absolute monetary level. Its three main sections connect homogeneity, the distinction between real and monetary economies, and equilibrium stability. The central argument is conditional: familiar invariance results survive many static, dynamic, and risk-bearing models, but become less secure when agents learn about unknown probability distributions. The equivalence of real and monetary economies requires additional, empirically restrictive assumptions.

Tintner begins with mathematical propositions establishing when optimization preserves homogeneity. A function homogeneous of degree zero remains unchanged when its arguments are multiplied by the same positive factor. For economic choice, the decisive move is to examine the objective function and constraints together: appropriate homogeneity in these components yields scale-invariant solutions. This framework encompasses competitive production and numerous forms of imperfect competition. Monopoly alone does not destroy homogeneity; what matters is how prices enter preferences, constraints, conjectures, and bargaining arrangements.

If the utility functions depend upon money income or absolute prices (money illusion, Tintner [71], p. 143) the solutions are no longer homogeneous.

This exception identifies the behavioral significance of the mathematical property. Agents who respond to monetary magnitudes independently of purchasing power need not preserve their choices under proportional price changes. Changing bargaining power and certain game-theoretical interactions can likewise undermine invariance. Where homogeneity holds, equilibrium determines relative prices, with one commodity serving as numeraire; without it, absolute prices can enter the determination of equilibrium.

The dynamic discussion introduces anticipated prices. Following Hicks, Tintner initially treats expectations as single-valued, interpreting this through known probability distributions whose dispersion can be neglected or represented by certainty equivalents. Homogeneity in current prices then requires the sums of the partial elasticities of anticipated prices with respect to current prices to share a common value. A simple investment program illustrates the result: proportional changes in anticipated returns, investment prices, and available funds leave the optimal allocation unchanged. Dynamics therefore need not overturn the static conclusion, provided expectations transform appropriately.

Risk introduces dispersion explicitly while retaining known distributions. Tintner assumes normally distributed investment yields with known means and covariances, then considers expected-gain maximization, Markowitz portfolio selection, and objectives combining expected returns with variance or standard deviation. The portfolio model is described as minimizing variance subject to a budget and minimum expected return, although its displayed objective bears a maximization sign. The common analytical concern is how the parameters must scale to preserve the solution.

Hence the classical propositions of static theory are preserved in the risk model. It should however be noted, that our parameters include now the variances and covariances of investment opportunities.

The qualification matters: these are invariance results involving an enlarged parameter set, not unrestricted claims that changing prices alone leaves portfolios unaffected. Risk remains compatible with homogeneity because the distributional parameters can participate in the required transformations.

Uncertainty changes the argument by making those parameters unknown. Tintner translates the Knightian distinction into a statistical contrast between large-sample knowledge and small-sample inference. Using conjugate Bayesian priors, he examines unknown means, unknown precision matrices, and their joint estimation. Posterior parameters combine prior information with sample observations. Consequently, scaling prior parameters while holding the evidence fixed generally does not produce a corresponding scaling of posterior beliefs. Portfolio decisions may remain homogeneous in posterior parameters without being homogeneous in the original priors.

Hence also in this case we cannot expect homogeneity of degree zero in a portfolio model, except in the case of no sample.

The operative mechanism is learning: new observations introduce terms that do not scale with the investor’s initial beliefs. Improper priors do not eliminate this difficulty. Although a fixed sample can support homogeneous solutions, successive samples change the estimated parameters. Tintner thus distinguishes invariance within a given informational situation from invariance as experience accumulates. He associates the resulting failure of homogeneity under uncertainty with Keynes.

The second main section asks when introducing money leaves relative prices and the real interest rate unchanged. Rosenstein-Rodan’s production model supplies one benchmark, without portfolio selection. Negishi’s neoclassical framework makes the demands on consumer preferences explicit: identity between real and monetary systems requires identical utility functions, specified separability conditions, and homogeneity in present consumption, anticipated consumption, and money holdings. These restrictions imply straight Engel curves through the origin.

It is very unlikely that these stringent conditions are fulfilled in reality.

Tintner supports this judgment with expenditure studies questioning both linear Engel curves through the origin and homogeneous utility. The monetary dichotomy is therefore a result requiring justification, not an automatic consequence of equilibrium analysis.

The final section treats stability through Walrasian price adjustment. Linearizing excess-demand dynamics yields convergence when the adjustment matrix has eigenvalues with negative real parts; gross substitution remains central, including when expectations are introduced. An inflationary modification makes excess demand depend on price changes and allows convergence toward constant rates of price change rather than fixed price levels. Across these models, the article’s contribution is to expose the assumptions behind invariance, monetary equivalence, and stability—and especially how learning under uncertainty complicates their extension beyond established informational conditions.