Gerhard Tintner, A Contribution to the Nonstatic Theory of Production (1942)

Gerhard Tintner’s contribution to an edited volume develops a mathematical theory of production in which firms plan through time under differing forms of anticipation. Its six sections move from static optimization to single-valued expectations, subjective risk, subjective uncertainty, flexibility, and models of expectation formation. The central conceptual move is to distinguish uncertainty about future outcomes from uncertainty about the probability distributions assigned to those outcomes. Production decisions consequently depend not simply on anticipated prices and technology, but on the firm’s evaluation of possible profits and confidence in its own forecasts.

We do not here consider any "objective" risk, but only the subjective estimate and opinion of the individual.

This restriction governs the argument. Tintner relates his terminology to Knight without identifying their distinctions, and aligns his conception of probability with Keynes rather than von Mises’s frequency definition. “Subjective risk” means that the firm knows its anticipated probability distribution with certainty; “subjective uncertainty” means that this distribution is itself only conjectured. The concluding section considers how past frequencies might inform subjective beliefs, but experience supplies possible foundations for anticipation rather than defining probability itself.

The opening static analysis establishes the machinery subsequently extended through time. Outputs enter positively and inputs negatively into a transformation function; a price-taking firm maximizes profit subject to that technological constraint. Lagrange multipliers yield marginal conditions linking prices to the derivatives of the transformation function. Differentiating these conditions supplies demand and supply responses, expressed through substitution or transformation elasticities. Tintner also considers expenditure, revenue, and aggregation across firms. This technical groundwork makes nonstatic production a systematic extension of constrained optimization rather than a separate account of business conduct.

Section II introduces a fixed planning horizon, dated inputs and outputs, anticipated interest rates, and discounted prices. With single-valued expectations, the firm maximizes total anticipated discounted profit subject to a transformation function embracing the entire production plan. Substitution and transformation now operate between commodities at different dates as well as between commodities at one date; interest-rate responses appear as weighted combinations of these intertemporal elasticities. Continuous production replaces finite sums with integrals and the transformation function with a functional. Time therefore changes both the valuation of production and the range of technologically connected choices.

Under subjective risk, future prices and interest rates instead have a joint probability distribution, while the production relationship remains anticipated with certainty. Planned quantities and the distribution’s parameters determine a distribution of discounted profit. Tintner then introduces a preference functional:

That is, we assume a risk preference functional which is fixed by the total shape of the probability distribution of profit, Q, over its whole range.

Expected-profit maximization becomes a special case rather than the universal objective. Preferences may also respond to variability, skewness, or other distributional characteristics. The firm maximizes its evaluation of the profit distribution subject to production constraints, and Tintner derives responses of planned inputs and outputs to changes in anticipated means, variances, and correlations. His generality lies in leaving the preference functional open, not in prescribing a particular attitude toward risk.

Subjective uncertainty adds another layer. The parameters describing anticipated prices and interest rates are themselves imperfectly known, so Tintner assigns them a “likelihood” distribution.

We have really a "probability distribution of probability distributions."

Integrating over these uncertain parameters produces a new distribution of anticipated profit, evaluated by a corresponding uncertainty-preference functional. Although the terminology invokes Fisher, Tintner notes that his likelihood resembles an a priori probability; the final section connects the problem with Bayes’s theorem. The distinction concerns confidence in the model of possible outcomes, not merely the dispersion of outcomes within an accepted model.

Flexibility and adaptability bring this hierarchy into the timing of commitments. A firm expecting better information may value the ability to revise distant decisions while committing itself in the near future. Tintner introduces multiple technological constraints and a further likelihood over the parameters of the preceding likelihood distribution. This formal device represents anticipated changes in forecasts, although it does not provide a worked-out process of learning or contingent replanning. The economic rationale is clearest in the concluding discussion:

The entrepreneur will have to make some sacrifice of anticipated profit in order to keep his enterprise more adaptable and flexible and to be able to make new decisions and change his plans if his knowledge increases in the future and uncertainty decreases (Hart, Stigler).

The final section asks how anticipations might arise from experience. Single-valued forecasts can project current values, simple or weighted historical averages, trends, or particularly influential past events. Under risk, distributional moments may similarly derive from historical observations. Genuine subjective uncertainty proves harder to model, especially for the innovating entrepreneur, whose evaluation need not rest exclusively on experience. Tintner ends by questioning whether a preference for improbable but highly profitable ventures is adequately explained by rational economic behavior rather than prestige or power. The contribution’s lasting interest is this conjunction of formal ambition and behavioral qualification: production planning incorporates distributions, confidence, and revisability, while the formation and evaluation of entrepreneurial expectations remain incompletely explained.