Gerhard Tintner’s journal article extends Hicks and Allen’s demand theory from contemporaneous choices to consumption planned across time. Its purpose is to derive income, price, and interest elasticities from intertemporal utility maximization, thereby providing a theoretical foundation for the dynamic demand functions associated with G. C. Evans and C. F. Roos. The article develops this argument in two sections: a detailed derivation for finitely many consumption dates, followed by a shorter continuous-time formulation using functionals and integral equations. Its central move is to treat commodities at different dates as jointly chosen components of one consumption plan, linked through discounted prices and a single budget constraint.
We propose to derive income, price, and interest elasticities of demand under the assumption that the individual has definite plans for the future and definite expectations of future incomes, prices, and interest rates.
This assumption defines both the reach and the limitation of the analysis. Tintner excludes uncertainty in Knight’s sense, while allowing that risk may be accommodated. The derivation takes expectations as given; it does not explain their formation or revision. “Dynamic” demand here concerns choices distributed across future dates and their sensitivity to expected economic conditions, rather than a fully specified process of adjustment through time.
In the discontinuous case, the individual plans consumption of multiple commodities at a finite number of dates. Expected prices and incomes are discounted by accumulated expected interest factors. Utility depends on the complete array of dated consumption quantities, permitting relationships between goods consumed at different times without requiring a separable utility specification. Tintner preserves the ordinal basis of Hicks and Allen’s approach:
This utility function may be replaced by an arbitrary utility index with positive derivative since only the ratios of the marginal utilities (marginal rates of substitution) enter into the theory.
The individual maximizes this utility subject to equality between total discounted expenditure and total discounted income. The constraint applies to the planning horizon as a whole, rather than requiring expenditure to equal income at every date. Saving consequently appears as the difference between income and expenditure within portions of that horizon. The first-order conditions equate each dated marginal utility to its discounted price multiplied by a common marginal utility of money. Together with the budget equation, these conditions determine demand, subject to further conditions whose fulfillment Tintner explicitly qualifies.
The connection with earlier dynamic demand theory is conditional rather than automatic:
The dependence of these expected quantities upon past incomes, prices, and interest rates forms the bridge between our analysis and the dynamic demand functions of Evans and Roos. If this dependence is known then the demand appears as a function of past factors.
Thus utility maximization supplies demand as a function of expected conditions; a separate account of how expectations depend on historical observations would turn that result into demand expressed through past variables. Tintner identifies this bridge without supplying the expectation mechanism itself.
The mathematical core differentiates the budget and optimality conditions to obtain a linear system for changes in consumption and the marginal utility of money. A determinant constructed from first and second utility derivatives yields a general demand differential. This general expression can accommodate connections among expected incomes, prices, and interest factors, although the subsequent derivations vary one quantity at a time while holding the others fixed.
The resulting elasticity relationships extend familiar static distinctions across commodities and dates. Demand’s elasticity with respect to income at a particular date equals its elasticity with respect to total discounted income multiplied by that date’s share of discounted income. With interest factors fixed, discounted and undiscounted income elasticities coincide. The price elasticity similarly separates into an income component and a substitution component, weighted by the share of total discounted income spent on the relevant dated commodity. Substitution therefore includes relations between consumption at different times, not merely between goods purchased simultaneously.
Tintner singles out the interest calculation as a new result:
The elasticities of demand with respect to the expected interest or rather accumulation rate have not been derived before.
The distinction matters: the formulas concern the accumulation factor, one plus the interest rate. Changing that factor at a given date changes the discounting of all incomes and prices from that date onward. The resulting demand elasticity combines an income effect, weighted by expected discounted saving over the remaining horizon relative to discounted income, with expenditure-weighted substitution elasticities over the same period. Using the full-horizon budget identity and the corresponding substitution identity, Tintner rewrites the expression in terms of saving and substitution before the affected date. The two forms expose the same intertemporal connection: demand responds through both the valuation of net resources and the relative attractiveness of dated consumption.
The continuous case retains this economic structure while replacing a finite consumption vector with consumption paths. Utility becomes a functional; the budget becomes an integral constraint; and functional marginal utilities equal discounted prices multiplied by a common multiplier. Differentiating these conditions produces integral equations determining functional demand elasticities. Unlike the discrete section, this closing section presents the general system rather than working through separate explicit elasticity formulas. The article’s contribution is therefore a unified comparative-static foundation for intertemporal demand: it incorporates saving, discounting, and cross-date substitution into ordinal utility theory, while leaving the historical determination of expectations as the additional link needed for empirical dynamic demand functions.
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