A mathematical theory of saving
This significant paper was published in The Economic Journal, and involved "a strategically beautiful application of the calculus of variations" (Paul Samuelson)[15] to determine the optimal amount an economy should invest (save) rather than consume so as to maximise future utility, or in Ramsey's words "how much of its income should a nation save?" (Ramsey, 1928).
Keynes described the article as "one of the most remarkable contributions to mathematical economics ever made, both in respect of the intrinsic importance and difficulty of its subject, the power and elegance of the technical methods employed, and the clear purity of illumination with which the writer's mind is felt by the reader to play about its subject. The article is terribly difficult reading for an economist, but it is not difficult to appreciate how scientific and aesthetic(審美眼・審美眼のある esθ[e]tik) qualities are combined in it together."[16] The Ramsey model is today acknowledged as the starting point for optimal accumulation theory although its importance was not recognised until many years after its first publication.
The main contributions of the model were firstly the initial question Ramsey posed on how much savings should be and secondly the method of analysis, the intertemporal maximisation (optimisation) of collective or individual utility by applying techniques of dynamic optimisation. Tjalling C. Koopmans and David Cass modified the Ramsey model incorporating the dynamic features of population growth at a steady rate and of Harrod-neutral technical progress again at a steady rate, giving birth to a model named the Ramsey?Cass?Koopmans model where the objective now is to maximise household's utility function.
A Contribution to the Theory of Taxation
Author(s): F. P. Ramsey
Source: The Economic Journal, Vol. 37, No. 145 (Mar., 1927), pp. 47-61 https://www.jstor.org/stable/pdf/2222721.pdf
A contribution to the theory of taxation
In this paper Ramsey's contribution to economic theory was the elegant concept of Ramsey pricing. This is applicable in situations where a (regulated) monopolist wants to maximise consumer surplus whilst at the same time ensuring that its costs are adequately covered. This is achieved by setting the price such that the markup over marginal cost is inversely proportional to the price elasticity of demand for that good. Like its predecessor this paper was published in The Economic Journal in 1927. Ramsey poses the question that is to be solved at the beginning of the article: "a given revenue is to be raised by proportionate taxes on some or all uses of income, the taxes on different uses being possibly at different rates; how much should these rates be adjusted in order that the decrement of utility may be a minimum?" (Ramsey 1927). The problem was suggested to him by the economist Arthur Pigou and the paper was Ramsey's answer to the problem.
