Royal Economic Society
Frank Ramsey’s A Mathematical Theory of Saving Orazio Attanasio University College London, EDePo@IFS, NBER Royal Economic Society Manchester - April 2015
1. Introduction 2. A Mathematical Theory of Saving 2.1 Individual behaviour 2.2 Factor Prices and Extensions 2.3 Equilibrium Factor Prices 2.4 Inequality 3. Influences and Anticipations 2 / 19
Outline 1. Introduction 2. A Mathematical Theory of Saving 2.1 Individual behaviour 2.2 Factor Prices and Extensions 2.3 Equilibrium Factor Prices 2.4 Inequality 3. Influences and Anticipations 3 / 19
Introduction In 1928, Ramsey published, at 25, his second paper in economics, on the theory of optimal saving. 4 / 19
Introduction In 1928, Ramsey published, at 25, his second paper in economics, on the theory of optimal saving. At the time he was the head of mathematics at Cambridge and had written important contribution in Mathematics and Logics. 4 / 19
Introduction In 1928, Ramsey published, at 25, his second paper in economics, on the theory of optimal saving. At the time he was the head of mathematics at Cambridge and had written important contribution in Mathematics and Logics. He was close to Keynes, Sraffa, Wittengestein. 4 / 19
Introduction In 1928, Ramsey published, at 25, his second paper in economics, on the theory of optimal saving. At the time he was the head of mathematics at Cambridge and had written important contribution in Mathematics and Logics. He was close to Keynes, Sraffa, Wittengestein. As a student he had worked for Pigou. (relevant for the taxation paper) 4 / 19
Introduction In 1928, Ramsey published, at 25, his second paper in economics, on the theory of optimal saving. At the time he was the head of mathematics at Cambridge and had written important contribution in Mathematics and Logics. He was close to Keynes, Sraffa, Wittengestein. As a student he had worked for Pigou. (relevant for the taxation paper) His contributions anticipated many subsequent developments: Optimal growth. Ramsey pricing and optimal taxation. Truth and probability : expected utility and choice under uncertainty. 4 / 19
Introduction A Mathematical Theory of Saving The paper is astonishingly modern. 5 / 19
Introduction A Mathematical Theory of Saving The paper is astonishingly modern. It contains the main results of optimal growth theory. 5 / 19
Introduction A Mathematical Theory of Saving The paper is astonishingly modern. It contains the main results of optimal growth theory. Cass and Koopmans re-derived the same results in the 1960s. - David Cass: “In fact I always have been kind of embarrassed because that paper is always cited although now I think of it as an exercise, almost re-creating and going a little beyond the Ramsey model.” 5 / 19
Introduction A Mathematical Theory of Saving The paper is astonishingly modern. It contains the main results of optimal growth theory. Cass and Koopmans re-derived the same results in the 1960s. - David Cass: “In fact I always have been kind of embarrassed because that paper is always cited although now I think of it as an exercise, almost re-creating and going a little beyond the Ramsey model.” It anticipates many further developments: Life cycle theory of consumption. OLG models. Theory of inequality. 5 / 19
Outline 1. Introduction 2. A Mathematical Theory of Saving 2.1 Individual behaviour 2.2 Factor Prices and Extensions 2.3 Equilibrium Factor Prices 2.4 Inequality 3. Influences and Anticipations 6 / 19
A MATHEMATICAL THEORY OF SAVING THE first problem I propose to taclile is this: how much of its income should a nation save? To answer this a simple rule is obtained valid under conditions of surprising generality; the rule, which will be further elucidated later, runs as follows. The rate of saving multiplied by the marginal utility of money should always be equal to the amount by which the total net rate of enjoyment of utility falls short of the maximum possible rate of enjoyment. In order to justify this rule it is, of course, necessary to make various simplifying assumptions: we have to suppose that our community goes on for ever without changing either in numbers or in its capacity for enjoyment or in its aversion to labour; that enjoyments and sacrifices at different times can be calculated independently and added; and that no new inventions or improve- are introduced save such as can be regarded ments in organisation as conditioned solely by the accumulation of wealth.' One point should perhaps be emphasised more particularly; it is assumed that we do not discount later enjoyments in com- parison with earlier ones, a practice which is ethically indefensible and arises merely from the weakness of the imagination; we shall, however, in Section II include such a rate of discount in some of our investigations. We also ignore altogether distributional considerations, assuming, in fact, that the way in which consumption and labour are distributed between the members of the community depends solely on their total amounts, so that total satisfaction is a function of these total amounts only. Besides this, we neglect the differences between different kinds of goods and different kinds of labour, and suppose them to be expressed in terms of fixed standards, so that we can speak simply of quantities of capital, consumption and labour without discussing their particular forms. Foreign trade, borrowing and lending need not be excluded, provided we assume that foreign nations are in a stable state, so 1 I.e. they must be such as would not occur without a certain degree of accumulation, but could be foreseen given that degree. No. 152.-VOL. XXXVIII. 0 0 A Mathematical Theory of Saving The paper sets to answer the following question: How much of its income should a nation save? 7 / 19
A Mathematical Theory of Saving A MATHEMATICAL THEORY OF SAVING The paper sets to answer the following question: THE first problem I propose to taclile is this: how much of How much of its income should a nation save? its income should a nation save? To answer this a simple rule is obtained valid under conditions of surprising generality; the The answer, of course, is: rule, which will be further elucidated later, runs as follows. The rate of saving multiplied by the marginal utility of money should always be equal to the amount by which the total net rate of enjoyment of utility falls short of the maximum possible rate of enjoyment. In order to justify this rule it is, of course, necessary to make various simplifying assumptions: we have to suppose that our community goes on for ever without changing either in numbers or in its capacity for enjoyment or in its aversion to labour; that enjoyments and sacrifices at different times can be calculated independently and added; and that no new inventions or improve- are introduced save such as can be regarded ments in organisation as conditioned solely by the accumulation of wealth.' One point should perhaps be emphasised more particularly; it is assumed that we do not discount later enjoyments in com- parison with earlier ones, a practice which is ethically indefensible and arises merely from the weakness of the imagination; we shall, however, in Section II include such a rate of discount in some of our investigations. 7 / 19 We also ignore altogether distributional considerations, assuming, in fact, that the way in which consumption and labour are distributed between the members of the community depends solely on their total amounts, so that total satisfaction is a function of these total amounts only. Besides this, we neglect the differences between different kinds of goods and different kinds of labour, and suppose them to be expressed in terms of fixed standards, so that we can speak simply of quantities of capital, consumption and labour without discussing their particular forms. Foreign trade, borrowing and lending need not be excluded, provided we assume that foreign nations are in a stable state, so 1 I.e. they must be such as would not occur without a certain degree of accumulation, but could be foreseen given that degree. No. 152.-VOL. XXXVIII. 0 0
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