No CrossRef data available.
Article contents
Marshall and Slutsky on the Theory of Demand
Published online by Cambridge University Press: 07 November 2014
Extract
This paper provides a reconciliation of the Marshallian and Slutsky theories of demand. Incidentally, it also demonstrates that vertically parallel indifference curves involve unitary price elasticity and clarifies Marshall's analysis of consumer's surplus.
In Figure 1 the consumer is assumed to be initially in equilibrium at A, where he purchases OA′ of X (a composite commodity) at a price of P, as indicated by price line FA, and devotes OM of his given money income to all uses, Y, other than expenditures on X. Thus Y represents dollars spent on all uses other than X. The price of X is then allowed to decrease to (P − ΔP) as indicated by price line FB and the quantity of X increases to (X + ΔX), or to OB′, while the price of Y remains constant at unity, and the quantity of Y decreases to ON. Since the consumer's money income remains constant, any change in the total amount spent on X must produce an equal and an opposite change in the total amount spent on all other goods. The change in the total amount spent on all other goods is defined as the difference between the amount spent on X in the initial position at A and that spent on X in the new position at B, or as:
.
- Type
- Articles
- Information
- Canadian Journal of Economics and Political Science/Revue canadienne de economiques et science politique , Volume 27 , Issue 2 , May 1961 , pp. 176 - 191
- Copyright
- Copyright © Canadian Political Science Association 1961
References
1 Cf., e.g., Stonier, Alfred W. and Hague, Douglas C., A Textbook of Economic Theory (2nd ed., London, 1952), 61.Google Scholar
2 Marshall, , Principles of Economics (8th. ed., London, 1936), Mathematical Notes I and II, 834.Google Scholar
3 Slutsky, Eugen, “On the Theory of the Budget of the Consumer” in Boulding, Kenneth and Stigler, George, eds., Readings in Price Theory (Homewood, Ill., 1952), 27–56 Google Scholar, esp. 40.
4 The Theory and Measurement of Demand (Chicago, 1938), 42–3.Google Scholar
5 Ibid., 41. See his Equation (3.21).
6 Ibid., 45, 41. Substitute X for Y in the quotation.
7 Stone, Richard, ed., The Measurement of Consumer's Expenditure and Behaviour in the United Kingdom, 1920–38, I (Cambridge, 1954), 262.Google Scholar
8 Ibid., 262. Stone follows Hicks in his argument. By employing our definitions and Stone's technique, all of the equations produced by Stone on page 262 can be produced in our terms. See Appendix.
9 Cf. Slutsky, , “Budget of the Consumer,” 33–4Google Scholar; 39.
10 Following ibid., 38.
11 Hicks, J. R., Value and Capital (2nd. ed., Oxford, 1948), 39–40 Google Scholar; Boulding, Kenneth, Economic Analysis (rev. ed., New York, 1948), 762 ff.Google Scholar
12 Samuelson, Paul A., “Constancy of the Marginal Utility of Income” in Lange, O. et al., eds., Studies in Mathematical Economics and Econometrics (Chicago, 1942), 75–91, esp. 85.Google Scholar Samuelson's case of a simultaneous doubling of all prices and of income apparently amounts to a change of scale in our terms, for then in our analysis the absolute price change would also be doubled, although proportionately it would remain the same.
13 Hicks, , Value and Capital, 35.Google Scholar See also his A Revision of Demand Theory (Oxford, 1956), 82.Google Scholar
14 Hicks, , Value and Capital, 330–3Google Scholar; and Revision of Demand Theory, 81–2, 101–2.
15 Thus the consumer must be allowed to readjust if he is taxed by R after a price decrease or if he is given a subsidy equal to R after a price increase. Cf. Hicks, , Revision of Demand Theory, 99 Google Scholar; and see also Machlup, Fritz, “Professor Hicks' Revision of Demand Theory ,” American Economic Review, 03, 1957, 119–35, esp. 122–3.Google Scholar
16 Marshall, , Principles, 124–37Google Scholar; and Samuelson, , Studies in Mathematical Economics, 80, esp. n. 5Google Scholar, and his essay, “Consumption Theorems in Terms of Overcompensation rather than Indifference Comparisons,” Economica (NS), XX, 02, 1953, 1–9.Google Scholar
17 My interpretation differs from that provided by Schultz himself in Theory and Measurement of Demand, 41. See Appendix.
18 Samuelson, , Studies in Mathematical Economics, 80, n. 5 and esp. n. 8Google Scholar; 84, 91.
19 Hicks, , Revision of Demand Theory, 15, 99–100 Google Scholar; Value and Capital, 33; and Machlup, , “Professor Hicks' Revision of Demand Theory,” 122–3.Google Scholar
20 Hicks, , Value and Capital, 330–3Google Scholar; Revision of Demand Theory, 76 ff.; 95–7.
21 Cf., Hicks, , Value and Capital, 332.Google Scholar
22 Hicks, , Revision of Demand Theory, 96.Google Scholar Hicks states specifically: “If the income effect is neglected (in Marshall's manner) … the increment of consumer's surplus is then the same as the compensating variation.”
23 Ibid., 76.
24 Ibid., 82, 102, 173; see also his Value and Capital, 330–2.
25 Ibid., 81–2, 101–2.