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Note on Edgeworth’s Taxation Phenomenon and Professor Garver’s Additional Condition on Demand Functions

  • Harold Hotelling
Chapter
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Abstract

In a recent paper1 I derived for demand functions for n commodities conditions which, I concluded, assure the satisfaction of all further conditions which may reasonably be applied to all sets of demand functions. Letting p1, p2, … p n , and q1, q2, …, q n be respectively the prices and quantities, the conditions are:
$$\frac{{\partial {p_i}}}{{\partial {q_j}}} = \frac{{\partial {p_j}}}{{\partial {q_i}}} < 0,\frac{{\partial \left( {{p_i},{p_j}} \right)}}{{\partial \left( {{q_i},{q_j}} \right)}} >0,\frac{{\partial \left( {{p_i},{p_j}{p_k}} \right)}}{{\partial \left( {{q_i},{q_j},{q_k}} \right)}} < 0, \ldots$$
These are equivalent to
$$\frac{{\partial {q_i}}}{{\partial {p_j}}} = \frac{{\partial {q_j}}}{{\partial {p_i}}},\frac{{\partial {q_i}}}{{\partial {p_i}}} < 0,\frac{{\partial \left( {{q_i},{q_j}} \right)}}{{\partial \left( {{p_i},{p_j}} \right)}} >0,\frac{{\partial \left( {{q_i},{q_j},{q_k}} \right)}}{{\partial \left( {{p_i},{p_j},{p_k}} \right)}} < 0, \ldots ,$$
and were known, at least in part, by Edgeworth. Similar conditions in which the inequality signs are all > apply for supply functions.

Keywords

Cost Function Similar Condition Empirical Result Political Economy Demand Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Harold Hotelling
    • 1
  1. 1.Columbia UniversityUSA

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