The general overcompensated theorem, 476. — The Waugh time-symmetric case, 477. — Inapplicability of the Waugh theorem, 477. — The anti-Waugh theorem, 478. — Utility areas versus consumer surplus areas, 480. — Second-round discussion and the dual Waugh theorem, 483. — Third-round discussions: producer benefit from price instability? 487. — No perpetual motion machine of the third kind in economics, 488. — Conclusion, 493.
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Paul A. Samuelson (1972) studied this question.