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Profitable Speculation and Linear Excess Demand

Lien, Da-Hsiang Donald (1984) Profitable Speculation and Linear Excess Demand. Social Science Working Paper, 521. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170919-164532686

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Abstract

Since Friedman maintained that profitable speculation necessarily stabilizes prices, there had been many debates. Farrell concluded these debates by showing that (i) for a two-period model, any continuous negatively sloped non-speculative excess demand function would validate Friedman's conjecture if there is no lag structure, and (ii) for a T-period model with T≥3, negatively sloped linear non-speculative excess demand is necessary and sufficient for Friedman's conjecture to be true if there is no lag structure. Later, Schimmler generalized Farrell's results to lag-responsive nonspeculative excess demand cases. However, there are some problems in Farell's and Schimmler's approaches which invalidate their proofs. In this paper, we will point out these problems and show that after correcting these slips, Farrell's two results are in fact correct. Also, we will redo Schimmler's problem for time-independent non-speculative excess demand functions. The conclusions derived are (i) for two-period models, any continuously differentiable non-speculative excess demand f(P_t,P_(t-1)) with f_1 (P_t,P_(t-1) )<0,f_2 (P_t,P_(t-1) )≤0 [where f_(t-s+1) (P_t,P_(t-1) )=∂f(P_t,P_(t-1) )/〖∂P〗_s , s=t-1, t] will validate Friedman's conjecture; (ii) for T-period models (T≥3), within the class of twice-continuously differentiable functions, linear non-speculative excess demand functions f(P_t,P_(t-1),⋯P_(t-T+1)) satisfying f_1<0,f_2=f_3=⋯= f_(t-T+1)=0 represent necessary and sufficient conditions for Friedman's conjecture to be true.


Item Type:Report or Paper (Working Paper)
Additional Information:I am indebted to James Quirk for helpful discussions and editings, also to Richard McKelvey and Jennifer Reinganum for comments on earlier drafts. All errors, of course, remain mine.
Group:Social Science Working Papers
Series Name:Social Science Working Paper
Issue or Number:521
Record Number:CaltechAUTHORS:20170919-164532686
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170919-164532686
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81601
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:20 Sep 2017 20:24
Last Modified:03 Oct 2019 18:44

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