Market equilibrium with heterogeneous recursive-utility-maximizing agents

Chenghu Ma

Economic Theory, 1996, vol. 7, issue 3, 567-570

Abstract: The paper by C. Ma [1] contains several errors. First, statement and proof of Theorem 2.1 on the existence of intertemporal recursive utility function as a unique solution to the Koopmans equation must be amended. Several additional technical conditions concerning the consumption domain, measurability of certainty equivalent and utility process need to be assumed for the validity of the theorem. Second, the assumptions for Theorem 3.1 need to be amended to include the Feller's condition that, for any bounded continuous function $f\in C(S\times{\Script R}^{n}_{+}), \mu\tilde (f(st_{\ast 1},\theta )\mid s_{t}=s)$ is bounded and continuous in $(s,\theta ).$ In addition, for Theorem 3.1, the price p, the endowment e and the dividend rate $\delta $ as functions of the state variable $s\in S$ are assumed to be continuous. The Feller's condition for Theorem 3.1 is to ensure the value function to be well-defined. This condition needs to be assumed even for the expected additive utility functions (See Lucas [2]). It is noticed that, under this condition, the right hand side of equation (3.5) in [1] defines a bounded continuous function in s and $φ.$ The proof of Theorem 3.1 remains valid with this remark in place. A correct version of Theorem 2.1 in [1] is stated and proved in this corrigendum. Ozaki and Streufert [3] is the first to cast doubt on the validity of this theorem. They point out correctly that additional conditions to ensure the measurability of the utility process need to be assumed. This condition is identified as condition $CE_{4}$ below. In addition, I notice that, the consumption space is not suitably defined in [1], especially when a unbounded consumption set is assumed. In contrast to what claimed in [3], I show that the uniformly bounded consumption set X and stationary information structure are not necessary for the validity of Theorem 2.1.

Date: 1996
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