The present paper examines the problem of aggregating infinite utility streams with a social welfare function that respects the Anonymity and Weak Pareto Axioms. The paper provides a complete characterization of domains (of the one period utilities) on which such an aggregation is possible. A social welfare function satisfying the Anonymity and Weak Pareto Axioms exists on precisely those domains that do not contain any set of the order type of the set of positive and negative integers. The criterion is applied to decide on possibility and impossibility results for a variety of domains. It is also used to provide an alternative formulation of the characterization result in terms of the accumulation points of the domain. and let X = Y N . We claim that Y (<) is not of order type μ, for if Y (<) is of order type μ, then Y contains a non-empty subset Y such that Y (<) is of order type σ . Then, defining:we see that Z is a non-empty subset of N. Therefore, Z(<) has a first element and so Y (<) has a last element. But, by Lemma 1, Y (<) cannot have a last element. This contradiction establishes the claim.Using Proposition 3, there is a function W : X → R satisfying the Weak Pareto and Anonymity Axioms, where X = Y N . This result is mentioned without proof in Basu and Mitra (2007b, footnote 9, p. 83). Example 3 DefineDefine A = A∩Y and B = B∩Y . If B is non-empty, then B is a non-empty subset of B and, therefore, B (<) has a last element (see Example 2 above), which we call b. If A is empty, then Y = B and Y (<) has a last element, contradicting Lemma 1. If A is non-empty, then for every y ∈ A , we have y < b. Therefore, b is a last element of Y (<), contradicting Lemma 1 again.If B is empty, then Y = A . Furthermore, A is a non-empty subset of A and, therefore, has a first element (see Example 2 above). Thus, Y (<) must have a first element, contradicting Lemma 1.The above cases exhaust all logical possibilities and, therefore, our claim is established. Using Proposition 3, there is a function W : X → R satisfying the Weak Pareto and Anonymity Axioms, where X = Y N . The impossibility resultWe will first present the impossibility part of the result in Theorem 1 for the domain Y = I, the set of positive and negative integers. Clearly, I(<) is of type σ and, therefore, of type μ. This enables us to illustrate our approach to the impossibility result in the most transparent way. We will then use Proposition 2 to show that when an arbitrary non-empty subset, Y , of the reals is such that Y (<) is of type μ, there is no social welfare function satisfying the Weak Pareto and Anonymity Axioms. Proposition 4 Let Y = I. Then there is no social welfare function W : X → R satisfying the Weak Pareto and Anonymity Axioms (where X = Y N ).PROOF: Suppose on the contrary that there is a social welfare function W : X → R satisfying the Weak Pareto and Anonymity Axioms (where X ≡ Y N = I N ).

We provide a sufficient condition on the production function under which eventually the most patient household owns the entire capital stock in every Ramsey Equilibrium, called the turnpike property. This generalizes the result in the literature which establishes the turnpike property using the capital income monotonicity condition. We then provide an example of a Ramsey Equilibrium in which the most patient household reaches a no capital position infinitely often. This is a strong refutation of the turnpike property on Ramsey equilibria. We also show that the constructed Ramsey equilibrium is inefficient in terms of the aggregate consumption stream that it provides.

* We thank the editor and two anonymous referees of this journal for their helpful comments and suggestions. We also thank the seminar participants at

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We provide a sufficient condition on the production function under which eventually the most patient household owns the entire capital stock in every Ramsey Equilibrium, called the turnpike property. This generalizes the result in the literature which establishes the turnpike property using the capital income monotonicity condition. We then provide an example of a Ramsey Equilibrium in which the most patient household reaches a no capital position infinitely often. This is a strong refutation of the turnpike property on Ramsey equilibria. We also show that the constructed Ramsey equilibrium is inefficient in terms of the aggregate consumption stream that it provides.