Notes on a ‘Constructive Proof of the Existence of a Collateral Equilibrium’

Abstract

In an interesting article in this journal, Ma (Comput Econ 45:1---30, 2015), claims that a constructive proof of existence of a Collateral Equilibrium (with a Leontief utility function) is provided in the paper. Moreover, there is also the additional claim that `on the basis of this proof, we can (and we shall) develop an algorithm for computing that equilibrium' (ibid, p. 1). Thirdly, the statements that `the algorithm is shown by simulation to be effective', and its effectiveness is demonstrated by `the accuracy of the equilibrium it provided'. These claims are, from a recursion theoretic (or computability theory) point of view, meaningless.