Summary: Models in which firms use rules of thumb or partial indexing in their price setting have become prominent in the recent monetary policy literature. The extent to which these firms adjust their prices to lagged inflation has been taken as fixed. We consider the implications of firms choosing the optimal degree of indexation so these simple pricing rules deliver prices as close as possible to those which would be chosen optimally. We find that the degree of indexation depends on the extent of persistence in the economy such that models with constant indexation are vulnerable to the Lucas critique. We also study the interactions between firms price setting and the macroeconomic environment finding that, for the models which appear most plausible on microeconomic grounds, the Nash equilibrium between firms and the policy maker is characterised by zero indexation and zero macroeconomic persistence.

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