Knowing What Others Know: Coordination Motives in Information Acquisition

In this appendix, we derive the objective function (equation 4) of our dynamic planning and price adjustment model from a fully specified dynamic general equilibrium model. The model we discuss here is similar to Hellwig (2004), with the main difference being the updating of information by firms. Consider a standard model of incomplete nominal adjustment with monopolistic firms, along the lines of Blanchard and Kiyotaki (1987), with nominal prices being preset, conditional on available information, before markets open. Time is discrete and infinite. There is a measure 1 continuum of different intermediate goods, indexed by i ∈ [0, 1], each produced by one monopolistic firm using labor as the unique input into production. There is a final consumption good, which is produced by a perfectly competitive final goods sector using the continuum of intermediates according to a Dixit-Stiglitz CES technology with constant returns to scale. On the consumption side, there is an infinitely-lived representative household, with preferences defined over the final consumption good and labor supply in each period. The household faces a Cash-in-Advance constraint, and has to finance consumption out of the current period’s nominal balances. Each period is separated into two stages: in the first stage, a nominal shock is realized in the form of a stochastic lump sum transfer to the representative household. At this point, each intermediate goods producers decides whether or not to pay a fixed labor cost to ‘plan’, by which he updates his information set in way that we will describe below. Intermediate firms then set prices on the basis of their information sets. In the second stage, markets open. Intermediates are traded at