The distribution of money and prices in an equilibrium with lotteries

Abstract

We construct a tractable 'fundamental' model of money with equilibrium heterogeneity in money balances and prices. We do so by considering randomized monetary trades in a standard search-theoretic model of money where agents can hold multiple units of indivisible 'tokens' and can offer lotteries on monetary transfers. By studying a simple trading pattern, we can analytically characterize the monetary distribution. Interestingly, such distributions match those observed in numerically simulated economies with fully divisible money and price heterogeneity.

Monetary Equilibrium and the Differentiability of the Value Function

“…To simplify the discussion, it is convenient to make four remarks all of which deal with the choices of consumption and production in a period, since these choices are intratemporal in nature. 8 (1) At the start of each period t the expected utility of the agent is…”

“…. 8 For more background and more details concerning the statements that follow, see the discussion in [7,14].…”

“…In the model, anonymous individuals face idiosyncratic trading shocks, sometimes being buyers and other times being sellers. This feature ensures an explicit role for money, but also causes individual money balances to evolve stochastically, with obvious drawbacks in analytical tractability (e.g., see [8,10,12,17]).…”

On Market Activity and the Value of Money

“…7 This is not equivalent to having divisible money as demonstrated in Camera (2005) since agents are constrained to unit holdings. Even greater flexibility can be achieved when agents can hold multiple money units and use randomized trades (see Berentsen, Camera and Waller, 2004).…”

The Distribution of Money Balances and the Nonneutrality of Money*

“…Examples where nonneutralities occur because of asymmetric injections are Kiyotaki and Wright (1993) type models, limited participation in financial markets (Lucas, 1990; Fuerst, 1992; Williamson, 2004), segmented markets (Alvarez et al, 2002), or overlapping generation models. Heterogeneity in money holdings plays a role (e.g., Scheinkman and Weiss, 1986; Levine, 1991; İmrohorğlu, 1992; Camera and Corbae, 1999; Molico, 1999; Berentsen, 2002; Deviatov and Wallace, 2001; Zhu, 2003; Berentsen et al, 2004; Bhattacharya et al, 2005).…”