General Equilibrium With Nonconvexities, Sunspots, and Money

Abstract

We study general equilibrium with nonconvexities. In these economies there exist sunspot equilibria without the usual assumptions needed in convex economies, and they have good welfare properties. Moreover, in these equilibria, agents act as if they have quasi-linear utility. Hence wealth effects vanish. We use this to construct a new model of monetary exchange. As in Lagos-Wright, trade occurs in both centralized and decentralized markets, but while that model requires quasilinearity, we have general preferences. Given our specification looks much like the textbook Arrow-Debreu model, we think this constitutes progress on the classic problem of integrating money and general equilibrium theory. We also use the model to discuss another classic issue: the relation between inflation and unemployment.

Inflation and Unemployment in General Equilibrium*

“…The following has been well known at least since the work of Rogerson (1988): efficient allocations in economies with indivisible labor generally have some agents, chosen at random, unemployed, while others are employed, even if they are ex ante identical; and these allocations can be supported as competitive equilibria where agents trade lotteries. As we discuss in detail below, another interesting feature of these economies emphasized in Rocheteau, Rupert, Shell and Wright (2006) is that agents act as if they have quasi‐linear utility. It turns out that one can use this result to construct a fairly general yet very tractable model of monetary exchange, using search theory, where (as in Lagos and Wright, 2005) some trades occur in centralized markets and some in decentralized markets.…”

“…Thus, if one is willing to embrace quasi‐linear utility, one can avoid having to track the distribution of money in the decentralized market as a state variable 1 . The observations in Rocheteau et al (2006) allow one to dispense with quasi‐linearity: as long as we have indivisible labor—or, for that matter, any indivisible commodity—identical results concerning the money distribution hold for any utility function (again assuming interior solutions). However, there are some advantages to using indivisible labor instead of quasi‐linear utility as a building block for monetary theory, including the fact that it generates unemployment.…”

“…Actually, even in this case, our results go through, but we need a different argument. Again, see Rocheteau et al (2006).…”

“…8 8 See Rocheteau et al (2006) for details, but basically the regularity condition is that we need to rule out , or equivalently , which implies a singularity in . In the indivisible‐labor literature, this case is known to occur only for one special utilty function; see e.g.…”

Uncertainty, Inflation, and Welfare

“…1 1 Alternatively, one can assume a general utility function as long as one assumes indivisible labor and allow agents to trade lotteries a la Rogerson (1988) following Rocheteau et al (2005). …”