Aggregate Demand Management in Search Equilibrium

Diamond states that where some economists attribute unemployment fluctuations to misperceptions of prices and wages, and others to lags in nominal adjustment (including staggered contracts), with a shared premise that fully flexible, correctly perceived prices would eliminate macro unemployment problems, “this paper introduces a third cause for macro unemployment problems – the difficulty of coordination of trade in a many-person economy.” Once the fictional Walrasian auctioneer is dropped and trade frictions are introduced, he argues, an economy can have macroeconomic unemployment problems even with correctly perceived, fully flexible prices and wages (Introduction).

The model has a continuum of identical, risk-neutral individuals with instantaneous utility equal to consumption minus production cost, maximizing the present discounted value of lifetime utility; production opportunities arrive as a Poisson process, each yielding a fixed output but costing a production cost drawn from a distribution, and individuals may hold at most one unit of unsold output at a time (they cannot consume their own output and cannot produce while holding unsold output), so they must find a trading partner to realize any return on production. The probability any given individual finds a trading partner arrives via a Poisson process whose rate depends positively on the economy’s aggregate employment rate (the fraction of individuals currently holding output for sale) (Section II).

Diamond shows the model has two central properties: there can be multiple steady-state rational-expectations equilibria, and all non-corner-solution equilibria are locally inefficient. The inefficiency comes from a trading externality – an individual’s production decision does not account for the fact that, by holding output for sale, they make it easier for others to find a trading partner – while the multiplicity of equilibria comes from the positive feedback this externality creates: a higher aggregate employment rate makes trade easier for everyone, which makes production more profitable, which can itself sustain the higher employment rate as a self-fulfilling steady state (Abstract; Section IV). In the model’s steady-state conditions, both the optimal individual production-cost cutoff and the aggregate employment rate are shown to be increasing in each other, which is what opens the door to multiple simultaneous solutions.

Diamond frames the result against Friedman’s (1968) definition of the natural rate of unemployment as the rate that remains once frictions are introduced into otherwise-Walrasian equations, and argues that “the result of actually modeling a competitive economy with trade frictions is to find multiple natural rates of unemployment.” This reframing is the basis for his key policy implication: because there can be more than one self-sustaining long-run unemployment rate, one goal of macroeconomic policy should be “to direct the economy toward the best natural rate (not necessarily the lowest) after any sufficiently large macro shock” (Introduction).

Individuals compare the expected lifetime-utility gain from production against its cost, accepting any opportunity whose cost falls below a reservation cutoff; this cutoff is shown to depend positively on the current employment rate, since a higher employment rate raises the expected value of successfully trading one’s output (Section III). Combined with the condition that the aggregate employment rate must be stationary (inflow into employment from successful production, balanced against outflow from successful sales), the model yields a steady-state relationship in which the equilibrium cost cutoff and the aggregate employment rate are mutually reinforcing, generating the possibility of multiple simultaneous steady-state solutions, including a zero-employment equilibrium at the low end (Section II, IV).

In a static version with an aggregate cost function for output and a probability-of-sale function that rises with aggregate output, Diamond shows that if individuals (correctly) treat the sale probability as a fixed parameter rather than something they influence, the resulting competitive-style equilibrium condition sets the sale probability equal to marginal cost, whereas the socially efficient condition would also add the marginal effect of one’s own output on others’ sale probability (Section V). Because this externality term is omitted from individual decisions, the decentralized outcome is locally inefficient (too little aggregate activity), and Diamond shows that a government subsidy to the cost of production, correctly calibrated, can induce individuals to produce at the socially optimal point.

Diamond shows that a permanent increase in the economy’s production-cost cutoff away from an uncorrected steady state raises expected lifetime utility for every individual as well as aggregate welfare, establishing that “without intervention, there is locally too little activity in the economy” (Section VI). He then derives the specific per-project production subsidy that a planner would set to correct this externality at the steady state, showing the optimal subsidy level is strictly positive – individuals must be subsidized to get them to internalize the beneficial effect their own production has on others’ ability to trade (Section VIII).

Solving for the policy that maximizes the discounted value of welfare subject to the economy’s employment-rate dynamics, Diamond derives an Euler equation characterizing the time path of the socially optimal cost cutoff, and shows that “the optimal…curve always lies above the private choice…curve” – meaning that, during a stabilization episode, the government should induce individuals to accept production opportunities that are more costly than what they would voluntarily accept on their own (Section VII). A worked numerical example with a simple matching function and a single production cost shows that, depending on the initial employment rate, the optimal policy can call for either accepting essentially all opportunities or accepting none, illustrating that the optimal response is sensitive to which “basin” of the multiple-equilibria structure the economy currently occupies (Section IX).

Diamond’s closing illustration imagines islanders who, once “employed,” pick coconuts from palm trees but face a taboo against eating their own nuts (representing how little of a modern economy’s output is self-consumed by its producer), so they must then search for a trading partner willing to swap nuts – and “the ease of finding a trading partner depends on the number of potential partners available,” so that production is not efficient even when everyone correctly anticipates how hard trading will be (Section X). The broader moral he draws is that a Walrasian auctioneer, by construction, leaves no unrealized mutually advantageous trades, but any real, complex economy without such an auctioneer “will always remain unrecognized and unrealized opportunities” for trade – opportunities that government policy can affect, both through small steady-state corrective interventions and through larger interventions when the economy has settled at an inefficient long-run equilibrium, with the pace of any such intervention itself optimally gradual rather than instantaneous because of the costs of adjusting too quickly.

Diamond is explicit that the model is “very special” – built on a highly artificial, stripped-down representation of production and trade – but states it serves two purposes: to form “a basis for further generalization,” and to contrast with models that simply assume away the trade-coordination problem by positing a frictionless matching mechanism (Section X). He frames the exercise as demonstrating the feasibility of building internally consistent, micro-founded macroeconomic models in which active macro policy has a genuine role to play, grounded in trading frictions rather than in price misperception or nominal rigidity.