We show that in almost every economy with separable externalities, every competitive equilibrium can be Pareto improved by a package of anonymous commodity taxes that causes prices to adjust and markets to reclear at different levels of individual consumption. This constrained suboptimality of competitive allocations might provide a rationale for economic policy in economies with externalities. It shows that policy makers should look for good tax packages that help everybody, rather than thinking taxes must inevitably be bad for some lobby that will oppose them.
We show that in almost every economy with separable externalities, every competitive equilibrium can be Pareto improved by a package of anonymous commodity taxes that causes prices to adjust and markets to reclear at different levels of individual consumption. This constrained suboptimality of competitive allocations might provide a rationale for economic policy in economies with externalities. It shows that policy makers should look for good tax packages that help everybody, rather than thinking taxes must inevitably be bad for some lobby that will oppose them.
When the asset market is incomplete, competitive equilibria are constrained suboptimal, which provides a scope for pareto improving interventions. Price regulation can be such a pareto improving policy, even when the welfare effects of rationing are taken into account. An appealing aspect of price regulation is that it that it operates anonymously on market variables.
Fix-price equilibria exist under weak assumptions. Such equilibria permit a competitive analysis of an economy with an incomplete asset market that is out of equilibrium. Arbitrage opportunities may arise: with three or more assets actively traded, an individual may hold an arbitrage portfolio at equilibrium.
The local existence of fix-price equilibrium for prices that are almost competitive may fail for robust examples. Under necessary and sufficient conditions for the local existence of fix-price equilibria, Pareto improving price regulation is generically possible.
In an incomplete asset market, firms assign values to investment plans by projecting their payoffs on the span of the payoffs of marketed assets; equivalently, firms employ the Capital Asset Pricing Model. This is a criterion that does not require firms to possess information, such as the marginal valuation of revenue across date – events by shareholders, which is not observable; rather, it is based on information revealed by the prices and payoffs of marketed assets. Under standard assumptions, competitive equilibria exist. But, competitive equilibrium allocations need not satisfy a condition of constrained pareto optimality that recognizes the incompleteness of the asset market; and, even in the absence of nominal assets, competitive equilibrium allocations are generically indeterminate – they are determinate if firm consider the commodity payoffs of shares.
A feasible social state is irreducible if and only if, for any non-trivial partition of individuals with two groups, there exists another feasible social state at which every individual in the first group is equally well-off and someone strictly better-off.
Competitive equilibria decentralize irreducible Pareto optimal social states.
Observability of an individual’s excess demand function for assets and commodities as all prices and revenue vary suffices in order to recover his von Neumann-Morgenstern utility function. This is generically the case, even when the asset market is incomplete and the cardinal utility indices state dependent, as long as there are at least two commodities traded in spot markets at each state of nature. On the contrary, if the response of individuals’ excess demand for assets as prices in spot commodity markets vary is not observable, recoverability fails when the asset market is incomplete. In particular, it is not possible to contradict the claim that the competitive allocation is fully optimal in spite of the incompleteness of the asset market.
Overlapping generations models with or without production or a portfolio demand for money display a fundamental indeterminacy. Expectations matter; and they are not, in the short run, constrained by the hypotheses of agent optimization, rational expectations, and market clearing. No short run policy analysis is possible without some explicit understanding of how agents expect the economy to respond to the policy. In this framework of perfect foresight and market clearing prices, it is possible to make Keynesian assumptions about the rigidity of money wages and the exogeneity of “animal spirits” of investors, to use the standard IS-LM apparatus, and to derive Keynesian conclusions about the short run effectiveness of policy. Alternatively, starting from difference but no less rational expectations, one can derive the “new classical” neutrality propositions.
JEL Classification: 023, 021
Keywords: Overlapping generations, Perfect foresight, Short run policy effectiveness
Let assets be denominated in an a priori specified numeraire.
Whether or not the asset is complete, a competitive equilibrium exists as long as arbitrage is possible when assets are free. Generically, the set of competitive equilibria is finite, and the equilibrium prices and allocations in the commodity spot markets are uniquely determined by the asset allocation in a neighborhood of a competitive equilibrium.
If the asset market is incomplete, a competitive equilibrium allocation is generically constrained suboptimal: there exists an arbitrarily small reallocation of the existing assets, which leads to a Pareto improvement in welfare when prices and allocations in the commodity spot market adjust to maintain equilibrium.
When government liabilities (including money) are held in private portfolios only as stores of value, and do not provide additional benefits (as liquidity services), the real variables in an economy with uncertainty are not affected by the government’s trading in assets. There are also policies which alter the money supply through taxes or subsidies, and affect the price of money without changing real variables.