This is an attempt to expose the essence of Samuelson's consumption loan paradox. It is maintained that the double infinity of traders and dated commodities allows for competitive equilibria that are not Pareto-optimal. While such models are most interesting in the dynamic setting, the fact that generations do not meet is not essential. The chain-letter aspect of the model reminds us that the appropriate form of the budget constraint is not obvious for the potentially infinitely long-lived economic entity (such as the corporation or the family). The analysis is related to recent contributions in the theories of general equilibrium, economic planning, and decentralization.

We analyze a banking system in which the class of feasible deposit contracts, or mechanisms, is broad. The mechanisms must satisfy a sequential service constraint, but partial or full suspension of convertibility is allowed. Consumers must be willing to deposit, ex ante. We show, by examples, that under the so‐called “optimal contract,” the postdeposit game can have a run equilibrium. Given a propensity to run, triggered by sunspots, the optimal contract for the full predeposit game can be consistent with runs that occur with positive probability. Thus the Diamond‐Dybvig framework can explain bank runs as emerging in equilibrium under the optimal deposit contract.

Can extrinsic uncertainty ("animal spirits," "market psychology," "sunspots,"...) play a significant role in rational expectations equilibrium models? We establish that extrinsic uncertainty cannot matter in the static Arrow-Debreu economy with complete markets. But we also establish that extrinsic uncertainty can matter in the overlapping-generations economy with complete markets but where market participation is limited to those consumers alive when the markets are open. Equilibrium allocations in which extrinsic uncertainty plays no role are Pareto optimal in the traditional sense. Equilibrium allocations in which extrinsic uncertainty does play a role are Pareto optimal in a (weaker) sense which is appropriate to dynamic analysis.

Can extrinsic uncertainty ("animal spirits," "market psychology," "sunspots,"...) play a significant role in rational expectations equilibrium models? We establish that extrinsic uncertainty cannot matter in the static Arrow-Debreu economy with complete markets. But we also establish that extrinsic uncertainty can matter in the overlapping-generations economy with complete markets but where market participation is limited to those consumers alive when the markets are open. Equilibrium allocations in which extrinsic uncertainty plays no role are Pareto optimal in the traditional sense. Equilibrium allocations in which extrinsic uncertainty does play a role are Pareto optimal in a (weaker) sense which is appropriate to dynamic analysis.

There have been two broad strategic approaches to the study of economic growth. The first, exemplified by Solow's paper (1956), attempts to explain how an enterprise economy will grow, given its technology and the market behavior of its consumers. The second approach, exemplified by Ramsey (1928), attempts to determine an optimal development strategy for a fully planned economy, given its technological constraints. These approaches fail to capture a central policy problem of a modern mixed'" economy in which the government can influence investment and saving, but only indirectly, by manipulating certain basic variables like the deficit and the money supply. Our paper represents an attempt to begin the analysis of this problem.1 The very term "mixed economy" implies that there are two centers of decision making and that the preferences of the consumers and of the government are distinguishable.2 It is not at all clear where the preferences of the government come from, or even whether governments have consistent preferences of the kind we will talk about. But a constant theme of policy literature is that government intervention in the economy is effective and can be judged as good or bad for the economy without direct reference to consumer preferences. This is particularly true of policy prescriptions for economic growth. It seems to us that postulating a social welfare