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Comment Karl Shell The static general equilibrium model has left us with a fundamental proposition in welfare economics: If "external effects" are absent from consumption and production, then a competitive equilibrium allocation is also a Pareto optimal allocation. Much of social policy may be thought of as an attempt to cope with or exploit these externalities. Phelps's paper on game-equilibrium growth focuses on a dynamic economy with consumption externalities. Individuals are neither perfectly selfish nor perfectly altruistic. The utility function of a generation depends upon its own consumption and upon the consumption of each of the future generations. Since Phelps's generations are not "hard atoms" (they are not perfectly selfish), equilibrium growth may not be Pareto optimal. Even if the generations are hard atoms-as in Hammond's paper-the equilibrium allocation may not be Pareto optimal. The fundamental theorem of welfare economics fails to apply because of two basic differences between the dynamic models and the essentially static Arrow-Debreu model. (1) In continuous-time models with infinite futurity, the set of agents (or generations) can be identified with the open half-time-line (running from today or time zero into the indefinite future). In discrete-time models with infinite futurity, the set of agents can be identified with the nonnegative integers. There are a finite number of agents in the basic Arrow-Debreu model. (2) In the Arrow-Debreu model, trades can be thought of as taking place in a single Walrasian market which includes all individuals under consideration. In the dynamic model, however, some generations do not 141 142 • ALTRUISM, MORALITY, AND ECONOMIC THEORY meet and hence cannot trade or make agreements. As Hammond's Pension Game illustrates, there is even a special problem for overlapping generations. While they can participate in some exchange, there may be limited ability to enforce agreement. I would like to illustrate the importance of these two qualities of the models-the infinity of traders and the nonsimultaneity of generations-in the context of a simple economy based on Paul Samuelson's famous consumption-loan model. Individuals live for two periods. There is no population growth. The representative of the tth generation has a simple il· f . f h f t( t t ) t + t h t· ut Ity unctIOn 0 t e orm U ct> ct + I = Ct Ct+ I, were Cs IS consumption of generation t in period s. The hard atoms of generation t care only for their own consumptions during the periods in which they are alive, namely periods t and t+l. Assume no production or storage possibilities and assume that each representative individual is endowed with one consumption unit for each of the two periods of his life. Period 1 2 3 4 5 0 1 0 0 0 0 1 1 1 0 0 0 -; 2 0 1 1 0 0 ;:s :9 .:= 3 0 0 1 1 0 "0 C .... 4 0 0 0 1 1 Figure 1. Endowment Matrix Notice that if the interest rate is zero (i.e. Ps =Pt for s =1,2, ... and t = 1, 2, ..., where Pt is the price of consumption in the tth period), then autarchy (no trade) is a competitive equilibrium. An allocation which is superior to this equilibrium allocation can be found. For example, require man one to give man zero a unit of consumption good in period one. Man zero is better off. Compensate man one by requiring man two to give man one a unit of consumption good in period two, and so forth, making the ur-father better off and no one worse off. Comment • 143 Period 1 2 3 4 5 0 2 0 0 0 0 1 0 2 0 0 0 ;; 2 0 0 2 0 0 ::s :s > 3 0 0 0 2 0 :f3 = ... Figure 2. Pareto Superior Allocation While the most natural interpretation of the consumption-loan model is in the dynamic setting, we could consider a Gedankenexperiment in which all traders meet in a single market. Nonetheless, we have exhibited a competitive equilibrium which is not Pareto optimal. The fundamental theorem of welfare economics does not hold because of infinity-infinity of traders and infinity of dated commodities. What is the "cure" for this inefficient competitive economy? Let the ur-father (man zero) invent money, declaring it to be worth one unit of consumption in any period. Man zero trades money for consumption in period one. Consumption is passed backward while the...


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