By Pierre Bourdieu
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We will briefly sketch the proof-idea here: Suppose there exists an optimal policy for the infinite horizon case different from the one for some finite horizon T. Then 00, such that the infinite horizon policy is better for all t > T. Obviously, this is a contradiction to the result that for sufficiently large finite planning horizons, the finite horizon policies are all the same. Thus, even if it is impossible in a society to reach agreement on an adequate planning horizon, the optimal policies and states there exists some period T < for all different, but sufficiently large, planning horizons is still exactly the same.
G. about the change of the production function for an infinite planning horizon. t~c. crucially depend on these assumptions. Of course, proponents of an infinite horizon will argue: All these arguments are technical obstacles and make it more difficult to follow ethical principles by using an infinite horizon. But why should it be better then to use a finite horizon, which is ethically indefensible if mankind is assumed to live forever? Considering today's arms race and the big risk of a nuclear holocaust, many people doubt for both probabilistic and human reasons if mankind is to live forever.
Notice, for u t ~ a~ the dynamic equation for Kt is nonwt - 1 • Thus the workers may increase decreasing with respect to their wage rate and therefore their utility without decreasing the subsequent capital stock. • ,T. 2) is trivial. Workers would set wages such that nothing remains left for the capitalists. w For u t > at' however, the situation is different. For larger values of the average wage rate wt ' the next periods' capital stock is smaller. Therefore future output to be distributed is also smaller and, depending on the workers' utility function, 39 workers' total utility may be smaller for larger values of wt ' t = O, ..