Economic and Game Theory
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"Inside every small problem is a large problem struggling to get out." | ||||||
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If the probability of death were 0 and the discount rate were d, the present value is x = p + x*( 1 - d ). This implies x = p/d. If the probability of death were s at the end of each period and the discount rate were d, the present value is x = p + ( 1 -s )*x*( 1 - d ). This implies x = p/[1-( 1 -s )*( 1 - d )] = p/[s + d - s*d]. If s*d is small enough, then approximately we have x = p/[s + d]. This proves the orgininal problem. [Manage messages]
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