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An egocentric young man (EYM) has just inherited a fortune F and is now planning...

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Accounting

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An egocentric young man (EYM) has just inherited a fortune F and is now planning how to spend it. If we let x(k) denote his capital at the beginning of year k, his holdings will be approximately governed by the difference equation x(k+1) = (0) = ax(k) u(k) F, where a > 1 (with a - 1 the interest rate of investment) and where u(k) is the amount spent in yeark. He decides that the enjoyment achieved in year k can be expressed as v(u(k)) where v), his utility function, is a smooth function, and that his total lifetime enjoyment is N J= v(u(k))3k, =0 where the term (0 1 (with a - 1 the interest rate of investment) and where u(k) is the amount spent in yeark. He decides that the enjoyment achieved in year k can be expressed as v(u(k)) where v), his utility function, is a smooth function, and that his total lifetime enjoyment is N J= v(u(k))3k, =0 where the term (0

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