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谈到幸福,有愿意探讨幸福函数的坛友吗?下边是我归纳的一点点前人关于幸福函数的认识。先看看这些,也许能节约大家翻阅大量文献的时间。
min∫0+∞[B-U(x)+V(l)]dt
s.t. dk/dt=f(l,c)-x
where,
0 lower limit of integration
+∞ upper limit of integration
B maximum value of satisfaction of demand, conditioned on long-run technical level available to make use of measurable resources or endowment
U(x) utility achieved by spend monetary earning at amount of x
V(l) payment earned by means of providing labour services at amount of l by individual or group of people, and paid by employer or business activity
t time
k capital
x expenditure for consumption
Replacing t of target function with c stated in constraint condition, we have the target function updated as
min∫0+∞((B-U(x)+V(l))/f(l,c))dc
Both expenditure x and labour input l are function of consumption c, so that
f(l,c)–x=(B–U(x)–V(l))/u(x), where u(x): marginal utiltiy
by means of minimizing integrated function, or making partial derivative of it equal to zero in this case; and so that it is clear to see that the left part of this function works as saving ratio (or investment ration), which is vitally important in terms of development, even progress, and the right one as another ratio of difference, between maximum value of satisfaction of demand and sum of utility at cost of x and salary at cost of l, and marginal utility u(x).
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