per dollar, the slope of the indifference

无差异曲线的斜率
curve is marginal utility, let's say, of X over marginal

就是边际效用 X除以
utility of Y and the slope of the budget set is P_X

Y的边际效用而预算集的效用又是P_X
over P_Y.

除以P_Y
So if I just put the P_X down here and the

所以如果我把这个P_X 放下面
marginal utility up there that just says the marginal utility

边际效用放上面就说明
of X divided by P_X equals the marginal utility of Y

X的边际效用除以P_X等于Y的边际效用
divided by P_Y.

除以P_Y
That's something that you could waste a huge amount of time on.

这些会花掉你大量的时间
I don't have to do it because I know that you all have seen it

我不需要做这些因为你们曾经见到过
before, and the one guy who hasn't seen it before is going

而那些没看过的人一定会
to figure it out himself.

自己算一遍的