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And our job is to find out what is the mathematical description of this path, this line in p-V's case that connects these two point.
我们的任务,就是找出，描述这条曲线的方程。
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Now, for those of you who took Economics 115 or equivalent, what is the name of this line I've just drawn?
我来问一下学过经济学115的同学,这条曲线叫什么名字
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So, this makes this chart shown in pink make a lot more sense, because if we're way out at very far distances, essentially what we have here is we're talking about two separate atoms.
因此综合考虑这些因素可以发现这条粉红色曲线很合理，因为如果我们离得非常远，本质上来说,我们讨论的就是两个分开的原子。
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The pink line here is the efficient portfolio frontier when we have only stocks and bonds to invest.
这条粉色曲线就是有效边界,这个投资组合只包括了股票和债券。
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And we can just extrapolate in a straight line We before saw some examples where I had an algorithm to generate points, and we fit a curve to it, used the curve to predict future points and discovered it was nowhere close.
我们可以干脆用一条直线来描述它,我们之前看到在一些例子中,我用一个算法去生成一些点，然后用一条曲线对它进行拟合，然后用这条曲线来预测未来的点,最后却发现结果完全不对。
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I can do that because it's reversible, and I can get a functional form out.
画出路径就意味着过程是可逆的，下面我们来看这条曲线的函数形式。
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The particle is moving along this arc.
物体沿着这条曲线运动
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That was way fewer responses than I wanted. Let's try again; what's the name of this downward sloping line that I've just drawn?
没几个人回答啊,我再问一遍,这条向下倾斜的曲线叫什么
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The work in this step is just the area under this curve.
而这一步过程的功,是这条曲线下面的面积。
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Number of policies doesn't affect the means but it affects that standard deviation, so it becomes very collapsed and this is the basic core idea of insurance.
保单的数量并不影响其均值,但是会影响其标准差,所以这条曲线非常陡峭,而这就是保险的核心原理
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If we did a--if we go another two decimals-- if we did a million policies, then we would--this would almost just be a spike here at that point, so that's the concept of insurance.
如果我们在一万后面加两个零,如果我们签了一百万份保单,那么这条曲线基本就是尖形了,这些都是保险的相关概念
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That's the curve that I got out.
得到了这条曲线。
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The exact shape of the curve is subject to discussion, but the point of diminishing marginal utility is that, as you get more and more money, the increment in utility for each extra dollar diminishes.
这条曲线的确切形状还有待讨论,但是边际效用递减规律的重点在于,你得到的钱越多,每额外的一美元的增长效用会相对减小
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As we know, this line here has twice the slope of the original line of the demand curve, so the slope of this thing is -2b.
我们都知道了,这条线的斜率,是需求曲线斜率的2倍,也就是说它的斜率是-2b
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That's a bell-shaped curve, but it's centered exactly on .2.
这是条钟形曲线,它关于x=0.2对称
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Let me finish the picture here; here's my demand curve, here's my constant marginal cost at c, and I want to use this picture on the left now to figure out what the monopoly quantity is.
先把图画完,这条是需求曲线,这个是边际成本常量c,下面我们通过左边的图像,来找出垄断产量
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You can see that it dominates the pink line.
可以看到这条蓝色曲线在粉色线之上。
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