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All right, good. So the pink line is actually going to get steeper, but I know what you mean.
说得很好,但粉色的线会变陡峭,我理解你说的意思了
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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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All right, where the green and the pink line intersect.
没错,就是绿线和粉线的交点
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The pink line takes two assets, one is stocks and the other is bonds, actually government bonds.
粉色线包含两种资产的投资组合，一个股票，另一个是债券，实际上是政府债券。
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I can try other portfolios; this one right here--I'm pointing to a point on the pink line-- that point right there, 50% stocks, 50% bonds.
还可以尝试其它组合;,这一点，粉色曲线上我指的这一点-,表示50%的股票，50%的债券。
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I don't know what percent; our oil reserves in the U.S. are pretty small, so we're kind of lying somewhere inside-- maybe on this pink line.
我不知道具体占百分之几;,美国的石油储备量是微不足道的，所以我们可能是位于这附近-,也许在这条粉线上面。
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The other thing I have down is population, although the population of the U.S. has been pretty steady -that pink line looks awfully steady -and I have interest rates.
我还做了另外一个数据,就是人口数,而美国的人口数量一直都很平稳,粉色的那条线看起来非常平稳,我还做了利率的数据
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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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Where the green and the pink line intersect.
在绿色与粉色线的交点处
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This point right here is, on the pink line, is a portfolio 100% bonds.
粉线上的这一点，是一个100%债券的投资组合。
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You should see that the blue line is better than the pink line because, for any expected return, the blue line is to the left of the pink line, right?
可以看到蓝线比粉线好,原因是对于任意的预期收益率，蓝线都在粉线的左边，对吧？
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Well, you can see the pink line shows the employment in Los Angeles, and indeed, it did move around corresponding to the booms and busts in the Los Angeles market but not so dramatically.
你可以看到那条粉线,表示了洛杉矶的就业情况,实际上,它紧随着洛杉矶市场,兴衰变动,只不过没有那么显著
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This is just a picture of that little box, so it's going to turn out it goes from, the pink line goes from here to here and the blue line goes from here to here.
这是那个小方格的放大图,这些线如图所示,粉色的线从这一点到这一点,蓝色的线从这一点到这一点
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It has dropped precipitously and you note that the pink line, which shows the rate of growth of home prices, the rate of growth of home prices, has fallen just right along with the traffic of homebuyers.
而且跌的很突然,再看粉色线,粉色线代表了房价增长率,房价增长率,与购房者残参观量一样下跌
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Let's just... We'll get there, just to remind you, the way we read this is you give me a quantity of Firm 2, I find Firm 1's best response by going across to the pink line and dropping down.
我们当然也能算出来,提醒一下各位,这个图像的个意思是任意给出公司2产量,然后通过这条粉色的线,就可找出与之对应的公司1的最佳对策
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So the pink line is going to move towards the vertical, and the blue line is going to move towards the horizontal, and notice that the amount of effort that we generate, goes down dramatically, goes down in this direction.
粉色的线最后会趋向垂直,蓝色的线最后会趋向水平,请大家注意下我们付出的努力,会朝这个方向大幅减少
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Conversely, if you think the goalie's going to shoot to the right with probability more than a ?, then the best you can do is represented by the pink line, and that's shooting to the left, or if you think the goalie's going to dive to the right with the probability more than a ?, the best you can do, your best response is to shoot to the left.
相反如果你认为门将扑向右侧的概率,大于?的情况下,此时你最佳策略用粉线表示,即从左路射门,也就是说如果你觉得门将扑向右路的,概率大于?的话,你最好选择从左路射门
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This pink line has to drop off from a all the way to c.
这条粉色的线要经过纵坐标a-c
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The way we read this graph, is you give me an S2, I read across to the pink line and drop down, and that tells me the best response for Player I.
这个图的作用是,给定一个S2,找到粉线对应的坐标,然后就能找出参与人I的最佳对策
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Now, just to repeat, again I know I've got some math phobics in the audience, let me just slow down a second, all I'm doing here is I'm saying look at this equation of the pink line, look at this equation of the blue line, X is when they cross, i.e., they are equal to each other.
我再重复一遍,我知道你们之中有些人数学不怎么好,我放慢一点说,我是这么解的,看这条粉线的方程,还有这条蓝线的方程,X是二者的交点,也就是说这点两个方程相等
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And let's just draw how those, that pink and blue line look in that box.
我们在方格内填充粉色和蓝色的线
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What do we call the point where the pink and the blue line cross?
蓝粉两线的交点叫什么
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What does it tell us that the pink and the blue line cross?
粉色的线和蓝色的线相交说明什么
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What does it mean to say the pink and the blue line cross?
这两条线相交到底说明了什么
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