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So I took this to the other side and I divided through by 2b and the b here cancels.
通过移项和通分成2b,就可以消去b了
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Good, so if I plug q2 = 0 into here, this term disappears and I just get a - c over 2b.
把q2=0代入到算式中,这部分就没有了,只剩/2b
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How far along do I have to go drop off a - c when I have slope -2b?
斜率-2b的线还要经过哪个横坐标呢
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What's that telling me is that if Player 2 chooses not to produce then Player 1's best response is a - c over 2b.
参与人2产量为0而参与人1最佳对策是,/2b,这能说明什么
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I'll just remind us of what these functions are; it's a - c over 2b - q2 over 2 and accordingly for Player 2.
再说一遍,参与人2的方程是,/2b - q2/2
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It'll give me q1* is equal to a - c over 2b - q1* over 2.
会得到,q1*=/2b-q1*/2
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Now, I claim that that quantity, a - c over 2b actually has another name.
2b这个值是个术语
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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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All right, so that's just solving out the algebra, so we're saying what q solves, a - c over 2b - q2 over 2 = 0.
没错,只需要解出当,/2b-q2/2=0,时q2的值即可
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Here's a - c over 2b and here's a - c over b.
这里是/2b,这里是/b
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I got to have a - c over 2b - q2 over 2.
应该是/2b - /2
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So this is a - c over b and this is a - c over 2b so this distance and this distance are meant to be the same.
这点是,/b,这点是,/2b,这两段长度应该是相等的
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So this monopoly quantity is indeed a - c over 2b.
因此垄断产量是/2b
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What's the name of the quantity a - c over 2b?
这个/2b叫什么
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Well, the monopoly quantity was a - c over 2b and the competitive quantity was a - c over b, just to remind you of those, they're on our picture.
垄断产量是/2b,完全竞争产量是/b,提示大家一下,这几点都在图上呢
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Well look, here I have a line of slope -2b.
看一下这里,这条线斜率是-2b
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I know that Player 2's best response for every possible choice of Player 1, which if we had done it would be q2 hat is going to a -c over 2b--q1 over 2, right?
参与人1不同策略下参与人2的最佳对策,即q2帽等于/2b - q1/2
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Answer a - c over 2b.
答案是/2b
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a - c over 2b.
是/2b
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The only place q1 appears here is here, so when I differentiate again I'm going to get -2b and sure enough that's negative, which is what I wanted to know, just to check that when I'm finding this thing, I'm finding a maximum and not a minimum.
只有这一处有q1,因此二阶导数是-2b,它肯定是个负数了,这正是我们想得到的结果,这就验证了我们刚才得出的,是最大值而不是最小值
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