Hello, Richie owns here. And I'm gonna take you through some economics 大家好，我是Richie，下面我要给大家讲点经济学
We're gonna start off with first big topic in here 我们将从第一个大的主题开始
which is micro macro economics and topics in demand and supply analysis. 微观宏观经济和供求分析
And the first LOS were gonna here，is the word of elasticity 第一个学习任务是弹性
you'll see from the LOS its calculate, interpret, and describe 你将从学习任务中看到它的计算、解释和描述
So you get the full hit here 你们要掌握它的全部知识点
The examiner wants you to be able to talk to him about elasticity 考官要求你能说清弹性所代表的的意义
talk about the implications of a given elasticity 以及特定弹性的含义
And as we'll see in a couple of examples, calculate it as well 而且像我们接下来看到的一些例子一样，能够计算它
A few different types 其中有几种不同的类型
So let's kick off with a really the grand daddy of them all own price elasticity of demand 我们先来看最基础的一个概念---需求价格弹性
often written as Pd, you can see the calculation top, right? 通常记作PEd，看到上面的计算公式了吧？
We have the percentage change in quantity over the percentage change in price 我们用需求量变化的百分比除以价格变化的百分比
What do we mean by that? 这是什么意思呢？
What we're looking at quite simply 很简单，
is what happens to the amount of good that is demanded, given a change in the price 就是价格变化引起的商品需求量的变化
So what's the change in the quantity actually sold if we change the price of the good? 所以，如果改变商品价格，实际销售量会如何变化呢?
Now, if you sit back and think about this logically 现在，如果你坐下来冷静地思考一下
you will come up with a correct answer in terms of whether they should be positive or negative 你就能得到关于他们应该是正值还是负值的正确答案
Just ask yourself quite simple 你就简单地问问自己
If the price goes up, what is likely to happen to the quantity that we sell? 如果价格上涨，我们的销售量会怎样?
And the answer is, as the price goes up, you would expect the quantity you sell to go down 答案就是随着价格上升，预期销售量会下降
And that certainly is the case for a normal good 正常商品肯定是这样的
However, we can get more excitable than that 然而，我们可以变得更加兴奋
We're gonna break this elasticity down into elastic and inelastic demand 我们将把需求弹性分为富有弹性的需求和缺乏弹性的需求
So start with elastic. What does that say? 先说富有弹性的吧，什么意思呢？
Well, if it's elastic demand, the percentage increase in price leads to a larger percentage decrease in quantities. 如果是富有弹性的需求，价格的上升会导致更大比例的需求量下降
For example, if we take our, let's say, soft drinks and we bump up the price by ten percent 举个例子，如果我们把，比如说软饮料的价格提高10%，
we lose more than ten percent of our sales 我们就会损失超过10%的销售量
So price goes up by ten percent，let's say quantity drops by fifteen percent 因此价格上涨10%，销量下降，比如说，15%
We would say that demand is elastic, the percentage change in quantity greater than price 我们就称这种需求是富有弹性的，也就是说销售量变化比价格变化大
how do we refer to that? Be careful here 如何体现呢？这里注意
We tend to refer to the price elasticity of demand in absolute terms 我们通常取需求价格弹性的绝对值
Absolute terms means we ignore the negative 绝对值意味着要去掉负号
We know the price elasticity of demand is going to be negative 我们知道，几乎所有的情况下需求的价格弹性总为负
in almost all cases. We just discussed that 刚才讨论过的
But if we talk about it in absolute terms 但是，如果我们取绝对值
and you can see here on the slide, these straight brackets here 如幻灯片上看到这些竖括号
these mean, we are talking in absolute terms 这意味着我们要计算绝对值
So when you ever see those straight brackets, ignore the negative 因此，当你看到这些竖括号时，请忽略负号
So we'll say we have elastic demand if our price elasticity of demand in absolute terms is greater than one. 因此，如果需求价格弹性的绝对值大于1，我们说是富有弹性的需求
Really what we mean, ignoring those absolute terms is it's less than negative one 我们忽略这些绝对值意味着它小于- 1
But that's a pain to keep having to say 但这么说很不方便
So we'll talk about absolute terms it's greater than one 所以我们将讨论绝对值，它大于1
Inelastic，be fairly obvious，inelastic. It is, in absolute terms less than one 缺乏弹性，很明显，缺乏弹性。从绝对值上说，它小于1
So percentage increase in price leads to a smaller percentage decrease in quantity demanded 也就是价格上涨引起需求量减少的比例相对更小
So now we bump our price up by ten percent 比如我们提高10%的价格，
and we lose only, let's say, five percent of our sales 而销量只下降5%
So all you need to do, really in terms of the interpretation here 所以你需要做的就是
is absolutely lodging your mind, absolute terms of one 完全印在你的脑海里，绝对值为1
If your PEd is greater than one, it's elastic 如果弹性大于1，是富有弹性的
less than one，we are talking inelastic 小于1，我们说是缺乏弹性的
Could you ask to calculate this? Will absolutely 你会要求计算这个吗？ 绝对会
I'm gonna see some more interesting and detailed examples of that in a moment 我马上会讲一些更有趣和更详细的实例
but in a very straightforward question 但是，一个非常明显的问题
No reason the examiner doesn't just give you some percentages 考官不会只是给你一些百分数
and get you immediately to interpret that is elastic or inelastic 让你立即理解它是富有弹性还是缺乏弹性的
Okay, next up, extreme examples 好了，说些极端例子
Economists love to talk extreme examples 经济学家喜欢讨论极端例子
There are very few situations where either would happen 这些情况极少发生
but it's worth just explaining it to the examiner, because again, it's in the readings 但向考官解释一下还是很有必要的，因为这一章里也有
So starting on the left with perfectly elastic demand 从左边这张图开始看，关于完全弹性
first thing to say, you've been through the base material 首先要说的是，基础知识已经学完了
You should see you have your classic diagrams here with 你会看到你的经典图表，
price on the vertical axis and quantity on the horizontal 价格在纵轴上，需求量在横轴上
So we're looking at what changes, in terms of the quantity for a change in price 我们考虑的是，价格变化时，需求量的变化
if it's perfectly elastic, then look what happens 如果是完全弹性，看看会发生什么
The demand is absolutely horizontal 需求曲线是水平的
Do you ever see that? 曾经见过这个吗？
Well, we're actually gonna see an example of that when we get to market structures 当我们讲到市场结构时，我们会看到一个这样的例子
So let's just hold fire on what that means 我们先来看看这是什么意思
But let's go to the right hand side with perfectly inelastic 我们来看看右侧的完全无弹性
Here you have a vertical demand curve 这里是垂直的需求曲线
The point being here, the same quantity is sold at every single price 意思是，不管需求量多少，价格都是一样的
So you can change the price to whatever you like 所以你可以随意改变价格
And the exact same quantities sold，very extreme, very unlikely 而卖出的数量是一样的，非常极端的情况，几乎不可能
The classic example given is a life saving drug 一个典型的例子是救命药
If you require one tablet littered to survive 如果你需要一粒来救命
then if it's very cheap, you're only going to buy one, because you don't need any more 那么即使它很便宜，你也只会买一个，因为你不需要更多
But if it's very expensive, you still have to buy one 但是如果很贵的话，你还是得买一个
Hence perfectly inelastic 因此完全无弹性
So recognize a couple of things 注意几点
If it's perfectly elastic, it is horizontal 如果是完全弹性的，它是水平的
perfectly inelastic, it is vertical 完全无弹性的，它就是垂直的
and then a nice line on point at the bottom there 然后在底部有一条漂亮的直线
only in these extreme examples 只有在这些极端的例子中
is the price elasticity of demand constant along the entire curve 需求的价格弹性沿整条曲线保持不变
Could be a nice little trick question, because we often show these demand curves as straight lines 这是一个很巧妙的问题，因为我们经常把需求曲线画成直线
Even if they are downward sloping 即使它们是向下倾斜的
we show it as a straight line 我们把它表示成一条直线
Just because it's a straight line does not mean PED is constant all along it 因为，它是一条直线并不意味着需求的价格弹性一直是常数
That's only the case here where you have perfectly elastic or perfectly inelastic curves 这只是完全弹性或完全无弹性曲线的情况
Okay, good stuff. Next up factors that influence this elasticity of demand. There are three of them 嗯，很好。接下来是需求弹性的影响因素，有三个
Whenever you see a list of three things in the syllabus 根据考试的性质，当你看到教学大纲中有三种类别时
given the nature of the exam, you should get excited. 你应该感到兴奋
Three things 三种类别
Your questions are objective test questions with three answers 你的问题是有三个选项的客观测试题
So you could be given these three, one of them would be slightly wrong 所以给你三个选项，其中一个可能会有点不准确
In the exam，you be asked to pick which one is least likely 在考试中，你被要求选择一个最不可能的
So any list of three definitions is goal just for you 任何包含三个定义的列表都是你的目标
So three of them，substitutes，proportion of income and time 其中三个影响因素是替代品，收入的比例和时间
I think they're fairly straightforward 我认为很简单
if you just think about them intuitively 如果你只是凭直觉判断
Let's start with substitutes, availability and closeness 我们先说替代品的可得性和相似性
Well, the more substitutes that are available, the more elastic demand will be 替代品越多，需求越有弹性
If you're looking at soft drinks, there are lots and lots and lots of other soft drink brands available 如果你想买软饮料，会有很多很多其他牌子可选
If one puts their price up, why would you stick with drinking Coke? 如果有人提高价格，你为什么还非要坚持喝可口可乐呢？
when you could switch to Pepsi and other taste differences 你可以转向百事可乐或者尝试一下其他口味
There's some people very passionate about it 有些人爱干这事
but if there are lots of substitutes available 但如果有很多替代品
an increase in price is likely to see a big drop in demand, because people can look elsewhere 价格上涨可能会导致需求大幅下降，因为人们可以去寻求别的选择
On the other hand, if you are the only supplier supplying that goods 另一方面，如果你是这种商品的唯一供应商
you have a lot more flexibility to put your price up 你就可以更灵活地提高你的价格
There's nowhere else for people to go to 人们没别的途径获取
The more substitutes there are,the more elastic your demand will be 替代品越多，你的需求就越有弹性
Secondly, proportion of income spent on the item 其次是某商品花费所占你收入的比例
the larger the proportion of income you spend, the more elastic your demand is 商品花费占你收入的比例越大，需求越有弹性
Because you notice it, if it's a huge part of your income 因为你会注意到，如果它占你收入的很大一部分
you're much more sensitive to price changes. Hence you're more elastic. 你会对价格变化更加敏感。因而更有弹性。
And finally, A kind of golden rule of economics, the time elapsed since the previous price change 最后是经济学中的一条黄金法则,前一次价格变化后的反应时间
The longer that time is, the more elastic the response will be 反应时间越长，需求的价格弹性越大
So what we're saying here as a kind of golden rule as to say 我们这里所说的黄金法则是
in the long run, responses are always more elastic 从长远来看，更长的反应时间代表更有弹性
Think of the price of gas going up 想想油价的上涨
First thing that happens in the price of gas goes up is everybody complains about it 油价上涨后的第一件事就是每个人都在抱怨
But in the short term, you can't really change your routine 但短期内，你不会改变你的日常计划
You can't change the use of your car, so you just have to get on with it 你不能改变你汽车的用途，所以你必须继续使用它
But in the longer term, you may then start to organize car pools 但时间久了你可能会开始组织合伙用车
You may buy a more efficient car. You may start to use public transport. 你可能买一辆更节能的汽车。你或许开始关注公共交通工具。
So you try and think of more creative ways around it in the long run 所以长期来看，你会试着想方法来解决这个问题
So in the short run, not that elastic 所以短期内没有那么大的弹性
As time passes, responses get more and more elastic 随着时间的推移，有更多的时间反应，变得越来越有弹性
Ok, so elastic 好的,富有弹性的
Next up, looking at elasticity on a straight line demand curve 接下来，看直线的需求弹性
We've mentioned this once already, but worth repeating 我们已经提到过一次了，但有必要重复一遍
just because that demand curve is a straight line does not mean elasticity is constant along it 因为需求曲线是一条直线，并不意味着它的弹性是恒定的
Why? Well, because we are not looking at the absolute change in quantity and price 为什么?因为我们没有考虑需求量和价格的绝对变化
Here, we're looking at the percentage change 这里是变化百分比
And what you'll see point a towards the left when you're this top end of the curve a点左边, 曲线的顶端,你会看到
and the price of there is very high, low quantity, high price. You tend to get very high elasticity. 价格非常高，销量少，价高。你会得到很高的弹性。
So very sensitive changes to price when you're down here 当在这里的时候，价格会有非常敏感的变化
and you've got a very low price play, high quantity, you tend to get low elasticity 价格很低，需求量很大，弹性很低
Now that extremes. As you come towards the middle 现在看极端情况。当你向中间靠近时
you will reach a point where you have unitary elasticity. That's where it's equal to one. 你会到达一个点，此处是单位弹性，它等于1。
In absolute terms, equal to one, we know it's minus one 如果绝对值等于1，我们知道其实是-1
Now, what does that mean for the supplier? What should you do as a supplier? 这对供应商意味着什么呢?作为供应商，你应该怎么做?
Well, if you're at the top end of the curve and you've got high elasticity, think what that means 如果在曲线顶端有高的弹性，想想这意味着什么
Slight change in price, big change in quantity 价格变化小的情况下，需求量变化较大
So for a slight change in price, big change in quantity, what do you want to do with your price? 价格变化不大，需求量变化很大，你会如何改变价格呢?
Well, drop it a little bit and pick up a huge amount of sales 好吧，稍微降低一点，就能获得巨大的销售额
On the other hand, low elasticity 另一方面是低弹性
Well, if I got very low elasticity, big change in price, I don't lose too many sales 如果弹性很低，价格变化很大，我就不会损失太大的销量
So I want to increase my price 所以我要提高价格
And what you'll do its head towards this unitary elasticity 将朝着这种单位弹性的方向移动
So not constant 所以不是常数
And you may be asked to tell the examiner as a supplier 考官可能会要你从供应商的角度来回答
where you are on the curve dictates what you should do with your prices 在曲线上的位置决定了你应该如何设置你的价格
You're looking to move towards unitary elasticity 现在你要考虑的是单位弹性
now, implications of that. Well, where can we maximize our revenue? 现在，这个的含义。我们在哪里可以实现收入最大化?
Well, for the reasons we've just discussed on the diagram 由于我们刚在图上讨论的原因
you want to move towards an elasticity of minus one,in absolute terms, one 你得朝着弹性为-1，绝对值是1，的方向移动
At that point, you will maximize your revenue 在此处，你的收入将最大化
Be careful here，in the world of economics, revenue is different to profit 这里注意，在经济学里，收入不同于利润
We are maximizing revenue here 我们要使收入最大化
for a lot of the rest of microeconomics will talk about maximizing profit 此外，微观经济学中还有一大块我们将会讲利润最大化
This is just revenue 这只是收入
because if we are in the inelastic range is discussed 因为如果我们是在缺乏弹性范围内讨论
increase your price, revenue goes up, you don't lose too many sales 提高你的价格，收入上升，你不会损失太多销量
in elastic range 在富有弹性的范围
Well, price increases，decrease total revenue, what you want to do? 价格上涨会减少总收入，那么你会怎么做?
If it's elastic, drop it and pick up a huge amount of sales 如果它是富有弹性的，降价会提升销量
some good points, perhaps not kind of the mainstream part of the syllabus 一些好的观点，也许不是教学大纲的主流
So it's good to pick up this interpretation 所以选择这个解释很好
because a lot of candidates will just think, if I can calculate you ask us to stay，I'm done 因为很多考生会想，如果我能计算你们要求的，那我就算完成了
There's much more to it than that 远不止这些
All right, here are the calculations 好吧, 这是计算
my view is always in economics 我的观点是,在经济学中
Anytime you see numbers, people jump all over it 只要看到数字，人们就会跳过去
There's an awful lot of economics in this syllabus to get through 课程大纲里有很多经济学知识要讲
Most of it is discussion 大部分是讨论
So people always wake up and come alive 所以，当人们看到数字时，他们总是会清醒起来，
when they see numbers and therefore get good at them 变得活跃起来，并因此变得擅长
So yes, absolutely get good at the numbers to keep pace with the average candidate 所以，是的，你一定要在数字上与一般考生持平
but make sure you can do that earlier discussion to get ahead of them 但是要确保分析好题目，以便可以领先他们
But this is how we can calculate it，a little bit of math 但这是我们计算它的方法,一点数学知识
Everyone looks a little bit of math. Percentage change in quantity or percentage change in price 一点数学知识。需求量变化百分比或价格变化百分比
We already know 我们已经知道
So we've talked about that. We know how it works to get inelastic and elastic 我们已经讨论过了。我们知道富有弹性与缺乏弹性的原理
But with a little bit of math that means we are looking at 基于数字所表示的意思，我们来看看
the percentage change in quantity,or percentage change in price, 需求量变化的百分比，或者价格变化的百分比，
which we can write as the change in quantity over the current quantity 也就是说，我们可以写为需求量变化比上当前的需求量
divided by the change in price of the current price 除以当前价格变化比例
You don't need to learn that 你不需要学习这些
It's just there for you if you like math 如果你喜欢数学，它就能用上
Because if you like math, you can work out what's happening 因为如果你喜欢数学，你可以算出发生了什么
So if you can see what the calculation is doing, all you need to do is get to this final version 如果你能看到计算过程，你所需要做的就是得出最终的结果
You can rearrange that middle version to get P zero over Q zero，current price, current quantity 你可以重新整理中间的形式,得到P0(当前价格)除以Q0(当前需求量)
multiplied by the change in quantity over the change in price 乘以，需求量变化量除以价格变化量
Now, as long as we have the demand function, we're gonna be very easily able to calculate this elasticity 现在只要有需求函数，就很容易计算出弹性
All need is the current price and the current quantity 所有需要的是当前的价格和当前的需求量
So as long as they're given, we're in business 我只要有了这些就可以了
then the change in quantity, given the change in price, 同样，给定价格变化，需求量的变化
well, if we have this demand function, which is quantity as a function of price 如果我们有这个需求函数，它是价格的需求量函数
It's gonna be the equation of a straight line 它是一条直线的方程
So quantity will be a，some sort of intercept plus b times price 需求量等于a（截距项）+ b*价格
b is the slope coefficient of price b是价格的斜率系数
In other words, if I change price by one dollar, quantity will change by b times one 换句话说，如果价格改变1美元，需求量将改变b乘以1
So the changing quantity given a one dollar change in price is b 价格变化1美元得到，需求量变化为b
therefore, b is the change in quantity over the change in price 因此，b是需求量变化除以价格变化
Now, that's the explanation 这就是解释
What you need to do is just learn that formula and be able to apply it 你需要做的就是学习这个公式并能够应用它
If they give me the current price, current quantity 如果已知当前价格，当前需求量，
and I have the slope coefficient for price from that function 然后从函数中得到斜率系数
then I can calculate elasticity at any point 然后我可以计算任意点的弹性
So let's try and put it into practice 所以让我们实例中运用一下吧
So here is a classic demand function for gasoline 这是一个经典的汽油需求函数
It is the quantity demanded one thirty eight, five hundred minus twelve, five hundred times the price Q=138500 - 12500*P
So we have the demand function that demand function is quantity demanded as a function of price. 需求函数是，需求量作为价格的函数
So as soon as you see that, what should jump salmon like to the forefront of your mind is 只要看到这个，你脑海中应该想到的是
here is the slope coefficient of price, twelve five hundred. So that's gonna help. 这是价格的斜率系数，12500。这会有帮助的。
Now, all I need is the current quantity and current price,and I mean 现在，我需要的是当前的需求量和当前的价格
what do they give me? 他们给了我什么?
Well, calculate the price elasticity of demand at a price of three dollars 计算价格为3美元时的需求价格弹性
So we have the current price 这是当前价格
We have the slope coefficient 斜率系数
What we're missing is the current quantity 我们缺少的是当前的需求量
Well, ok, I can calculate the current quantity if I just put my price into the demand function 如果我把价格代入需求函数，我就能计算出当前需求量
So let's move on and do that 我们继续
So from the question, the price is three, put the price of three into that demand function 从问题来看，价格是3，把它代入需求函数
And calculate a quantity of one hundred and one thousand，pretty straightforward 计算出需求量为101000美元，非常简单
And we already know the change in price over the change in quantity is minus twelve five hundred 我们已经知道价格变化量除以需求量变化量是-12500
It was the slope coefficient in that demand function 它是需求函数中的斜率系数
So how do I calculate my price elasticity? 如何计算价格弹性呢?
Well, current price, given in the question，there it is, three dollars 问题中给出了当前价格, 就是这个，3美元
current quantity 当前的需求量
We put three dollars into the demand function 我们将3美元代入需求函数中
and it spat out one o one 除以101000
multiplied by that slope coefficient of minus twelve and a half 乘以斜率系数, -12500
That gives us minus point three seven, their end of the calculation 得到-0.37，这是计算的最后结果
But make sure you can go on and do the interpretation 但是要确保你可以给出解释
In absolute terms, minus point three seven is less than one hence, would say demand is inelastic -0.37的绝对值小于1，因此，需求是缺乏弹性的
Classic question. I would say that as a calculation is pretty straight down the middle 经典的问题。我想说，作为一个计算是很简单的，在中间往下
And you want to be fairly comfortable trying to do that 你想要舒服地尝试去做
because it could as about to see get a little bit more exciting 因为它会变得更令人兴奋
Moving on 继续
Couple of other elasticity 其他弹性
sees these are just good fun 看到这些只是好玩而已
If you get the basics of price elasticity of demand, then cross price and income aren't too bad at all. 如果你掌握了需求的价格弹性，交叉价格弹性和收入弹性就不难了
Cross price, first of all, the formula is almost identical 对于交叉价格弹性，首先, 公式几乎是一样的
The only difference is we are looking at two different goods 唯一不同的是这里是两种不同的商品
So classic example，at the top, we got the price of coffee going up and the demand for tea going up 经典的例子是，在上面，咖啡价格上升，茶的需求上升
So two different goods 两种不同的商品
We have the same formula, percentage change in quantity over percentage change in price 我们有相同的公式，需求量变化百分比除以价格变化百分比
But the percentage change in quantity of tea divided by the percentage change in price of coffee 但茶的需求量变化百分比除以咖啡价格变化百分比
That gives us, in this example, sixteen six，eleven one, that gives us point six seven 题目中给我们的数据是16.65%、11.1%，得到0.67
Now, we're not overly excited this time about whether that's greater than or less than one 现在，我们不太关心它是大于还是小于1
What we're excited about here with cross price is whether it's positive or negative 对于交叉价格弹性，我们关注的是它是正的还是负的
Here, you can see it came to a positive number 这里，你可以看到它变成了一个正数
What does that mean while the goods are substitutes? 当商品是替代品时，这意味着什么?
Well, does that make sense? 这说得通吗?
Yes, the price of coffee went up,more people started drinking tea 是的，咖啡的价格上涨了, 越来越多的人开始喝茶
That means tea in this case is a substitute for coffee 这意味着在这个例子中，茶是咖啡的替代品
People turned away from coffee and drank tea instead 人们不再喝咖啡，而是喝茶
The bottom half of the slide, pizza and cola 下半页中，披萨和可乐
the opposite，price of pizza goes up 相反，披萨的价格上涨
A huge amount of cola is sold with pizza deliveries 大量的可乐是随披萨一起被卖出的
So if the price of pizza goes up, fewer people are ordering pizza 因此，如果披萨的价格上涨，购买披萨的人减少
the demand for cola a drops 可乐需求量也下降
we get a negative cross price elasticity 交叉价格弹性为负
Hence, those goods are complements 因此，这些商品是互补的
Selling pizza helps sales of cola 卖披萨有助于可乐的销售
So we've got own price, we've got cross price 学习了需求的价格弹性，交叉价格弹性
Finally moving on，we have the word of income elasticity of demand 最后，我们来学习需求的收入弹性
This is the sensitivity of quantity demanded to changes in the level of income 这是需求量对收入水平变化的敏感性
not price, but the level of your income 不是价格，而是收入水平
So what happens the percentage quantity demanded, given a change in how much you've got to spend? 那么考虑到你的支出的变化，需求量百分比会如何变化呢?
Well, once again, we're interested here to see if it's positive or negative 再一次，我们想知道它是正的还是负的
and we break it down into normal goods and inferior goods 我们把它分成正常商品和劣质商品
for normal good 对于正常商品
The more you earn, the more you demand 你挣得越多，你的需求就越多
So you'll get a positive income elasticity 所以你将会得到一个正的收入弹性
But there are such things, inferior goods 但也有这样的东西，劣质商品
examples here taken from the CFA syllabus, bus travel and rice 比如CFA考试大纲里的例子，巴士旅行和大米
So you may be offended here if you're a big fan of either of those two 所以如果你是这两个商品的爱好者，可能会觉得被冒犯了
But let's think bus travel. The idea is at the moment as a candidate for the CFA program 但是让我们想想巴士旅行。目前一般认为，作为CFA考生
you have to travel by bus 你不得不乘坐巴士
But once you get your CFA charter, obviously you're gonna make millions and millions and millions of dollars 但是一旦你拿到了CFA证书，显然你将会赚到数百万美元
and you'll have your own chauffeur,and you'll never need to take a bus again 你将会有自己的司机，你再也不用坐巴士了
So as you earn more, the amount of bus travel you will buy will drop. That will give you 因此，当你赚得更多的时候，你乘坐公交出行的次数就会减少
a negative income elasticity 你得到一个负的收入弹性
So inferior goods have negative income elasticity. 劣质商品具有负收入弹性
That's the entire suite of elasticity 这是完整的弹性理论
All we need to do to finish off is just a couple of extra examples 最后我们再举几个例子
to show how it could get a little bit more entertaining 来看看它是如何变得更有趣的
So moving on, we have this example, which brings in both income and cross price elasticity 好，继续，有这个例子，它包含了收入和交叉价格弹性
Hopefully, you can see what's happening here，if you saw the earlier example 如果你看到前面的例子，希望你能看到这里发生了什么
we're just extending it 我们只是在扩展它
Earlier we said the quantity of gas demanded was a plus b times the price of gas 前面我们说天然气需求量是a 加上b乘以天然气价格
Now we say, plus, it's always going to be a negative coefficient for normal goods 对于正常商品，它总是负的斜率系数
But we're now adding in other factors 但我们现在加入了其他因素
Not only does the price of gas effect the demand for gas 不仅汽油的价格影响汽油的需求，
but also the level of income, also the price of bus travel and the price of buying cars 还有收入水平、公共交通工具的价格和购车的价格
So there's a price of this product 这是产品的价格
There's our income level and as the price of other products 这是我们的收入水平和其他产品的价格
So the demand function can start to get quite long winded 需求函数会变得很长
Don't think of it as more complicated，it's just longer 不要以为它更复杂，它只是长
Ok, so we have that demand function 好，我们有了需求函数
What do we need to start answering questions? 我们还需要已知什么才能答题呢?
Well, the examiner is gonna start giving us information 考官会给我们一些信息
So if we click on and see the question with data in it with all using the demand function 如果我们点开,这里有含有数据的题目,包括需求函数涉及的参数
given assuming an average price for cars of twenty two thousand 假定汽车的平均价格22000美元
income of forty thousand 收入40000美元
bus travel of twenty five dollars and a price of three dollars, 公共汽车旅行25美元，以及汽油价格为3美元
let's get the income elasticity and the cross price elasticity 让我们计算收入弹性
of gasoline with respect to the price of bus travel 和汽油对公共汽车旅行的交叉价格弹性
This takes a while to work through, but once you get through it 这需要点时间来完成，但是一旦你完成了
it will start to become a kind of a very mechanical process 它就会开始变成一种非常机械的过程
So first steps, but all the information we have into that demand function 第一步，所有在需求函数中的信息
And that's what we've done on the next slide 这就是我们在下一张幻灯片中所做的
So you can see the quantity demanded of gas was fifteen minus three times the price of gas 所以你可以看到天然气的需求量是15减去3，乘以汽油的价格
which we slotted in plus point two times our income level 加上0.02乘以我们的收入水平
Let's just leave that for the moment 先把它放一放
plus point one one times price bus travel 加上0.11乘以乘坐巴士的价格
which we put in minus point zero zero eight times the price of cars, which have also slotted in 这里是-0.008乘以汽车价格，汽车价格也下降了
So the quantity of gas demanded shortens down to that，do the math 因此，天然气需求量下降到这个水平
You get eight point six plus point zero two times the level of income 计算得到8.6加上0.02乘以收入水平
Now, we just highlighted that, because now you can see the slope coefficient for income point zero two 现在，我们强调一下,你可以看到收入的斜率系数,0.02
There is the slope coefficient for income 这是收入的斜率系数
So if we're gonna calculate the income elasticity of demand 如果我们要计算需求的收入弹性
It's going to be our current income level 它将是我们当前的收入水平
Our current quantity demanded 除以当前的需求量
times the change in income，change in quantity, which is the slope coefficient 乘以，需求变化量除以收入变化量，也就是斜率系数
That's that trick, that little calculation we talked about earlier 这就是我们之前讲过的计算方法
So we have all the information we need 我们有了所有需要的信息
Our current income level is forty thousand 我们目前的收入水平是40000美元
There it is，what is the quantity demanded about that income level? 在这里，在此收入水平之下需求量是多少?
Well, let's just finish off the calculation 让我们算完
Eight point six plus point zero two times that forty gives us nine point four 8.6+0.02(40)，得到9.4
there is our current quantity demanded 这有我们的当前需求量
multiplied by point zero two, the slope coefficient change of income, given change in price 乘以0.02(给定价格变化,收入变化的斜率系数)
Multiply that out, and you get point zero eight five 乘以它，就得到0.085
could not be asked as a calculation？ Well, yes, it could 会不会出计算题？嗯，是的，它会
it's not the most likely thing in the world.，it's quite long 这不是很容易, 它很长
And people say, well, I'm never gonna get this done in ninety seconds 人们会说，我根本不可能在90秒内完成这个
but things balance out in the exam 但是在考试中事情是平衡的
As I always say, this might be a slightly longer question will be the shorter ones 就像我常说的, 这可能是一个稍微长一点的题目，也会有一些比较短的
But if I was you, I try and practice a few of these,little and often 但如果我是你，我会尝试和练习少许这些题目
because candidates who don't like economics often focus on just 因为不喜欢经济学的考生往往只专注于
making sure they can get those numbers right 确保他们能得到正确的数字
Okay, one more calculate cross price elasticity 再计算一下交叉价格弹性
So we did the income. What about cross price for bus travel? Exactly the same calculation. 巴士旅行的交叉价格弹性是多少?完全一样的计算。
So once again, put all the data that we have into the equation 再一次，把所有的数据代入方程
This time，let's leave out the price of bus travel 这次，我们不谈乘巴士旅行的费用
And that equation slims down to this six point six plus point one one times the price of bus travel 这个方程可以简化为6.6+0.11乘以乘公共汽车的价格
Well, that means here point one one is our slope coefficient 这意味着，0.11是斜率系数
So that's going to go into our final answer 这就是最终答案
We need the current price of bus travel 我们需要巴士旅行的当前价格
It's given to us, it's twenty five, and we slot that in to work out the quantity of gas demanded 它是25，我们把它代入,计算出天然气需求量
Well, at that price, it's nine point three five 在这个价格下，需求量是9.35
Once again, multiply it out and you'll get point two nine four 再乘一次，就得到0.294
If you practice one of those every two weeks until the exam 如果你考试前每两周就做一次这样的练习
it would be absolutely permanent in your brain 你的大脑就会永久记住它
Obviously, you've got hundreds and thousands of things to keep practicing 显然，你有太多的事情需要练习
I know that's an issue 我知道这是个问题
But if you could just do one of these every two weeks, it would sit nicely in your head 但如果你每两周做一次，它就会很好地印在你的大脑里