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Office Hours: The Solow Model

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    ♪[音乐] ♪
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    我在网上看了数据
    也和大量的学生谈过
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    发现这问题大家都不会
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    所以觉得是时候做个视频讲解了
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    课后辅导时间：索洛模型
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    有关索洛模型的稳定状态
    我们之前已有教学视频
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    现在来解其中一道题目
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    A国的GDP产出
    以下列方程式表示：
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    GDP=5√K
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    A的资本存量K为1万
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    若该国GDP的25%用于生产投资
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    则该国总投资额为多少？
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    另外，若年资本折旧率为1%
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    那该国当年的GDP
    是增加、减少还是持平？
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    一如既往，最好先看过视频
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    然后试着自己做做看
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    若还有问题，可以再回来
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    大家一起解决
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    准备好了没？
    此问题其实有两部分
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    首先得算出该国的投资总额
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    然后判断GDP是否增长
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    幸运的是
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    第一问是解开
    第二问的必要步骤
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    解题前先告诉大家
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    题目中的相关信息已写在
    白板右上角供大家参考
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    同往常一样
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    最好先理出解题步骤
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    第一个问题相当简单
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    只要从GDP等式中解出投资要素
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    把K代入
    解出投资额(I)
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    解第二问
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    则需首题答案
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    也就是通过投资所累积的资本量
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    下一步计算出因为折旧
    而损失的资本量
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    最后比较投资额与资本折旧
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    藉此判断在此时
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    该国的资本存量
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    以及GDP是增是减
    或是持平
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    不妨以图表来详解问题
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    这里y轴代表GDP
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    以往索洛模型的问题
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    各位看过的标记或许并非GDP
    而是「总产出」或「Y」
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    而x轴衡量的是实物资本(K)
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    已知该国GDP等于5√K
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    我们已预先绘制好图表
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    此方程式表明
    GDP为资本(K)函数
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    资本K增加
    GDP随之增加
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    根据收益递减定律
    GDP增长幅度相对较小
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    要注意的是
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    这里将其他可能影响GDP的
    因素视为定量
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    例如教育、人口及想法点子
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    因此资本增加遂成唯一
    带动该国GDP增长的要素
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    此例中，该国资本存量为一万美元
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    代入方程式中，则GDP为500
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    既知该国GDP=5√K
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    而我们也知道投资额
    为GDP的25%
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    因此可将GDP代换成5√K
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    解题步骤一便完成了
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    因为已算出GDP为500
    其25%就是125
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    因此该国投入资本累积的
    额度就是125美元
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    解题的第二步就完成了
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    很快地说明几点
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    事实上y轴还衡量
    好几项变量
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    除GDP外，也包含投资
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    最后还要加上资本折旧
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    若在y轴上标记所有变量
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    看起来会很拥挤
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    所以只标注GDP
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    另外，若投资额为125
    而GDP总额是500
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    那剩余的GDP又到哪去了？
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    消费，
    简言之就是买东西
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    这视频结束前
    我们要解决的问题之一
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    也能测试你对此概念的理解
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    话说该国累积的资本额为125
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    但我们仍不知
    该国整体的资本存量
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    到底是增加、减少或持平
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    因为我们还不知道
    资本存量的消耗量
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    或折旧幅度
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    现实生活中
    机器会出故障，笔记本电脑会损坏
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    想想你自己生活中的实物资本
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    因iPhone摔坏而须再买的经验
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    还有即使旧机堪用
    你仍然买新手机的情况
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    所以即使投资对
    资本存量有所贡献
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    这1万美元还是
    会因为像iPhone摔坏
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    这样的事情发生而有所损耗
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    画成图表有助理解这种损耗
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    题目条件告知
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    资本存量的折旧率为1%
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    资本的1%
    以图形表示大致就像这样
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    当资本存量为1万，1%就是100
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    因此得出资本存量每年的消耗
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    或折旧额度为100美元
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    这样解题的第三步就完成了
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    算出投资和资本折旧后
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    便可比较两者
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    若该国投资额是125美元
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    且资本折旧是100美元
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    那么投资便大于资本折旧
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    因此本年度资本存量会增加25美元
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    也就是这两条曲线间的差距
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    现在可回答最后的问题了
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    该国的资本存量变多了
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    因此GDP也增长了
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    这即是我们得出的答案
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    根据方程式GDP=5√K
    (GDP和K正相关)
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    只要资本K增加
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    GPD就会增加
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    只要一国投资大于资本折旧
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    该国资本存量和GDP将持续增长
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    直到投资与折旧相等
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    届时经济模型将达稳定状态
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    因投资带来的资本增加
    将刚好被折旧损失抵销
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    因此资本存量与GDP都维持不变
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    一如既往
    请告诉我们你的看法
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    若想尝试更多练习
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    视频末尾还有更多
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    有关索洛模型
    与稳定状态的习题
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    ♪[音乐] ♪
Title:
Office Hours: The Solow Model
Description:
more » « less
Video Language:
English
Team:
Marginal Revolution University
Project:
Office Hours
Duration:
06:39

  • Samson Zhong

    Ms. He:

    Thanks for your feedback on my subtitle of the video clip, for which I have to tell you on which reference I based my translation.

    The original text:
    00:02:14,987 --> 00:02:19,016
    And K, "physical capital",
    is measured on the x-axis

    First, to be exactly, in economics, “physical capital” or just capital is a factor of production (or input into the process of production), consisting of machinery, buildings, computers, and the like. The production function takes the general form Y=f(K, L), where Y is the amount of output produced, K is the amount of capital stock used and L is the “amount of labor” used.

    "Physical" is used to distinguish physical capital from “human capital” (a result of investment in the human agent), circulating capital, and financial capital "Physical capital" is fixed capital, any kind of “real” physical asset that is not used up in the production of a product. (https://goo.gl/9KkygV)

    Hence, I am afraid we should make a point to differentiate these various capitals when translating them, and that’s why you can easily find the translation “物質資本” by googling it. (https://goo.gl/gsjEAx)

    According to the definition by National Academy of Educational Research,
    物質資本指傳統的「人造的生產工具」，如建築物、機器設備等，都是物質設施。 教育經濟學的研究中，特別著重物質資本與人力資本獲利性的比較。根據沙查波羅(G. Psacharopoulos)研究顯示：在開發中國家，物質資本的投資收益率不及人力資本；但是在已開發國家，物質資本的投資卻優於人力資本。
    (https://goo.gl/q0FdZ6)

    Hope these points are solid enough to prove that “物質資本” is not mistranslation, let alone “physical capital” is a term, not an adjective.

    00:02:14,987 --> 00:02:19,016
    And K, physical capital,
    is measured on the x-axis

    (My translation)
    00:02:14,909 --> 00:02:18,644
    而X轴则表示「物质资本」
    而非现在看到的K

    (Your suggestion)
    02;15 original translation has a misunderstanding
    "而X轴则表示「实际的」资本
    而非现在看到的K"

    00:02:14,987 --> 00:02:19,016
    And K, physical capital,
    is measured on the x-axis

    (My translation)
    00:02:14,909 --> 00:02:18,644
    而X轴则表示「物质资本」
    而非现在看到的K

    (Your suggestion)
    02;15 original translation has a misunderstanding
    "而X轴则表示「实际的」资本
    而非现在看到的K"

  • YIJUN HE

    Sam,

    As I said in my message, translation of "physical capital" is not the problem.

    The original text:
    00:02:14,987 --> 00:02:19,016
    And K, "physical capital",
    is measured on the x-axis

    Your translation basically means
    "x-axis measures physical capital,
    not the K you are seeing here"

    Hope it helps.

  • YIJUN HE

    Sorry I misspelled your name, Samson! I'm terribly sorry。抱歉！

  • Samson Zhong

    1. The Title “Office Hour” is capitalized, which implies it can be a proper noun instead of the generic nouns as a period of time in which students can bring their questions to the teachers. And the way MRUniversity makes a reference to it corroborates this:
    “’New Office Hours’ on Solow model and steady state”
    (a new installment of this series of videos is available now)
    https://goo.gl/tgsgO4

  • Samson Zhong

    (My translation)
    00:02:14,909 --> 00:02:18,644
    而X轴则表示「物质资本」
    而非现在看到的K

    (Your suggestion in the message box)
    02;15 original translation has a misunderstanding
    "而X轴则表示「实际的」资本
    而非现在看到的K"

    1. The only diofference is 实际的 and 物质资本
    2. 而X轴则表示「物质资本」does not necessarily mean x-axis measures physical capital. Let's lookn at the simplest model Supply and Demand. In Chinese, when we say X-axis X軸代表需求, people would know that it mean all the changes developed regarding this factor is "marked" on x-axis. Actually, "measure" here means"to find the exact corresponding number or amount and because it is not a fixed one, so we say "X轴则表示「物质资本」. If you use Google Translation, there is no correlation between 表示 and Measure.

  • Samson Zhong

    Ms. He:
    I am afraid you did not put my translation in context, the speaker compared the typical chart students might h. ve seen and the present one she is going to use.

    00:02:08,752 --> 00:02:10,561
    以往新古典经济增长模型的问题
    In previous Solow questions,

    38
    00:02:10,641 --> 00:02:14,315
    各位看过的标记或许并非GDP
    而是「总产出」或「Y」
    you may have seen this label does
    total output or Y instead of GDP.

    39
    00:02:14,909 --> 00:02:18,644
    而X轴则表示物质资本
    而非现在看到的K
    And K, physical capital,
    is measured on the x-axis

  • Samson Zhong

    2. Isn’t this video a SDH Master track, if so, Amara Ondemand Handbook dictates subtitles “Must include all relevant on-screen texts.”
    Hence, should we omit the opening headline “MRUniversity: Learn Economics, Understand Your World”?

  • YIJUN HE

    Samson, I think I'm correct on this one. If you don't agree, you can run it by our other teammates or third-party translators.

    Original sentence:
    “And K, "physical capital",
    is measured on the x-axis”

    This is your translation
    "而X轴则表示「实际的」资本
    而非现在看到的K"

    So basically your translation means
    "x-axis represents physical capital,
    not the K you are seeing now."

    Thanks

  • Samson Zhong

    3. 0:31~0:35 (Did you look this up?)
    If the country devotes 25% of its GDP
    to making investment “goods”,

    　投資財是一種提供生產增加資本的財貨。在經濟上，財貨的支出，不是投資，就是消費。就投資而言，其財貨的支出有下列三種特性：(1)可以累積資本，擴大資本的存量；(2)具有耐久性或長久性，在於未來獲得利益；(3)由於用於生產或投資，有時不能滿足其消費慾望。 　　視教育為一種投資財，是基於：(1)是對於未來消費能力的增進；(2)是將來賺錢能力的加強；(3)是社會聲望、社會地位及發展潛能的增進。其中特別是第二點，布勞格(M.Blaug,1972)研究英、美、墨西哥、印度等國，其人民教育程度與收入的關係，發現三種事實： 　　1.如果不考慮教育程度，則個人一生收入，隨年齡而增加，至四十五歲而達到高峰，以後就有逐年下降的趨勢。 　　2.個人所受教育愈長，起薪就愈高，並且薪資上升幅度較為陡峭。 　　3.個人所受教育愈長，到達最高收入額愈遲，且其退休時的收入亦愈高。 　　因此，僅就經濟利益的觀點言，顯見個人投資於教育，對未來的收入的確是有利的。至於國家與社會，在人力素質提高後，產業結構的改變與生產力的增加，導致整個社會的富裕，亦可視為是一種投資。
    https://goo.gl/Pa2hwe
    投資財Investment Goods
    https://goo.gl/85jHF7

  • Samson Zhong

    "x-axis represents physical capital,
    not the K you are seeing now."
    "而X轴则表示「实际的」资本
    而非现在看到的K"
    1. You put it in similar way
    2. Could you please tell me the difference between "X轴则表示「物质资本」" and "而X轴则表示「实际的」资本" ?

  • Samson Zhong

    Ms. He:
    I think we should figure out what the verb "measured" means in "And K, "physical capital",
    is measured on the x-axis.
    1. Could you help me define the word "measured" in the context? Then we can work together to find the Chinese word that is closest to it.

  • Samson Zhong

    4. 0:42~0:47
    is the country's GDP increasing, decreasing, or remaining constant “in ‘that’ steady state”?

    If we refer back to the same term “steady state” at 0:16~0:19
    , I see no reason to not translate it here as稳定状态

  • Samson Zhong

    00:02:14,987 --> 00:02:19,016
    And K, physical capital,
    “is measured” on the x-axis
    而x轴衡量的是实物资本(K)

    00:02:05,687 --> 00:02:08,903
    As you can see,
    GDP “is measured” on the y-axis.
    这里y轴代表GDP
    In Chinese:
    衡量: ①比较；评定：衡量得失｜衡量利弊｜衡量是非。 ②估量，考虑：这件事该不该做，你要好好衡量一下。(https://goo.gl/ESVsNU)

    1. Why could the same phrase “is measured” be translated into two different Chinese words衡量 and 代表 ?
    2. In Chinese, 衡量 is an active verb, and thus requires an actor. But in economics, we have to figure(算出) the equation and then draw the graph using the corresponding amounts we get from the equation. Therefore, it may be strange to say x轴衡量的是实物资本(We use the X-axis to figure out K). Actually, we “put” the amounts of K “on “ the x-axis. These numbers just reflect what we get from the equation.

  • Samson Zhong

    5. 2:53~ 2:57
    I guess 帶入 and 代入 are interchangeable
    https://goo.gl/aCjVi2

  • Samson Zhong

    3:28~3:32
    因此该国投入资本累积的/额度就是125美元
    累积的(adj) 额度(noun)
    Common Guidelines – “Avoid breaking grammatical units”
    “Your line breaks shouldn’t divide proper nouns, auxiliary verbs from the word they modify, nor prepositions and adjectives from their nouns”

  • Samson Zhong


    There are many Chinese translations for the term "The Solow Model, " I suggest we should keep the English along with the Chinese translation. https://goo.gl/F06hzo

    梭羅－史旺模型（Solow–Swan model），又稱索洛增长模型（Solow growth model）、新古典经济增长模型、外生经济增长模型（exogenous growth model）

Chinese, Simplified subtitles

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