数学 & ECON代写 | 33189 LC Mathematical Methods for Economics Assignment

本次ECON经济学代写的主要内容是经济学中的LC数学模型方法

作业占模块评估的50%。它被标记为100。

建议您将数学正确性和解释质量视为同等重要。 “说明质量”在“ MFE评估标准”文件中的“一般课程信息”中进行了讨论。

每个问题都带有相等数量的分数。除非另有说明(Q3),否则每个子问题(a),(b),(c)等均带有相同数量的该问题的分数。

发布时间:3月1日星期一(第5周)。

在Canvas上提交,截止日期为:3月22日星期一中午12点(第8周)。

提出问题的禁运:您可以在3月15日(星期一)下午5点之前问我有关床单的问题,但不要在那之后问(即上交之前的最后一周)。关键是这些互动是出于学习和教学的目的。新知识需要时间来吸收。如果您完全陷入困境,我将提供足够的帮助以使您感动。

标记和反馈:4月19日星期一。
知识方面

请查阅附近的MME评估标准,以获取关于我以及(可能)第二年和最后几年寻找的数学和定量方法标记的摘要。

如果您要教另一个低于您的水平的学生,请说明您应该采取的方式。根据您达到此标准的程度来判断“解释质量”。

o让您的学生尽可能清楚地了解事情,但不要重复他们可能已经知道的事情。

o注意清楚明了,措辞以及“获得正确答案”。不要只是向他们扔代数。

o用正确,简洁的英语句子解释您的工作,并忽略与所提问题无关的内容。

o如果您的答案似乎太短/太长,则可能说明的解释太少/太多,在这种情况下,授予的分数将令人失望/令人失望。

1个

o《问题与答案》和《课堂答案》中的答案提供了有用的指南。

o这些要求的原因是该模块强调交流以及数学技能。如果您无法与其他人交流,那么了解数学就没什么用了。

关于其中的某些事情,您应该做出自己的判断,而不是问我们要做什么“正确”的事情。做出这样的判断是标记您的内容的一部分。像您未来的职业生涯一样,您将获得一定程度的自立,这将归功于他们的功劳。

使用提示。

物理方面

请以pdf文件格式提交您的答案。

请只提供一个pdf文件。您可以将通过电话或

扫描仪和键入的文本。

为了清晰起见,任何文字照片都应全幅显示,而不是从角度看。提交前,请先检查其可读性。

为了我们双方的缘故,请清楚地写下您的答案,并使它们易于阅读和标记。理想情况下,请先准备一个粗糙的版本,然后提交一份公平的副本。如果您的答案占几页,请寻找一个更简洁的版本,这可能会获得更多的分数。

请包括页码和问题编号。

不符合这些要求的答案将根据如何处罚

他们为标记创建了很多困难。

即使在截止日期之前开始提交,在截止日期之后收到的答案也算作迟到,并每天被罚款5分。为什么不在截止日期之前提交一两天呢?

2个

问题1。

最后,实际问题

假设𝑓:R3→R,其中𝑓由𝑓(𝑥1,𝑥2,𝑥3)≡3𝑥1-2𝑥3+𝑥1(2𝑥2-1)+(𝑥1+𝑥2-𝑥3)2 -𝜋4定义。

(a)证明𝑓是向量的二次函数。

(b)找出critical的临界点𝑥∗。

(c)确定𝑓是否具有唯一的全局最小值或唯一的全局最大值,或都不具有𝑥∗。

问题2。

通过(当然)适当的解释,找到关于点2的函数f(x)= x3 x2的二阶泰勒多项式(泰勒向量二次方)。有条理。

1 23
(a)[此问题分数的50%。]使用数值方法,在

问题3。

电子表格,以查找功能的关键点
𝑓:R2→R,其中𝑓(𝑥,𝑥)≡𝑒𝑥𝑝(−3𝑥)+𝑒𝑥𝑝(−𝑥)+5𝑥2𝑥2。

121212

系统地解释您答案的代数方面,并整洁地呈现数值计算:例如,从电子表格输出中进行编辑。

暗示。参见第3周的在线技能(幻灯片),第31页起。电子表格中合适的列标题是出现在p上的那些。 34:

Iter x1 x2 f g1 g2 H11 H12 H21 H22 DET h1 h2

(DET是Hessian的决定因素。)请注意,不必为后三列制定完整的代数公式,因为它们都可以用前几列来表示。

(b)[此问题分数的25%。]在找到的要点上是否存在严格的局部最小值或最大值?解释。

(c)[此问题分数的25%。]找到至少一个其他关键点,

Assessment:

33189 LC Mathematical Methods for Economics MME 50% Assignment – Questions

Organizational Aspects

The Assignment counts for 50% of the module assessment. It is marked out of 100.

You are advised to think of mathematical correctness, and quality of explanation, as equally important. ‘Quality of explanation’ is discussed in the document MFE Assessment Criteria, in General Course Information.

Every question carries an equal number of marks. Unless otherwise stated (Q3), every sub-question (a), (b), (c) and so on carries an equal number of the marks for that question.

Published: Mon 1 March (in Week 5).

Submit on Canvas by: 12 noon, Mon 22 March (in Week 8).

Question-asking embargo: You can ask me questions about the sheet till 5 pm, Mon 15 March, but not after that (i.e. not in the last week before hand-in). The point is that these interactions are for the purpose of learning and teaching. New knowledge takes time to absorb. I will provide enough help to get you moving, if you’re completely stuck.

Marks and Feedback by: Mon 19 April.
Intellectual Aspects

  • Consult MME Assessment Criteria nearby, for a summary of what I and (probably) other markers of mathematical and quantitative methods in the second and final years are looking for.
  • Explain in the way you should, if you were to teach another student just below your level. ‘Quality of explanation’ is judged on how well you meet this criterion.

o Make things as clear as possible to your pupil student, but don’t repeat things they probably already know.

o Pay attention to clarity and wording as well as to ‘getting the right answer’. Don’t just throw algebra at them.

o Explain what you’re doing, in proper, concise, English sentences, omitting material irrelevant to the question posed.

o Ifyouranswersseemdisproportionatelyshort/long,perhapsyouareproviding too little/much explanation, in which case the marks awarded will be disappointing/disappointing.

1

o The answers in Problems and Answers and Class Answers provide a useful guide.

o The reason for these requests is that the module stresses communication as well as mathematical skill. It is of little use knowing the maths, if you can’t communicate it to someone else.

  • About some of these things, you should make your own judgement, rather than asking us what is the ‘right’ thing to do. Making such judgements is part of what you are marked on. Credit will be given for a reasonable amount of self-reliance, as it will in your future career.
  • Use the Hints.

    Physical Aspects

  • Please submit your answers in a pdf file.
  • One pdf file only, please. You may mix in the same file pictures taken by phone or

    scanner, and typed text.

  • In the interests of legibility, any photographs of text should be full-on, not from an angle. Please check for legibility before submitting.
  • For both our sakes, please write your answers clearly and make them easy for us to read and mark. Ideally, prepare a rough version first, but submit a fair copy. If your answer occupies several pages, look for a more concise version, that will probably gain more marks.
  • Please include page numbers and question numbers.
  • Answers that do not conform to these requests will be penalized according to how

    much difficulty they create for the markers.

  • Answers received after the deadline, even if submission began before the deadline, count as late, and are subject to the usual 5-marks-per-day penalty. Why not submit a day or two before the deadline?

2

QUESTION 1.

At Last, the Actual Questions

Supposethat𝑓:R3 →R,where𝑓isdefinedby𝑓(𝑥1,𝑥2,𝑥3)≡3𝑥1 −2𝑥3 +𝑥1(2𝑥2 −1)+ (𝑥1 +𝑥2 −𝑥3)2 −𝜋4.

  1. (a)  Show that 𝑓 is a vector quadratic function.
  2. (b)  Find a critical point 𝑥∗ for 𝑓.
  3. (c)  Determine whether 𝑓 has a unique global minimum, or unique global maximum, or neither at 𝑥∗.

QUESTION 2.

With (of course) suitable explanation, find the second-degree Taylor polynomial (Taylor vector quadratic) for the function f (x) = x3 x2 about the point 2 . Be systematic.

1 2 3
(a) [50% of the marks for this question.] Use numerical methods, implemented on a

QUESTION 3.

spreadsheet, to find a critical point of the function
𝑓:R2 →R,where𝑓(𝑥 ,𝑥 )≡𝑒𝑥𝑝(−3𝑥 )+𝑒𝑥𝑝(−𝑥 )+5𝑥2𝑥2.

121212

Explain the algebraic aspects of your answer systematically, as well as presenting the numerical calculations neatly: for instance, edited from spreadsheet output.

Hint. See Week 3 Online Skills (Slides), pp. 31 onward. Suitable column headings in your spreadsheet are those that appear on p. 34:

Iter x1 x2 f g1 g2 H11 H12 H21 H22 DET h1 h2

(DET is the determinant of the Hessian.) Note that it is not necessary to work out full algebraic formulae for the last three columns, since they can all be expressed in terms of the previous columns.

  1. (b)  [25% of the marks for this question.] Is there a strict local minimum or maximum at the point you have found? Explain.
  2. (c)  [25% of the marks for this question.] Find at least one other critical point, and determine whether the function has a strict local minimum or strict local maximum there.

    Don’t copy spreadsheet files to each other – it will only end in tears.

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