为了进一步拓展国际影响力，培养具备经济学思维与全球视野的青年人才，伦敦政治经济学院经济学会（LSE规模最大、最具影响力的学术社团之一）联合LSE教授团队与阿思丹国际竞赛平台合作共同推出权威性的全球赛事——LSE 经济学挑战 （LSESU Economics Society Economics Challenge）。

赛事由 LSE 经济学学会严格命题与学术审核，融合高中与大学层次的经济学内容，旨在为全球优秀高中生提供与LSE学术体系接轨的机会，激发他们的研究热情与批判思维，成为迈向世界顶尖学术殿堂的重要舞台。

宏观经济学 Macroeconomics

① If the consumer price index was 75 in the base year  and 130 in the following year, then the inflation rate was

a.57%      b.58%      c.73%      d.42%

Explanation:

Inflation rate = percentage change of CPI = ((130/75)-1)x 100%

② Assume the MPC = 0.75 and considering only the multiplier effect, if government taxation increases by $60

billion, then national income will

a.Decrease 45 billion.      b.Decrease 240 billion.

c.Increase 240 billion.      d.Decrease 180 billion.

Explanation:

multiplier = 1/(1-MPC) = 1/ (1-0.75) =4.

Potential change in national change income = multiplier x tax change x MPC = 4x60x0.75=180

微观经济学 Microeconomics

① Ms. Jane resigned from her job with a $60,000 annual salary to open a coffee shop in her apartment. Her

coffee shop’s annual revenue is $80,000, and her costs for coffee beans, facility maintenance, water, and

electricity amount to $30,000 per year. Should Ms. Jane be satisfied with her coffee shop’s annual profit?

a.Yes, because her accounting profit is $50,000

b.Yes, because her economic profit is $50,000

c.No, because her economic loss is $20,000

d.No, because her economic loss is $10,000

Explanation:

Economic profit = Accounting profit – Implicit cost = $80,000 - $30,000 - $60,000 = -$10,000.

②Dawn, Inc. produces and sells notebook in a perfectly competitive market at the price of $3 per unit and hires all the workers it needs at the wage rate of $23. Assume worker is the only variable input, and the firm’s production schedule is provided in table.

Determine the profit-maximizing number of workers the firm should hire.

a.1      b.2      c.3      d.4

Explanation:

The firm maximizes profit where the value of the additional worker’s contribution (Marginal revenue) is just equal to orgreater than the wage(Marginal cost). Hiring a third worker would add only $21 of revenue while costing $23, leading to a loss. Thus, the profit-maximizing number of workers is 2.

定量基础 Quantitative Foundations

① Researcher Keynes is doing a field experiment.He discovers a random variable X that takes: ● X =2 with probability 0.4 ● X =10 with probability 0.6 What is E[X]and Var[X]?

（研究员凯恩斯正在做一项实地实验。他发现了一个随机变量X，其取值如下： ● X = 2 的概率为 0.4 ● X = 10 的概率为 0.6 求 E[X] 和 Var[X]。）

A.15.36,6.80

B.5.20,15.36

C.5.20,6.80

D.6.80,15.36 

Explanation:

The expected value of a discrete random variable is calculated as the sum of each possible value multiplied by its probability.For random variable X,which takes the value 2 with probability 0.4 and 10 with probability 0.6,E [X]=(20.4)+(100 .6)=0.8 +6=6.80.The variance of a discrete random variable is calculated as E[X²]-(E[X])². First, calculate E[X²]:E[X²]=(2²0.4)+(10²0.6)=(40 .4)+(1000 .6)=1.6 +60 =61.6.Then, Var[X]=61.6 -(6 .80)²=61.6 -46.24 =15.36.

② A researcher has a null hypothesis that study hours have no effect on exam scores.Using data, the researcher obtains an estimate of the effect of 2.5 with a standard error of 0.5.What is the value of the t-statistic in this context?

（一位研究者提出原假设：学习时间对考试成绩没有影响。利用数据，该研究者得到效应估计值为2.5，标准误为0.5。在此情况下，t统计量的值是多少？）

A.0.20

B.1.25

C.2.50

D.5.00 

Explanation:

The t-statistic measures the ratio of the magnitude of an estimate to its standard error.It is calculated as the estimate divided by the standard error.Substituting these values into the t-statistic formula gives 2.5 /0.5 =5.00.

TMUA风格的数学 TMUA-style Mathematics

① How many solutions are there to (1 + 3 cos 3 θ )2 = 4 in the interval 0° ≤ θ ≤ 180° ?

（在区间 0° ≤ θ ≤ 180° 内，方程 (1 + 3 cos 3θ)² = 4 有多少个解？）

A.3

B.4

C.5 

D.6

Explanation:

We have (1 + 3cos3θ)2 = 4 if and only if 1 + 3cos3θ = ±2. We consider each possibility separately.

We have1 +3cos3θ = 2

if and only if 3cos3θ = 1

if and only if cos3θ = 1/3.

Since 0° ≤ θ ≤ 180° , we have 0° ≤ 3θ ≤ 540° , and there are 3 values of 3θ which have cos3θ = 1/3 in this interval. (One is between 0° and 90° , one is between 270° and 360° , and one is between 360° and 450° , by considering the graph of y =cosx.)

Now considering the other possibility, we have1 +3cos3θ = − 2

if and only if 3cos3θ = − 3

if and only if cos3θ = − 1.

Again, 0° ≤ 3θ ≤ 540° , but this time there are only 2 values of 3θ which satisfy the equation: 3θ = 180 and 3θ = 540° .

Neither of these values of 3θ overlap with the values of 3θ found earlier, so in total there are 3 +2 = 5 values of 3θ in the interval 0° ≤ 3θ ≤ 540° , and hence 5 solutions to the originalequation in the given interval. The correct answer is option C.

② Let x be a real number.

Which one of the following statements is a sufficient condition for exactly three of the other four statements?

（设 x 为一个实数。以下哪一个陈述是其余四个陈述中恰好有三个成立的充分条件？）

A. x ≥ 0

B. x = 1

C. x = 0 or x = 1 

D. x ≥ 0 or x ≤ 1

E. x ≥ 0 and x ≤ 1

Explanation:

We work through them sequentially:

A If x ≥ 0, then B may be false, C may be false, D may be false and E may be false

B If x=1, then A is true, C is true, D is true and E is true

C If x=0 or x=1, then A is true, B may be false, D is true and E is true

D If x ≥ 0 or x ≤ 1, then A may be false (for example if x = − 1), B may be false, C may be false and E may be false

E If x ≥ 0 and x ≤ 1, then A is true, B may be false, C may be false and D is true

The correct option is therefore C, which is sufficient for exactly three of the other four statements.

1、哪些人可以参加LSE经济学挑战？

LSE经济学挑战适合9-12 年级学生参加，参赛者需以个人形式参与。

2、LSE经济​学挑战赛可以以中文参与吗？

目前LSE经济学挑战赛仅以英文作为参赛语言，参与者可以根据个人情况选择线上或线下参与比赛。​

3、如何参加剑桥圣凯瑟琳学院经济学夏校？

您需要先参加LSE经济学挑战，对于在挑战中获奖的选手将有机会参加剑桥圣凯瑟琳学院经济学夏校，此夏校仅针对国际经济学竞赛中顶尖获奖选手开放。