Measure 4: Increase "Project-style" Major Exercises for Students to Apply Mathematics to Solve Economic Problems.


Table 3.6. Illustrative table of using Excel in estimation problems


STT

x i

n i

n i . x i

x i 2 .n i

1

1

5

5

5

2

1.2

3

3.6

4.32

3

1.3

2

2.6

3.38

4

1.4

1

1.4

1.96

5

1.5

27

40.5

60.75

6

1.7

6

10.2

17.34

7

1.8

7

12.6

22.68

8

1.9

3

5.7

10.83

9

2

60

120

240

10

2.1

2

4.2

8.82

11

2.2

6

13.2

29.04

12

2.3

4

9.2

21.16

13

2.4

4

9.6

23.04

14

2.5

23

57.5

143.75

15

2.6

1

2.6

6.76

16

2.7

1

2.7

7.29

17

3

5

15

45

Total

160

315.6

651.12

Sample mean

1.9725

Mean of square

4.0695

Sample variance

0.17874

Adjusted sample variance

0.17987

Calibration sample deviation

0.42411

Accuracy of estimate

0.06572

Bottom

1,90678

Upper bound

2.03822

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Measure 4: Increase "Project-style" Major Exercises for Students to Apply Mathematics to Solve Economic Problems.


Technique 3.4: Select illustrative examples in the teaching of Mathematics courses related to knowledge of some specialized subjects in Economics in the training program, to train skills: Problem solving and decision making in economic analysis; Modeling practical economic situations; Using mathematical language; Applying knowledge in practice.

The following problems illustrate the use of Math tools to solve problems in specialized KT subjects.

Problem 1. Applying XSTK to calculate expected profits in financial investment (Integrated with the subjects of Stock Market and Corporate Finance)


Mr. An works for a company with a monthly savings of 3,000,000 VND and is considering two investment channels as follows:

- Option 1: This amount will be deposited in the bank with a stable interest rate of 1,800,000 VND/year.

- Option 2: Invest 100,000 VND in the stock market to buy a stock, then receive an annual dividend of 5,000 VND/year and expect the market price of that stock to be 105,000 VND after one year.

This is the result Mr. An obtained after collecting data, using calculations (in fact many investors use Probability models) to process the data.

The problem situation is Which strategy choice is optimal?

Consider option A: If Mr. An deposits money in the bank, he will earn 1,800,000 VND/year, which means the profit rate is 1,800,000/3,000,000 = 6%/year.

Consider option B: If Mr. An invests in stocks, his investment information is as follows:

- The investment amount is 100,000 VND

- Income after 1 year of investment is: 5000 (105000 100000) 10000 / share (this is a Stock Market subject)

- Profit rate is: 10000/100000 = 10%/year

Thus, if you invest in the above stock, the investment profit includes dividends from the stock (5,000 VND/share) and profits from stock price increases (5,000 VND/share). With 3,000,000 VND, An can buy 300 shares and the corresponding income is 3,000,000 VND (300 shares x 10,000 VND/share) (this is a Corporate Finance subject).

Therefore, in terms of profit margin to evaluate investment efficiency, we choose option 2, that is, investing in stocks will have a higher profit. However, the risk level of the two options is different. If Mr. An deposits money in the bank, the profit will be 6%/year. If Mr. An buys stocks and holds them until the end of the year, he may or may not receive the expected dividend because the stock price can fluctuate up or down, making option 2 a loss. In terms of risk level, it is clear that depositing money in the bank can be considered risk-free, but if investing in


The probability of stock price fluctuations is higher. This shows that the option with higher expected value always has higher risk, that is, expected profit and risk are two quantities that vary in the same direction. This problem continues to be discussed in detail in the subjects: Investment Economics, Choices under Uncertain Conditions,...

Problem 2. Applying XSTK to the problem of choosing a business plan (Integrated with the subject of Management Accounting)

At HAT company, there is data on the business performance report according to the contribution balance in November 2016 as follows: (consumption output of 4,500 products), unit: 1,000 VND.

Table 3.7. Report on the results of production and business activities of HAT company



Total

Calculated for 1 product

Proportion

1. Revenue

300000

60

100%

2. Variable costs

225000

45

75%

3. Contribution margin

75000

15

25%

4. Fixed cost

25000



5. Profit

50000




In December, the manager wanted to increase profits compared to the previous month, so he proposed to reduce the selling price by 2,000 VND/product and increase advertising costs on the media by 8,000,000 VND (this is a subject of Management Accounting). So, the question is, is the manager's plan feasible?

The given problem situation is the administrator's solution feasible?

Faced with the above situation, financial analysts calculated the probabilities of this option being implemented into the company's business model. To do so, they conducted a market survey and assumed that after market research, the results of a sample survey at a number of dealers when implementing the above option were as follows: The expected consumption output would increase by 20% to 50%, the probability that the consumption output would increase by 20% was 60%, and the probability that the consumption output would increase by 50% was 40%.


From the results of the probability survey, accountants can calculate the profit corresponding to the survey results. Specifically:

- If the consumption level increases by 20% then:

Unit contribution margin is equal to: (600002000)4500013000 VND/product.

Contribution margin increased: (5000.120%.13000)750000003000000 VND

Profit increase: 3000000 8000000 5000000

7,000,000 VND)

- If the consumption level increases by 50% then:

copper (profit decreased)

Increased contribution balance: (5000.150%.13000)7500000022500000 VND

Profit increase: 22500000 8000000 14500000

Hence, the profit increase when calculated is:

copper

5000000.60%14500000.40%2800000

VND (profit increased by VND 2,800,000).

The results show that the plan proposed by the manager can bring additional profits to the company. Therefore, the company should implement this plan. Through the above situation, students realize that conducting surveys and collecting data using the XSTK model allows businesses to verify the feasibility of a business plan and then decide whether to implement that business plan or not?

Technique 3.5: Build an open homework system, helping students learn about applying Math tools to solve exercises in specialized subjects of the Economics block or practical Economics situations, to practice skills: Problem solving; Self-study.

The following exercises illustrate the use of Math tools to solve some technical situations. Teachers need to build a system of illustrative exercises for students to study at home and suggest that students find out more about practical technical situations that require the use of Math tools to solve.

Exercise 1. (Exercise applying XSTK to solve insurance problems). Suppose you have a motorbike worth 10 million VND. A company invites you to buy insurance with the following conditions: Every year you must pay a certain insurance premium, in return if you lose your motorbike, the insurance company will reimburse you 8 million VND.


(i.e. 80% of the value of the vehicle). What is the highest insurance premium you would accept? Now suppose you read the People's Police newspaper and learn that in the past year, the rate of motorbike theft in the city was 0.1% (i.e. 1 in 1,000 motorbikes was stolen). How does this new information affect your decision about the maximum insurance premium you would accept?

The given problem situation is a person thinking about how to protect personal property?

The solution that most people accept is to buy insurance for their car. However, whether or not he buys insurance, he still faces the risk of theft. So what should be done to minimize this loss? This question directs students to build a mathematical expectation model to calculate the expected level of assets to be kept in all possible cases. We have to compare between 2 cases: The case of buying insurance and the case of not buying insurance.

Table 3.8. Insurance premium cases


Insurance

Thief

(p = 0.1%)

No theft (p = 99.9%)

Expected Asset Value (E(X))

Do not buy

0 million

10 million

(99.9%).10 million

Have buy

(0.1%).8 million

10 million

(99.9%)10 million + (0.1%)8 million


Thus, if insurance is purchased, the expected value will be:

EV BH

99.9%.10tr

0.1%.8tr –

BH,

where BH is the insurance premium.


If no insurance is purchased, the expected value will be:

EV KBH

99.9%.10tr

0.1%.0

99.9%10 million.


Therefore, if you base your decision solely on expectations, you will buy

insurance if

EV BH EV KBH , meaning if BH < 8,000 VND. Fee 8,000

This is called the fair premium. After doing all these calculations, let us ask ourselves again, what is the maximum insurance price that we are willing to pay? And if the insurance price is not 8,000 VND but 10,000 VND, will we be willing to buy the insurance?


From practicing this situation in class, we can draw some initial comments directly related to the problem for students as follows: Why do we buy insurance (demand for insurance)? We buy insurance to reduce the variation in consumption level. Note that by spending only 8,000 VND a year, we will not be afraid of losing everything when losing our car. Thus, variation or variance is one of the measures of risk. In statistics, people use variance to measure the variation of a random quantity. "Variation" here means variation compared to the average value (or expected value).

Starting from the TT problem, students can ask questions: Will the company always sell the desired amount of insurance? The theft rate this year increased compared to last year?,... Therefore, the insurance companies themselves also have to bear the risks when implementing the above insurance project. So what do they do to minimize the risks they will encounter? This is the premise for students to enter the newer mathematical models and economic models, more extensive and inheriting the Probability models that have been built from the subject of XSTK such as: Profit, risk, risk measurement, risk reduction, profit maximization, application of options in business,...

Exercise 2. (Exercise on applying expectation and variance in choosing investment options). An investor is considering investing in two projects A and B in two independent fields. The ability to recover capital after 2 years (in

%) of two projects are random variables with the following probability distribution table:

Table 3.9. Project Table A


DISTANT

65

67

68

69

70

71

73

P(X A )

0.04

0.12

0.16

0.28

0.24

0.08

0.08


Table 3.10. Project Table B


X B

66

68

69

70

71

P(X B )

0.12

0.28

0.32

0.20

0.08


Please evaluate the ability and risk level of capital recovery of the above two investment projects?


Calculate the expectation and variance respectively:

69.16%; D ( X A ) 3, 0944; M ( X B )

68.72%; D ( X B)

1, 8016

M ( X A )

So if you choose an investment option with a higher expected return rate, choose option A, but if you need to choose an option with a lower return risk, choose option B.

Exercise 3. Require students to research and create examples and exercises on KT that require using Math tools to solve similar problems to the two above.

3.2.2.4. Measure 4: Increase the number of large-scale "project"-style exercises for students to apply Mathematics to solve information problems in economics.

Forging purpose

practice

The purpose, meaning and implementation of this measure can be visualized through the following diagram:


Project-based learning, group work

CDIO Method

Most professional skills

industry

economy

Increase large-scale "project"-style exercises for students to apply

Mathematics solves practical problems in economics.


4.2. Instructions for student presentation

in front of class and discuss

4.3. Requirement to solve the problem using the part

soft


4.1. Give students related exercises

with economic practice

Figure 3.3. Diagram of measure 4


a. Purpose of the measure

This measure will contribute to training the following skills: Problem solving and decision making in economic analysis (Skill 9); Modeling practical economic situations (Skill 6); Using mathematical language (Skill 1); Applying knowledge in practice (Skill 7); Collecting, analyzing and processing information (Skill 8); Applying information technology (Skill 10); Teamwork (Skill 2); Self-study (Skill 5).

According to Marxist-Leninist philosophy, each person always exists in close connection with others, each individual is a unit that makes up the collective, linked to the collective through the interests of the individual and the interests of the collective. In the process of movement, many conflicts will appear, but they are the driving force for development, the basis for resolving conflicts is the harmonious combination between the individual and the collective, the awareness and responsibility of each individual before the collective.

LXVugotxki believes that high-level psychological functions appear first at the interpersonal level between individuals, they exist first at the internal psychological level. Therefore, according to him, in a classroom, it is necessary to emphasize assisted discovery more than self-discovery. From there, a teaching principle is to organize students to learn with the help and support of teachers and classmates, learning together will help students acquire knowledge better. Jean Piaget (1896-1980) with the theory of social cognitive conflicts said: While interacting together, social cognitive conflicts appear, creating cognitive imbalances among people. Debates occur continuously and are resolved. In the process, incomplete arguments and reasoning will be supplemented and adjusted. Thus, learning is a social process, in the process, people continuously struggle to resolve cognitive conflicts [62].

Group learning method will help students have the opportunity to exchange and learn from each other through group activities. This method helps meet the requirement: learning to live together, one of the four goals of UNESCO on teaching in the present era. Moreover, according to "National training laboratories, Bethel, Maine", learning by mutual exchange method will help students acquire 70% of knowledge [126].

The role of group work and self-study is undeniable in university education, however, in fact, survey results at the University of Social Sciences and Humanities show that these skills have not been developed.

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