Solutions to Guided Analysis 4
pdf
keyboard_arrow_up
School
York University *
*We aren’t endorsed by this school
Course
3411
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
14
Uploaded by ChancellorClover5549
Solutions To Guided Analysis 4 Part I: 1
) Anna:
Best at: Math (Score: 25)
High school counselor might recommend: Considering fields that require strong quantitative and problem-solving skills, such as engineering, computer science, or finance.
Beatrice:
Best at: Science (Score: 18)
High school counselor might recommend: Exploring careers in the natural sciences, healthcare, or engineering due to her strong aptitude in science.
Clara:
Best at: Math (Score: 14), with relatively balanced scores in other areas.
High school counselor might recommend: Exploring interdisciplinary fields or careers that value a well-rounded skill set, where Clara's balanced abilities could be an asset.
These recommendations are based on the students' individual strengths and can help guide them towards areas of study and future careers that align with their aptitudes. It's important to note that these are just suggestions, and students should also consider their personal interests and passions when making decisions about their future paths.
2) Here's a ranking of the students according to their aptitudes in each field:
Science:
Beatrice (Score: 18)
Anna (Score: 20)
Clara (Score: 5)
Math:
Anna (Score: 25)
Clara (Score: 14)
Beatrice (Score: 12)
Lit and Writing:
Anna (Score: 17)
Clara (Score: 17)
Beatrice (Score: 10)
Summary: Anna excels in Math and is competitive in Science and Lit/Writing.
Beatrice is strongest in science but has lower scores in Math and Lit/Writing.
Clara performs relatively well in Math and Lit/Writing but has the lowest score in Science.
These rankings provide a comparison of each student's performance in different fields of expertise based on their aptitude test scores. Keep in mind that these are relative rankings based on the given scores and may not necessarily indicate absolute proficiency in each subject.
3) Considering the individuals will choose the job that offers the highest salary, let's determine the likely outcome for each student:
Anna:
Science Position ($120,000) - Anna's best fit based on aptitude.
Salary: $120,000
Beatrice:
Lit and Writing Position ($50,000) - As it offers the highest salary among the available positions.
Salary: $50,000
Clara:
Lit and Writing Position ($50,000) - As it offers the highest salary among the available positions.
Salary: $50,000
Comparison to the School Counselor's Recommendation:
The school counselor recommended Anna to consider fields involving mathematics, such as engineering, computer science, or finance. However, Anna ended up in a Science position, which was her strongest aptitude, aligning with the counselor's suggestion for a highly valuable job.
The counselor's recommendations for Beatrice and Clara were not explicitly mentioned in the previous context. However, the outcome reflects that they both chose the Lit and Writing Position, possibly indicating a different direction than the counselor's suggestions.
It's important to note that individuals may consider various factors beyond the salary, such as personal interests, work-life balance, or long-term career goals, when making decisions about their careers. The outcome reflects thei
r choices based on the salary offered for each position.
Part II
4) To compute the total happiness for each student in each career choice, we can consider both the inherent happiness associated with each job and the additional happiness derived from the annual income. Let's calculate the total happiness for each student in each career choice:
Total Happiness for Anna:
Science: (Science Happiness + (Income * 0.001)) = (65 + (120,000 * 0.001))
Math: (Math Happiness + (Income * 0.001)) = (90 + (90,000 * 0.001))
Lit and Writing: (Lit/Writing Happiness + (Income * 0.001)) = (20 + (50,000 * 0.001))
Total Happiness for Beatrice:
Science: (Science Happiness + (Income * 0.001)) = (70 + (120,000 * 0.001))
Math: (Math Happiness + (Income * 0.001)) = (60 + (90,000 * 0.001))
Lit and Writing: (Lit/Writing Happiness + (Income * 0.001)) = (50 + (50,000 * 0.001))
Total Happiness for Clara:
Science: (Science Happiness + (Income * 0.001)) = (20 + (120,000 * 0.001))
Math: (Math Happiness + (Income * 0.001)) = (60 + (90,000 * 0.001))
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Lit and Writing: (Lit/Writing Happiness + (Income * 0.001)) = (80 + (50,000 * 0.001))
Total Happiness:
Anna:
Science: (65 + 120) = 185
Math: (90 + 90) = 180
Lit and Writing: (20 + 50) = 70
Beatrice:
Science: (70 + 120) = 190
Math: (60 + 90) = 150
Lit and Writing: (50 + 50) = 100
Clara:
Science: (20 + 120) = 140
Math: (60 + 90) = 150
Lit and Writing: (80 + 50) = 130
These values represent the total happiness each student would receive in each career choice, considering both the intrinsic happiness associated with the job and the additional happiness derived from annual income.
5) To determine which position each student will end up working in, we need to compare the total happiness for everyone in each career choice. The students will choose the job associated with the most happiness.
Anna's Total Happiness:
Science: 185
Math: 180
Lit and Writing: 70
Anna would choose the Science position as it offers the highest total happiness (185).
Beatrice's Total Happiness:
Science: 190
Math: 150
Lit and Writing: 100
Beatrice would choose the Science position as it offers the highest total happiness (190).
Clara's Total Happiness:
Science: 140
Math: 150
Lit and Writing: 130
Clara would choose the Math position as it offers the highest total happiness (150).
Overall, Happiness Generated:
Overall, the firm would have Anna in the Science position, Beatrice in the Science position, and Clara in the Math position.
The total happiness generated would be the sum of the happiness values for Anna, Beatrice, and Clara in their respective chosen positions.
These choices are made based on the individuals' preferences for the jobs associated with the most happiness, combining both the inherent job satisfaction and the additional happiness derived from income.
Part III
6) The adjusted income (after tax) is calculated as 70% of the original income (100% - 30% tax). Let's recalculate the total happiness for each student in each career choice:
Adjusted Income:
Adjusted Income = Original Income * (1 - Tax Rate)
Total Happiness with Tax Adjustment:
Total Happiness = Inherent Happiness + (Adjusted Income * 0.001)
Now, let's calculate the adjusted total happiness for each student in each career choice:
Adjusted Total Happiness:
Anna:
Science: (65 + (120,000 * 0.7 * 0.001))
Math: (90 + (90,000 * 0.7 * 0.001))
Lit and Writing: (20 + (50,000 * 0.7 * 0.001))
Beatrice:
Science: (70 + (120,000 * 0.7 * 0.001))
Math: (60 + (90,000 * 0.7 * 0.001))
Lit and Writing: (50 + (50,000 * 0.7 * 0.001))
Clara:
Science: (20 + (120,000 * 0.7 * 0.001))
Math: (60 + (90,000 * 0.7 * 0.001))
Lit and Writing: (80 + (50,000 * 0.7 * 0.001))
Therefore, A
djusted Total Happiness:
Anna:
Science: (65 + 84) = 149
Math: (90 + 63) = 153
Lit and Writing: (20 + 35) = 55
Beatrice:
Science: (70 + 84) = 154
Math: (60 + 63) = 123
Lit and Writing: (50 + 35) = 85
Clara:
Science: (20 + 84) = 104
Math: (60 + 63) = 123
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Lit and Writing: (80 + 35) = 115
These adjusted values represent the total happiness each student would receive in each career choice after the imposition of a 30% income tax, considering both the inherent happiness associated with the job and the additional happiness derived from the adjusted annual income.
7) Anna's Adjusted Total Happiness:
Science: 149
Math: 153
Lit and Writing: 55
Anna would choose the Math position as it offers the highest adjusted total happiness (153).
Beatrice's Adjusted Total Happiness:
Science: 154
Math: 123
Lit and Writing: 85
Beatrice would choose the Science position as it offers the highest adjusted total happiness (154).
Clara's Adjusted Total Happiness:
Science: 104
Math: 123
Lit and Writing: 115
Clara would choose the Lit and Writing position as it offers the highest adjusted total happiness (115).
Overall, Happiness Generated:
Overall, the firm would have Anna in the Math position, Beatrice in the Science position, and Clara in the Lit and Writing position.
The total happiness generated would be the sum of the adjusted happiness values for Anna, Beatrice, and Clara in their respective chosen positions.
These choices are made based on the individuals' preferences for the jobs associated with the most adjusted happiness, considering both the inherent job satisfaction and the additional happiness derived from the adjusted income after a 30% income tax.
8) To compare the students' overall happiness with and without the income tax, we need to consider the additional happiness generated from the revenue used for public goods (infrastructure, museums, orchestras, etc.). The additional happiness generated per $1,000 spent is given as "1 point of happiness." Let's incorporate this into the calculation:
Total Happiness with Tax Adjustment and Public Goods:
Adjusted Total Happiness = Inherent Happiness + (Adjusted Income * 0.001) + (Tax Revenue * 0.001)
Adjusted Total Happiness with Public Goods:
Anna:
Science: (65 + 84 + (30,000 * 0.001)) = 149 + 30 = 179
Math: (90 + 63 + (27,000 * 0.001)) = 153 + 27 = 180
Lit and Writing: (20 + 35 + (15,000 * 0.001)) = 55 + 15 = 70
Beatrice:
Science: (70 + 84 + (30,000 * 0.001)) = 154 + 30 = 184
Math: (60 + 63 + (27,000 * 0.001)) = 123 + 27 = 150
Lit and Writing: (50 + 35 + (15,000 * 0.001)) = 85 + 15 = 100
Clara:
Science: (20 + 84 + (30,000 * 0.001)) = 104 + 30 = 134
Math: (60 + 63 + (27,000 * 0.001)) = 123 + 27 = 150
Lit and Writing: (80 + 35 + (15,000 * 0.001)) = 115 + 15 = 130
Now, let's compare the overall happiness with income tax and public goods to the overall happiness without the income tax. We can calculate the differences in overall happiness for each student. The higher the adjusted total happiness, the better the outcome.
Overall, considering the public goods generated by the income tax, the students might experience higher overall happiness compared to the scenario without the income tax. The exact comparison will depend on the specific values and choices made by the individuals.
9) If the revenue from the income tax is completely wasted and no happiness is generated from the spending of the tax revenue, then the additional happiness term related to the tax revenue becomes zero. In this case, the calculation for overall happiness with tax adjustment and public goods is simplified to:
Adjusted
Total
Happiness=Inherent
Happiness+(Adjusted
Income×0.001) Adjusted
Total
Happiness=Inherent
Happiness+(Adjusted
Income×0.001)
Now, let's calculate the adjusted total happiness for each student in each career choice without the additional happiness from the tax revenue:
Adjusted Total Happiness without Public Goods:
1.
Anna:
Science: 65+84 = 149
Math: 90+63 = 153
Lit and Writing: 20+35 = 55
2.
Beatrice:
Science: 70+84 = 154
Math: 60+63 = 123
Lit and Writing: 50+35 = 85
3.
Clara:
Science: 20+84 = 104
Math: 60+63 = 123
Lit and Writing: 80+35 = 115
Comparing this scenario with the one where the income tax revenue contributes to public goods and generates additional happiness, we can observe that the overall happiness without the income tax is higher for each student. In this case, the wasted revenue from the income tax negatively impacts the overall happiness, making the scenario without the tax preferable for the students.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
10) The level of passion for a job is subjective and depends on various factors, including personal interests, job satisfaction, and intrinsic motivation. However, we can make some observations regarding the no-tax and the 30% tax cases:
Passion for Jobs:
No-Tax Case: In the no-tax case, students are making career choices based solely on their inherent happiness and aptitude for the job. They are not influenced by income taxes or public goods. As a result, their passion for the job might be driven more by their personal interests and satisfaction with the nature of the work.
30% Tax Case: In the 30% tax case, students are influenced by the income tax, which affects their adjusted income and overall happiness. If the tax revenue contributes to public goods, it might affect their passion for the job positively, as they might derive satisfaction from the societal benefits. However, if the tax revenue is wasted, it could negatively impact their passion, as they see a portion of their income going to waste.
Apt Matching with Jobs:
No-Tax Case: In the no-tax case, students are selecting jobs based on their individual preferences, skills, and aptitudes. Matching with jobs is more directly aligned with their inherent strengths and interests.
30% Tax Case: In the 30% tax case, the adjusted income and overall happiness are influenced by the tax rate. If the tax revenue contributes to public goods, there might be an alignment between societal benefits and the students' job choices, contributing to a sense of societal contribution. However, if the tax revenue is wasted, this alignment might be disrupted, potentially leading to a less apt match between their jobs and societal contributions.
In summary, the level of passion and apt matching with jobs is likely to be higher in the no-tax case, where individuals make career choices based solely
on their personal preferences and aptitudes without the influence of income taxes and public goods. The 30% tax case introduces additional factors that can either enhance or diminish the alignment between individual satisfaction, societal benefits, and job choices, depending on how the tax revenue is utilized.
11) The preference for living in a high-income tax country or a low-income tax country depends on various personal factors and individual priorities. Here are some considerations for both scenarios:
Living in a High-Income Tax Country:
Pros:
High-income tax countries often offer robust public services, such as healthcare, education, and infrastructure, funded by tax revenue. This can contribute to a higher quality of life for residents.
Access to well-funded public goods and services can enhance societal well-
being and provide a safety net for citizens.
Greater potential for addressing social inequality and supporting those in need.
Cons:
Higher income taxes mean individuals retain a smaller portion of their earnings, which might affect personal disposable income.
Some people may disagree with the government's spending priorities or efficiency in utilizing tax revenue.
Potential for complex tax structures and regulations.
Living in a Low-Income Tax Country:
Pros:
Lower income taxes mean individuals keep a larger portion of their earnings, potentially leading to higher disposable income.
Individuals have more flexibility in how they allocate their money and resources.
Simpler tax structures and potentially fewer regulations.
Cons:
Public services and infrastructure might be less well-funded, leading to potential gaps in healthcare, education, and other essential services.
There might be less support for social programs and a greater reliance on individual responsibility.
Income inequality and social disparities may be more pronounced.
Ultimately, the preference for living in a high-income tax country or a low-
income tax country depends on individual values, priorities, and the perceived balance between personal financial autonomy and the benefits derived from public services. Some people prioritize a strong social safety net and well-
funded public goods, while others prioritize maximizing personal income and financial autonomy. It's essential to consider one's own values and priorities when making such a decision.
12) A
verage income tax rates in the United States, Canada, and Germany:
United States:
The top federal income tax rate in the U.S. is 43.4%, which starts at $406,750 USD for a single person.
If the income is earned in California, the top rate can be as high as 56.7%1.
The average income tax rate among the top 50% of taxpayers was 14.6% in 2018, with an average tax paid of $20,6632.
Canada:
In Canada, the federal income tax brackets range from 15% to 33% for individuals.
The lowest tax bracket is 10% for an individual earning $11,000 or less in 2023, and it jumps to 22% for those earning over $44,725.
These thresholds increase to $11,600 and $47,150 in 20243.
Germany:
The top tax rate in Germany is 50.5%, starting at $283,326 USD for a single person.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
E
xpectations regarding job satisfaction and efficiency based on the discussion above:
Job Satisfaction:
Job satisfaction is subjective and influenced by various factors, including job tasks, workplace culture, and personal fulfillment. It's challenging to make a direct comparison between countries, as job satisfaction is highly individualized.
Efficiency and Job Matching:
Efficiency and job matching depend on factors such as education, skill development, and the alignment of individual aptitudes with job requirements. Countries with robust education and workforce development programs may facilitate better job matching and efficiency.
Considerations:
High-income tax countries often provide robust social services, potentially contributing to job satisfaction for those valuing societal benefits.
Lower income tax countries might provide individuals with more financial autonomy, potentially impacting job satisfaction positively for those prioritizing personal income.
In conclusion, job satisfaction and efficiency in job matching are complex and multifaceted. It's challenging to make definitive predictions based solely on income tax rates. Cultural, societal, and individual factors play crucial roles in shaping people's perceptions of job satisfaction and efficiency in job matching.