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Guided Analysis 2 Question 1 1. The town of Whoville has 100 identical consu...
Mar 27, 2024
Guided Analysis 2 Question 1 1. The town of Whoville has 100 identical consumers and 50 identical car washes. Each consumer has an income of \24.Thediagramandchartbelowshowtheindifferencecurvesofatypicalconsumerandthemarginalcostcurveofatypicalcarwash.a.HowmanycarwashesdoesanindividualconsumerinWhovilledemandifitcosts24. The diagram and chart below show the indifference curves of a typical consumer and the marginal cost curve of a typical car wash. a. How many car washes does an individual consumer in Whoville demand if it costs \3 3 ? b. Describe the aggregate demand curve of Whoville's demand for car washes. c. Describe the aggregate supply curve for car washes in Whoville. d. The market for car washes is in equilibrium What is the price of a car wash today? e. Suppose that in the long run there is no entry or exit from the car wash industry. What can you conclude about the fixed costs at an individual car wash? Question 2 In the gadget industry, each firm must have one gadget press, regardless of how many gadgets it produces. The cost of a gadget press is the only fixed cost that firms face in this industry. Entry by gadget firms can bid up the cost of gadget presses. The following charts show (1) the demand for gadgets; (2) the marginal cost of producing gadgets at each individual firm; and (3) the cost of a gadget press as a function of the number of firms in the industry: \begin{tabular}{|l|l|} \hline Price & \begin{tabular}{l} Quantity \\ Demanded \end{tabular} \\ \hline 1 & 800 \\ \hline 2 & 700 \\ \hline 3 & 600 \\ \hline 4 & 500 \\ \hline 5 & 400 \\ \hline 6 & 300 \\ \hline \end{tabular} \begin{tabular}{|l|l|} \hline Quantity & \begin{tabular}{l} Marginal \\ Cost \end{tabular} \\ \hline 1 & $1\$ 1 \\ \hline 2 & 2 \\ \hline 3 & 3 \\ \hline 4 & 4 \\ \hline 5 & 5 \\ \hline 6 & 6 \\ \hline \end{tabular} \begin{tabular}{|l|l|} \hline Number of Firms & \begin{tabular}{l} Cost of \\ Gadget Press \end{tabular} \\ \hline 0−750-75 & $6\$ 6 \\ \hline 76−15076-150 & 10 \\ \hline 151−225151-225 & 15 \\ \hline 226−300226-300 & 18 \\ \hline>300 & 21 \\ \hline & \\ \hline \end{tabular} What is the long-run equilibrium price of gadgets? (Hint: Start by figuring out, for each price, the number of firms and the profits at each firm.)
A
Key Concept
Consumer Equilibrium
Explanation
An individual consumer's demand is determined by the point where the price equals the marginal rate of substitution (MRS), which is the slope of the indifference curve. At a price of $3, the consumer will choose the quantity where the MRS equals 3, assuming the budget constraint and indifference curves are standard.
B
Key Concept
Aggregate Demand Curve
Explanation
The aggregate demand curve for car washes is the horizontal summation of all individual demand curves. It shows the total quantity of car washes demanded by all consumers at different prices.
C
Key Concept
Aggregate Supply Curve
Explanation
The aggregate supply curve for car washes is the horizontal summation of the marginal cost curves of all car washes. It shows the total quantity of car washes that producers are willing to supply at different prices.
D
Key Concept
Market Equilibrium
Explanation
The price of a car wash in equilibrium is where the aggregate demand equals the aggregate supply. This is the price at which the quantity of car washes demanded by consumers equals the quantity supplied by producers.
E
Key Concept
Zero Economic Profit
Explanation
If there is no entry or exit in the long run, it suggests that firms are making zero economic profit, as entry would occur if firms were making a positive economic profit, and exit would occur if they were making losses.
F
Key Concept
Long-Run Equilibrium Price
Explanation
In the long run, the equilibrium price is where the price equals the marginal cost and the average total cost, which includes the cost of the gadget press. This ensures firms make zero economic profit.
9:50 PM Tue Mar 26 47%47 \% AA eclass.yorku.ca Guided Analysis 4 Happiness, Comparative Advantage, and Income Taxes This question takes a break from looking at industries, firms, from comparing short- and long-run changes. Instead, it explores the relationship between comparative advantage and prices, as well as the impact of income taxes on career choices and overall happiness. Note how this is an example of "making up numbers" to "tell a story." Once you solved this question, take a step back - what insight are you taking away from this computation? Does it change how you see some policy-debates? Which ones and how? Assume three students taking an aptitude test in high school and the following tables show their respective results. \begin{tabular}{l|l} Anna & Score \\ \hline Science & 20 \\ \hline Math & 25 \\ \hline Lit \& Writing & 17 \end{tabular} \begin{tabular}{l|l} Beatrice & Score \\ \hline Science & 18 \\ \hline Math & 12 \\ \hline Lit \& Writing & 10 \end{tabular} \begin{tabular}{l|l} Clara & Score \\ \hline Science & 5 \\ \hline Math & 14 \\ \hline Lit \& Writing & 17 \end{tabular} Part I: Looks at the information content of prices and how that aligns with comparative advantage. 1. What is each student best at? What might a high school counselor likely recommend they consider as an area for future work? 2. For each field of expertise, write down a ranking of the students according to their respective aptitudes. What is each student relatively best at? Assume now a firm has three positions to fill. Each of the three positions requires a different expertise, and the value of the position to the firm is reflected in the salary: \begin{tabular}{|c|c|} \hline Skill & Salary before tax \\ \hline Science & $120,000\$ 120,000 \\ \hline Math & $90,000\$ 90,000 \\ \hline Lit \& Writing & $50,000\$ 50,000 \\ \hline \end{tabular} The firm likes to hire the most able person for each job among those people who would consider the job. Hiring the most able person is most important for the most valuable jobs. But people do not have to accept the firm's offer. Indeed, every person choses the job which offers the highest salary. 3. Which position will each student end up working in? At which salary level? Compare this outcome to the school counselor's recommendation from a).
Answer
Anna is best at Math, Beatrice is best at Science, and Clara is best at Lit & Writing. A high school counselor would likely recommend they consider future work in their respective best areas.
Solution
a
Comparative Advantage: Comparative advantage occurs when a person can perform an activity at a lower opportunity cost than others
b
Analysis of Scores: Anna scored highest in Math, Beatrice in Science, and Clara in Lit & Writing, indicating their comparative advantages
c
Counselor's Recommendation: Based on their highest scores, Anna should consider a career involving Math, Beatrice in Science, and Clara in Lit & Writing
Key Concept
Comparative Advantage
Explanation
Comparative advantage suggests that individuals should specialize in areas where they have the lowest opportunity cost, which is reflected in their highest aptitude scores.
Answer
Ranking for Science: 1) Beatrice, 2) Anna, 3) Clara. Ranking for Math: 1) Anna, 2) Clara, 3) Beatrice. Ranking for Lit & Writing: 1) Anna and Clara (tie), 3) Beatrice. Each student is relatively best at the subject they scored highest in.
Solution
a
Ranking by Aptitude: Students are ranked in each subject based on their scores to determine their relative strengths
b
Relative Best: Anna is relatively best at Math, Beatrice at Science, and Clara at Lit & Writing, as indicated by their highest scores compared to the other subjects
Key Concept
Relative Advantage
Explanation
Relative advantage is determined by comparing the aptitude of each student in different subjects, indicating which subject they are most skilled in relative to the others.
Answer
Anna will work in Science at 120,000,BeatriceinMathat120,000, Beatrice in Math at 90,000, and Clara in Lit & Writing at $50,000. This outcome differs from the school counselor's recommendation, as students choose jobs based on salary rather than their best subject.
Solution
a
Job Selection Criteria: Students choose the job with the highest salary offered to them, which may not align with their comparative advantage
b
Job Allocation: Anna takes the Science job as it offers the highest salary, Beatrice takes Math, and Clara takes Lit & Writing based on the remaining salaries
Key Concept
Job Selection Based on Salary
Explanation
Despite having a comparative advantage in a particular field, individuals may choose a career based on the highest salary offered, which can lead to a misallocation of skills.
9:51 PM Tue Mar 26 47%47 \% eclass.yorku.ca Part II Considers what happens when the students take their individual happiness into account when making a career choice. From each career choice, the students derive the following happiness \begin{tabular}{|l|l|l|l|} \hline & Anna & Beatrice & Clara \\ \hline Science & 65 & 70 & 20 \\ \hline Math & 90 & 60 & 60 \\ \hline Lit \& Writing & 20 & 50 & 80 \\ \hline \end{tabular} Moreover, each of the students receives "1 point of happiness" for each $1,000\$ 1,000 of annual income. 4. Compute the total happiness that each of the students would receive in each career choice. As before, the firm likes to hire the most able person for each job among those people who would consider the job. But now every person choses the job (among those the person might be offered) which is associated with the most happiness. 5. Which position will each student end up working in? What is the overall happiness generated? Part III Looks at the impact an income tax can have on the outcome in part II. Assume that the government now imposes a 30\% income tax - before each of the students makes their career choice. 6. Compute the total happiness that each of the students would receive in each career choice. 7. Which position will each student end up working in? What is the overall happiness generated? Part IV Asks you to apply the above results. 8. Assume that the revenue from the income tax is put to good use, building infrastructure, supporting museums and orchestras, etc. so that overall each $1,000\$ 1,000 spend generates " 1 point of happiness." How does the student's overall happiness with the income tax compare with their happiness without it? 9. Assume that revenue from the income tax is completely wasted, so that no happiness is generated from the spending of the tax revenue. How does the student's overall happiness with
Answer
Anna will work in Math, Beatrice in Science, and Clara in Lit & Writing. The overall happiness generated is 250 points.
Solution
a
Calculation of Total Happiness without Tax: Total happiness is the sum of happiness from career choice and happiness from income
b
Anna's Total Happiness: For Science 65+70×1=13565 + 70 \times 1 = 135, for Math 90+90×1=18090 + 90 \times 1 = 180, for Lit & Writing 20+50×1=7020 + 50 \times 1 = 70
c
Beatrice's Total Happiness: For Science 70+70×1=14070 + 70 \times 1 = 140, for Math 60+90×1=15060 + 90 \times 1 = 150, for Lit & Writing 50+50×1=10050 + 50 \times 1 = 100
d
Clara's Total Happiness: For Science 20+70×1=9020 + 70 \times 1 = 90, for Math 60+90×1=15060 + 90 \times 1 = 150, for Lit & Writing 80+50×1=13080 + 50 \times 1 = 130
e
Job Allocation based on Maximum Happiness: Anna chooses Math, Beatrice chooses Science, and Clara chooses Lit & Writing
f
Overall Happiness: Sum of individual happiness from chosen careers 180+140+130=450180 + 140 + 130 = 450
Key Concept
Marginal Utility of Income
Explanation
Each additional $1,000 of income generates one point of happiness, which is added to the happiness derived from the career choice to determine the total happiness.
Answer
Anna will work in Math, Beatrice in Science, and Clara in Lit & Writing. The overall happiness generated after tax is 250 points.
Solution
a
Calculation of Total Happiness with Tax: Total happiness is the sum of happiness from career choice and happiness from after-tax income
b
Anna's Total Happiness with Tax: For Science 65+49×1=11465 + 49 \times 1 = 114, for Math 90+63×1=15390 + 63 \times 1 = 153, for Lit & Writing 20+35×1=5520 + 35 \times 1 = 55
c
Beatrice's Total Happiness with Tax: For Science 70+49×1=11970 + 49 \times 1 = 119, for Math 60+63×1=12360 + 63 \times 1 = 123, for Lit & Writing 50+35×1=8550 + 35 \times 1 = 85
d
Clara's Total Happiness with Tax: For Science 20+49×1=6920 + 49 \times 1 = 69, for Math 60+63×1=12360 + 63 \times 1 = 123, for Lit & Writing 80+35×1=11580 + 35 \times 1 = 115
e
Job Allocation based on Maximum Happiness after Tax: Anna chooses Math, Beatrice chooses Science, and Clara chooses Lit & Writing
f
Overall Happiness after Tax: Sum of individual happiness from chosen careers after tax 153+119+115=387153 + 119 + 115 = 387
Key Concept
Income Tax Impact on Utility
Explanation
The imposition of a 30% income tax reduces the marginal utility of income, thereby affecting the total happiness derived from each career choice.
Answer
The students' overall happiness with the income tax remains the same as without it if the tax revenue generates an equal amount of happiness.
Solution
a
Government Spending Efficiency: The efficiency of government spending is such that each $1,000 spent generates one point of happiness
b
Tax Revenue Happiness: The total tax revenue is 30%×3×$70,000=$63,00030\% \times 3 \times \$70,000 = \$63,000, which generates 63 points of happiness
c
Distribution of Happiness: Since the tax revenue generates the same amount of happiness as the loss of income, the overall happiness remains 450 points
Key Concept
Government Spending and Utility
Explanation
If the government spending is as efficient as the private spending it taxes, the overall happiness in the economy remains unchanged.
Answer
The students' overall happiness with the income tax is lower if the tax revenue does not generate any happiness.
Solution
a
Inefficient Government Spending: If the tax revenue does not generate happiness, it represents a loss of utility
b
Loss of Happiness: The total loss of happiness due to the tax is 63 points (the happiness that would have been generated by the income)
c
Overall Happiness with Wasted Tax Revenue: The overall happiness is reduced to 450−63=387450 - 63 = 387 points
Key Concept
Tax Efficiency and Utility
Explanation
When tax revenue is wasted and does not generate happiness, it results in a net loss of utility in the economy.
8. Assume that the revenue from the income tax is put to good use, building infrastructure, supporting museums and orchestras, etc. so that overall each $1,000 spend generates "1 point of happiness." How does the student's overall happiness with the income tax compare with their happiness without it? 9. Assume that revenue from the income tax is completely wasted, so that no happiness is generated from the spending of the tax revenue. How does the student's overall happiness with the income tax compare with their happiness without it? 10. Compare the no-tax and the 30% tax cases: In which case, do you expect the students to be more "passionate" about their jobs? In which case, do you expect them to be more aptly matched with their job? Why? 11. Given your discussion in parts 8-10 would you prefer to live in a high-income tax country or in a low-income tax country? 12. Find out the average income tax rate in the U.S., Canada, and a country of your choice. Hint: Pick Germany or France, if that makes it easier. Hint: You cannot just take the average among all the tax brackets - because the number of people in each bracket is likely different. If you compare only some income brackets, which ones are the most relevant in the context of the above question? Hint: Do not forget to mention your sources. Given the discussion in this question, would you expect people in the U.S. or in Canada or in another country to be on average "happier" with their job (i.e. with the tasks, not with the income)? Where would you expect more people to be more efficiently (according to aptitude) matched with their job?
Answer
The student's overall happiness with the income tax is higher compared to without it if the tax revenue generates "1 point of happiness" per $1,000 spent.
Solution
b
Happiness Points: If each $1,000 of tax revenue generates "1 point of happiness," then the total happiness generated is proportional to the amount of tax revenue collected and effectively used
Key Concept
Public Goods and Utility
Explanation
Public spending on goods and services that provide widespread benefits can increase the overall happiness or utility of individuals in the economy.
Answer
The student's overall happiness with the income tax is lower compared to without it if the tax revenue is completely wasted and generates no happiness.
Solution
Key Concept
Wasted Resources and Utility
Explanation
Taxation that does not lead to improvements in public welfare or personal utility results in a decrease in happiness compared to a scenario without such taxation.
Answer
Students are expected to be more passionate about their jobs in the no-tax case and more aptly matched with their job in the 30% tax case if the tax revenue is used effectively.
Solution
b
Job Matching and Public Investment: Effective use of tax revenue can lead to better education and infrastructure, improving job matching by enhancing skills and mobility
Key Concept
Job Passion vs. Efficient Job Matching
Explanation
While keeping more income may increase job passion, effective public investment from tax revenue can lead to a more efficient job market and better job matching.
Answer
Personal preference for living in a high-income tax country or a low-income tax country depends on the perceived value of public goods and services funded by taxes.
Solution
b
Personal Utility Maximization: The choice also depends on one's personal utility maximization, which includes both financial and non-financial factors
Key Concept
Personal Utility from Public Goods
Explanation
The preference for living in a high or low-income tax country is influenced by how much one values the public goods and services that taxes fund.
Answer
The average income tax rates in the U.S., Canada, and Germany vary, and the most relevant income brackets for comparison are the median income brackets.
Solution
b
Median Income Relevance: The median income bracket is most relevant for this analysis as it represents the income level where half of the population earns more and half earns less
Key Concept
Average Income Tax Rate Calculation
Explanation
The average income tax rate should be calculated by considering the distribution of taxpayers and focusing on the median income bracket to reflect the tax burden on the typical taxpayer.
Answer
Job satisfaction and efficient job matching may vary across countries and depend on factors beyond average income tax rates, such as the effectiveness of public services and cultural attitudes towards work.
Solution
Key Concept
Multifaceted Influences on Job Satisfaction
Explanation
While tax rates can influence job satisfaction and matching, other factors like public service quality and cultural attitudes play significant roles in determining these outcomes.
The town of Whoville has 100 identical consumers and 50 identical car washes. Each consumer has an income of 24. The diagram and chart below show the indifference curves of a typical consumer and the marginal cost curve of a typical car wash.
Quantity=1 MC=3 Quantity=2 MC=4Quantity=3MC=4 Quantity=3 MC=5 Quantity=4 MC=6Quantity=5MC=6 Quantity=5 MC=7 Quantity=6 MC=8Quantity=7MC=8 Quantity=7 MC=9 Quantity=8 MC=$10 How many car washes does an individual consumer in Whoville demand if it costs S3?  Describe the aggregate demand curve of Whoville's demand for car washes.  Describe the aggregate supply curve for car washes in Whoville.  The market for car washes is in equilibrium What is the price of a car wash today?  Suppose that in the long run there is no entry or exit from the car wash industry. What can you conclude about the fixed costs at an individual car wash?
A
Key Concept
Individual Consumer Demand
Explanation
An individual consumer's demand for car washes at a price of 3dependsontheirmarginalbenefitcomparedtothemarginalcost.Ifthemarginalbenefit(reflectedbytheirwillingnesstopay)isatleast3 depends on their marginal benefit compared to the marginal cost. If the marginal benefit (reflected by their willingness to pay) is at least 3, they will demand the service. Without specific information on the consumer's marginal benefit or the shape of their demand curve, we cannot determine the exact quantity demanded.
B
Key Concept
Aggregate Demand Curve
Explanation
The aggregate demand curve for car washes in Whoville is the horizontal summation of the individual demand curves of the 100 consumers. It will slope downward, reflecting the law of demand, which states that quantity demanded increases as price decreases, ceteris paribus.
C
Key Concept
Aggregate Supply Curve
Explanation
The aggregate supply curve for car washes in Whoville is the horizontal summation of the marginal cost curves of the 50 car washes. It will slope upward, indicating that as the price increases, the quantity supplied increases, reflecting the law of supply.
D
Key Concept
Equilibrium Price
Explanation
The equilibrium price is where the quantity demanded equals the quantity supplied. Given the information provided, we cannot determine the exact equilibrium price without the demand curve. However, it will be at a price where the market clears, meaning all consumers willing to pay at least the market price can find a car wash, and all car washes willing to accept the market price can sell their service.
E
Key Concept
Fixed Costs and Industry Entry/Exit
Explanation
If there is no entry or exit in the long run, it suggests that all car washes are earning normal profits, and the fixed costs are such that they do not incentivize new firms to enter or existing firms to exit the market. This implies that the industry is in a long-run equilibrium.
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