Rationality, opportunity cost and marginal analysis

Explain what economics means by a rational decision (comparing benefits and costs and choosing what best suits your goals). Give an example of a rational decision and one of a poorly thought-out decision from a purchase in your daily life.

In the "ultimatum game," a participant A receives $\$100$ and must propose a division of that money with participant B (for example, keeping $\$70$ and offering $\$30$ to B). If B accepts the proposal, the money is split accordingly; if B rejects it, both receive $\$0$.

1. a) The traditional hypothesis of a purely self-interested individual predicts that A will offer the minimum possible amount ($\$1$) and that B will always accept it because it is greater than zero. However, in actual experiments, offers below $\$25$ are systematically rejected by B. Interpret this result: is B acting irrationally by preferring to earn $\$0$ rather than accept an unfair offer? Justify your answer by distinguishing between "rationality" (consistency between ends and means) and "strictly monetary self-interest."
2. b) Model a situation in which donating money to a nonprofit organization provides a person with positive net utility, showing that altruism fits within rational choice theory.
3. c) If the federal government introduces an $80\,\%$ federal income tax deduction for donations to nonprofit organizations, the amount donated by taxpayers increases significantly. Explain how this empirical fact shows that supportive behaviors still respond to the logic of opportunity cost and incentives.

Define opportunity cost in your own words and calculate it in this case: on Saturday, you can go to the movies (ticket for $\$10$ plus $\$4$ for transportation) or work for four hours in a store for $\$40$. If you go to the movies, what is the full opportunity cost of your decision?

You have an important exam on Monday and you are invited to a party on Sunday night. Identify the opportunity cost of going to the party: not just the money you spend, but what you give up. Explain how you would weigh it.

You are offered two summer jobs: in one you would earn $\$600$ a month delivering orders; in the other, $\$500$ a month at the front desk of a hotel full of foreign tourists where you would practice your English.

1. a) What is the opportunity cost of choosing the first one?
2. b) What additional information would you need to decide rationally?

Emma has $\$30$ and three options for Saturday: a concert she values at $70$ points, dinner and a movie she values at $60$, or staying at home and saving the money, which she values at $25$.

1. a) If she chooses the concert, what is her opportunity cost?
2. b) Does her decision change if her valuation of the dinner rises to $75$ points? Explain what has changed.

A classmate in 2nd year of Bachillerato states: "Since I have been awarded a full scholarship that covers tuition, accommodation, and materials for university, doing the degree will be completely free for me; therefore, my opportunity cost during those years will be zero." In addition, they have been offered an immediate job at a company with a net salary of $\$1,050$ per month (12 monthly payments per year).

1. a) Economically refute your classmate's statement by distinguishing between explicit costs and implicit costs, and quantify the annual opportunity cost of choosing to study.
2. b) Suppose that at the end of the first year they decide to drop out because they lack motivation and say: "I lost an academic year, but at least I didn't lose any money because the scholarship covered everything." Critically evaluate this statement using the concepts of sunk cost and opportunity cost.
3. c) Design an economic decision rule that allows them to assess whether it is worth accepting a part-time job of $15$ hours per week for $\$450$ per month during the academic year, considering the impact that those hours may have on their academic performance and on the likelihood of prolonging their studies.

Two students are looking for a laptop with identical features. In an online store with more than 300 models available:

• Carlos spends 35 hours thoroughly analyzing technical forums, comparison tables, and deals to find the optimal option, purchasing the device for $\$620$.

• Lucía checks only the 3 top-selling models for 45 minutes (0.75 hours) and buys one for $\$660$.

1. a) Assuming that the opportunity cost of free time for both students is valued at $\$8$ per hour, calculate the total effective cost of the purchase for each of them and determine who made an economically more efficient decision.
2. b) Using the principle of marginal analysis, conceptually formulate the optimal information search rule that determines the exact point up to which it is rational to continue gathering data before making a consumption decision.
3. c) "Choosing with incomplete information is indisputable proof that human beings are irrational." Refute this statement by demonstrating why information is an economic good with a cost and how "bounded rationality" is entirely consistent with rational choice theory.

Andrea is considering pursuing a four-year college degree or joining the labor market immediately with a job that offers her $\$1,150$ net per month (12 monthly payments per year).

If she chooses to study:

• Tuition and materials cost $\$1,600$ per year.

• She will work weekends, earning $\$350$ net per month (12 payments).

• Upon graduating, she expects to get a job with a net salary of $\$1,850$ per month (12 payments).

1. a) Calculate the total economic cost (direct costs plus net opportunity cost of forgone earnings) of pursuing the four-year college degree.
2. b) Calculate how many years of working as a graduate she will need to pay off that economic cost through the salary differential compared to the option of not having studied.
3. c) Suppose Andrea fails several classes and needs a fifth year without working part-time to finish the degree, paying $\$1,100$ in additional tuition. Quantify how much her total cost increases and justify why academic delay has an economic impact far greater than merely paying repeated tuition.

The figure shows the production possibilities frontier of a bakery that splits its oven between bread and pastries, with three points marked: A, B, and C.

1. a) Explain what each of the points A, B, and C indicates about the bakery's use of resources.
2. b) What would have to happen for point C to no longer be unattainable?

A bakery can produce these combinations of bread and pastries each day: $(100, 0)$, $(90, 40)$, $(70, 70)$, $(40, 90)$, and $(0, 100)$.

1. a) Calculate the opportunity cost, in units of bread, of moving from $40$ to $70$ units of pastries.
2. b) Is the opportunity cost the same when moving from $70$ to $90$ units of pastries? Compare both intervals and explain what the difference might be due to.

A farm can produce these combinations of corn and wheat (in metric tons) each week: $(0, 50)$, $(10, 45)$, $(20, 35)$, $(30, 20)$, and $(40, 0)$, where the first figure is corn.

1. a) Calculate the opportunity cost, in metric tons of wheat, of moving from $10$ to $20$ metric tons of corn.
2. b) Compare that cost with the cost of moving from $30$ to $40$ metric tons of corn and explain why it might increase (land more or less suited to each crop).

Two economies, Arcadia and Betania, have the same endowment of productive factors and start in 2025 from identical Production Possibility Frontiers (PPF) between consumer goods (food, leisure, clothing) and capital goods (machinery, R&D facilities, infrastructure).

• Arcadia decides to allocate $85\,\%$ of its resources to consumer goods and $15\,\%$ to capital goods.

• Betania decides to allocate $40\,\%$ to consumer goods and $60\,\%$ to capital goods.

1. a) Explain the difference in the immediate material standard of living of the population of both countries in 2025 and define the opportunity cost borne by the society of Betania in the present.
2. b) Predict, with justification, how the PPF of each economy will shift after a decade (year 2035) and in which of the two countries per capita consumption is likely to be higher at that future time.
3. c) A political leader in Betania states: "To maximize long-term growth, we must allocate $100\,\%$ of our resources to capital goods for the next three years." Refute their proposal by explaining the economic, human, and sustainability limits imposed by the opportunity cost of growth.

Explain what it means to think "at the margin" and apply it to this decision: a pizzeria sells the second slice at half price. What exactly does a rational customer compare before accepting the offer?

The first slice of pizza tastes heavenly; the fourth one you can barely finish. Explain what this example shows about the additional (marginal) benefit of each unit and what the principle that sums it up is called.

The additional satisfaction Emma gets from each milkshake on a Saturday afternoon is: milkshake $1$: $20$ points; milkshake $2$: $14$ points; milkshake $3$: $7$ points; milkshake $4$: $2$ points.

1. a) Explain what these numbers show and what the principle they reflect is called.
2. b) If each milkshake costs $\$6$ and Emma values each point of satisfaction at $\$1$, decide how many milkshakes it is worth her buying, reasoning milkshake by milkshake.

An online academy charges $\$60$ per month per student. Each additional student costs $\$25$ a month in tutoring hours; the remaining costs (platform, licenses) do not change with the number of students.

1. a) Set out in marginal terms whether it is in the academy's interest to accept one more student.
2. b) What additional cost, hard to measure, should the academy watch as it grows (quality, tutor overload)? Reason your answer.

Each additional hour of study for an exam raises the expected grade as follows: hour $1$: $+10$ points; hour $2$: $+8$; hour $3$: $+5$; hour $4$: $+2$; hour $5$: $0$. Each hour of study costs an hour of sleep or leisure that you value at $4$ points.

1. a) How many hours is it worth studying? Reason hour by hour, comparing additional benefit and cost.
2. b) What is the principle shown by the decreasing additional benefit numbers called?

The owner of a burger food truck generates $\$10,000$ in revenue per month, with variable costs of $\$4,800$ and fixed costs of $\$2,200$. She is considering adding a second vehicle in another area of the city. For this second truck, she forecasts:

• Monthly sales of $\$4,600$.

• Specific costs for the new truck: space rental and depreciation of $\$1,100$/month, and variable costs equivalent to $50\,\%$ of its own revenue.

• Cannibalization effect: it will reduce sales of the first truck by $10\,\%$ (assume that the variable costs of the first truck decrease by that same proportion of $10\,\%$, while its fixed costs remain constant).

• To coordinate both trucks, the owner must give up a weekend culinary consulting job for which she earned $\$600$ per month.

1. a) Calculate in detail the marginal revenue, total marginal cost (including the opportunity cost of time and the net impact on the first truck), and the marginal profit of opening the second vehicle.
2. b) Justify economically whether she should expand the business or not.
3. c) What is the minimum monthly revenue that the second truck would need to generate for its opening to start being profitable, holding all other factors constant?

You have a total of 12 hours to split among preparing for three AP exam subjects: History, Mathematics, and Economics. Your current estimated score (without additional hours) and the projected score increase for each 2-hour study block are shown in the following table:

1. a) Apply the equimarginal principle to determine the optimal allocation of the 12 hours (6 blocks of 2 hours) across the three subjects. Detail the order in which you allocate each time block and calculate the total points gained.
2. b) Compare the total increase from your optimal allocation with the one you would obtain if you applied a simple egalitarian criterion (allocating 4 hours to each subject). Justify economically what accounts for the difference based on the law of diminishing returns.
3. c) Suppose the college degree program you aspire to pursue weights Economics at 0.2 and the other two subjects at 0.1 in the admissions process. Predict how the marginal decision rule changes and determine the new optimal allocation of the 12 hours to maximize your admission score.

You have already paid for the monthly bus pass ($\$21$) and you discover that walking to school takes only ten minutes longer. Explain why the money for the pass should not influence today's decision and what that type of cost is called.

You have paid $\$12$ for a non-refundable movie ticket. Twenty minutes in, the movie bores you completely, but your friends say: "stay, you've paid for it".

1. a) Explain why the $\$12$ is a sunk cost and what you should actually compare to decide whether to stay.
2. b) Give another everyday example in which people make poor decisions by failing to ignore a sunk cost.

Your family paid $\$200$ for the annual pass to the city swimming pool. A bike-share program appears that lets you exercise for free, and you like it more.

1. a) What should you compare to decide whether to keep going to the pool, and what should you do about the $\$200$ already paid?
2. b) Explain why people find it so hard to ignore money already paid and what that error is called.

A fruit store is usually open from 9:00 to 14:00 and from 17:00 to 20:00 (8 hours a day). Its rent is $\$1,200$ per month ($\$40$ per day) and the contracted electricity power represents $\$6$ per day. The owner is considering opening two extra hours every evening (from 20:00 to 22:00). An advisor recommends not opening, using the following calculation: "Your fixed costs are $\$5.75$ per opening hour. Two more hours will cost you $\$11.50$ in fixed costs, plus $\$24$ for the store assistant's wages and $\$5$ in variable electricity (total: $\$40.50$). Since you will take in about $\$36$ during those hours, you will lose $\$4.50$ every evening."

1. a) Identify and justify the economic reasoning error that the advisor makes when applying marginal analysis.
2. b) Calculate the actual net marginal result per evening if she decides to open from 20:00 to 22:00.
3. c) If a survey reveals that of the estimated $\$36$ in sales during the new opening hours, $\$14$ come from regular customers who previously shopped before 20:00 and are now simply postponing their purchase, what is the true marginal revenue and what decision should the owner make?