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?

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).

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.

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.