Rationality, Opportunity Cost, and Marginal Analysis

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

• Carlos spends 35 hours thoroughly analysing 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.

Define opportunity cost in your own words and calculate it in this case: on Saturday, you can go to the cinema (ticket for $\$200$ plus $\$80$ for transport) or work for four hours in a shop for $\$800$. If you go to the cinema, what is the full opportunity cost of your decision?

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.

The figure shows the production possibility 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.

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 additional satisfaction Ainhoa 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 Ainhoa values each point of satisfaction at $\$1$, decide how many milkshakes it is worth her buying, reasoning milkshake by milkshake.

A fruit shop 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 shop 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?

You have paid $\$240$ for a non-refundable cinema ticket. Twenty minutes in, the film bores you completely, but your friends say: "stay, you've paid for it".

1. a) Explain why the $\$240$ 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.