Week 1 — What Does a Choice Cost? Opportunity Cost on the Labor-Hours Frontier — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

Assignment 1 of the term — price a choice by what it gives up, read the frontier that pictures a whole economy's trade-off, and explain it to someone new to economics.

This week you learned that every choice gives something up, and you drew a whole economy's trade-off as a production possibilities frontier. In this assignment you work four short problems on one small economy, interpret each one, and explain the trade-off to someone who has never studied economics. This week's lecture tutorial, quiz, discussion, and Model Workshop practise the same ideas from other angles.

The task

The labor-hours frontier is an illustrative dataset constructed for this course (not real data). An economy has 24 million labor-hours. A unit of consumer goods takes 3 labor-hours and a unit of capital goods takes 6. Consumer goods x go on the horizontal axis and capital goods y on the vertical axis. A news commentator says that building more capital goods "costs the country nothing, because the workers are paid either way." Your job is to check that claim the way an economist would, starting with one person's evening and scaling up to the whole economy.

Work these four problems, showing your arithmetic:

1. A free evening of 5 hours could earn 18 dollars an hour at a shift. What is the opportunity cost, in dollars, of spending that evening at a free concert?
2. An economy has 24 million labor-hours, and one unit of capital goods takes 6 labor-hours. If every hour goes to capital goods, how many million units of capital goods can it make?
3. Moving along the frontier from (8, 0) to (2, 3) gives up 6 units of consumer goods to gain 3 units of capital goods. What is the opportunity cost of one capital good, in consumer goods?
4. A unit of consumer goods takes 3 labor-hours and a unit of capital goods takes 6. How many million labor-hours does the combination (2, 2) need?

Beside each answer, add one brief interpretation:

• Problem 1: say your result in words as the pay you give up, and explain why the concert's cost is not zero even though the ticket is free, using the words price and opportunity cost.
• Problem 2: write the result as a point on the diagram, with consumer goods on the horizontal axis and capital goods on the vertical axis, and explain what an endpoint of the frontier means, using the word scarcity.
• Problem 3: say in words what the slope means for this economy, and explain why someone who answers 0.5 has flipped the ratio, by naming which good is given up.
• Problem 4: compare the hours needed with the 24 million that exist, say whether (2, 2) lies on, inside, or outside the frontier, say how many labor-hours sit idle, and give the macro reading of that idle time. Then label each of these two statements positive or normative and give the reason: (a) "This economy is producing inside its frontier." (b) "This economy should put its idle labor-hours to work building capital goods."

Explain it to a non-expert

A family member hears that the country plans to build more roads and machines and asks you, "So what do we give up?" Write a 3–5 sentence message that explains opportunity cost in everyday words, uses this economy's frontier to say what one capital good costs, and names one limit, including that the numbers are illustrative and that a real frontier bows outward. Explain any technical term in everyday words. More than one good answer is possible.

For a different, ungraded example, imagine a neighbor who asks what a city gives up by turning a parking lot it already owns into a park. Model answer: "The park is not free even though the city already owns the land. Its cost is the best other use of that lot, such as parking spaces drivers would pay for, and economists call that the opportunity cost. That tells you what the city gives up; whether the park is worth it is a separate question that depends on what people value."

Use that pattern for the labor-hours frontier, with your own wording and evidence.

Show your arithmetic. A reader should be able to reproduce every number you report from the hours and wages without guessing which values or steps you used.

Deliverables

Submit a single report containing:

• the four answers, each with the arithmetic shown and the brief interpretation the task names for that problem;
• your message to the family member, explaining opportunity cost, saying what one capital good costs, and naming one limit; and
• a one-line restatement of the hours and wages you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled sketch of the frontier with the combination (2, 2) marked and a short note. Every form is graded by the same scoring criteria. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without a chatbot or other AI tool. You may use a calculator, a spreadsheet, or a graphing tool for the arithmetic and the sketch. Submitting AI-generated work as your own, or copying another student's work, is an integrity violation under the course policy.

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