Principles of Economics and Management I

Session 1 ยท Economic Thinking and Scarcity

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Affiliation

Introduction

โ„น๏ธ About This Course

Principles of Economics and Management I

Master in Applied Mathematics for Economics and Management.

Course Instructor: Paulo Fagandini.

We are going to build economic intuition and vocabulary, useful for anyone heading into banking, insurance and investment. Also, we are going to present the core models of Economics.

This is a 6 ECTS course, with 168 total hours of work. We have 13 weeks (including the midterm), leading to 39 to 42 (if you count the final) hours in class room. This means you are expected to dedicate, along the semester, 126 hours of self study to this course.

๐Ÿ“š Bibliography

Introductory, open access (CC BY):

  1. OpenStax, Principles of Microeconomics, 3rd ed.ย (Shapiro, MacDonald, Greenlaw).
  2. OpenStax, Principles of Macroeconomics, 3rd ed.ย (Greenlaw, Shapiro et al.).

Formal treatment, for going deeper:

  1. Varian, Intermediate Microeconomics with Calculus, any edition.
  2. Blanchard, Amighini and Giavazzi, Macroeconomics: A European Perspective, 3rd ed.

The syllabus maps every session to chapters in all four. Inside the decks, a ๐Ÿ“– note at the foot of a slide tells you exactly which section an example came from, and links straight to it in the free online book. ๐Ÿ”–

๐Ÿงพ Assessment, Weights and Dates

Periodic assessment, two in-person written tests:

Test Date Content Weight
Midterm 28/10/2026, 18:00, session 7 Block 1, Microeconomics 50%
Final 11/01/2027, 16:30 Block 2, Macroeconomics 50%

To pass: at least 10 out of 20, the weighted average rounded to the nearest integer, so a 9.50 average already passes.

The resit is on 29/01/2027 at 13:00, and it is open to everyone, including anyone who took the tests and did not pass. ๐Ÿ“…

โš ๏ธ Rules in the Exam Room

๐Ÿงฎ Calculator: basic scientific only. Graphing calculators are not allowed.

๐Ÿ“ต Devices: earphones, a smartwatch, a smartphone or any electronic device during a test counts as fraud.

The full rules, the reading map and the calendar are (or will soon be) in the syllabus, on the course page. ๐Ÿ”—

๐Ÿ—“๏ธ What the Course Covers

# Block 1 ยท Microeconomics # Block 2 ยท Macroeconomics
1 Economic thinking and scarcity 8 GDP, measurement and growth
2 Consumer choice 9 Unemployment, inflation, labor
3 Demand and elasticity 10 Money, banking and inflation
4 Production, costs, market structures 11 Monetary policy
5 Market equilibrium and taxes 12 Fiscal policy
6 Uncertainty, risk and information 13 The open economy

Session 7 is the midterm, so there is no session 7 deck. One theme per session, and every part of every session ends in exercises. ๐Ÿงฉ

๐Ÿ—บ๏ธ Todayโ€™s Map

Scarcity forces choices. Everything today answers one of two questions about them.

Part 0 ยท What is economics? The subject, its two levels, and the difference between describing and prescribing.

Part 1 ยท How does one agent choose? Surplus, opportunity cost, sunk costs, and choosing at the margin.

Part 2 ยท How does a whole society choose? Specialization, the production possibilities frontier, and why its shape is the same opportunity cost, scaled up.

We follow a constructivist approach in each of the major modules. ๐Ÿงฑ

Part 0 ยท What Is Economics?

๐Ÿค” Let Us Start With a Question

You only have 24 hours in a day.

You want to study, sleep, work, see your friends, train.

Does it all fit?

No. You have to choose.

That feeling, of having to choose, is where economics starts. ๐Ÿ‘‡

โš–๏ธ Scarcity

If you could have everything you wanted, there would be nothing to decide.

Scarcity: human wants for goods, services and resources exceed what is available.

Resources (labor, time, land, raw materials) exist in limited quantity. Wants, on the other hand, look unlimited.

โณ The Scarcest Resource

Time is the purest example of scarcity.

Rich or poor, everyone has exactly 24 hours a day.

Every hour spent studying is an hour not spent sleeping. Scarcity forces a choice, always.

๐Ÿ’ก The Definition

So we arrive at what economics really is:

Economics: the study of how people make decisions under scarcity.

Decisions by individuals, households, firms, society. It is about choice.

๐Ÿ”ฌ Two Levels of Analysis

Economics looks at the world at two scales:

๐Ÿ”Ž Microeconomics: the decisions of individual agents. A household, a firm, a specific market.

๐ŸŒ Macroeconomics: the economy as a whole. Growth, unemployment, inflation, the aggregate.

๐Ÿ“Š Micro and Macro Side by Side

Microeconomics Macroeconomics
Looks at Agents and markets The whole economy
Examples The price of bread, wages in a sector GDP, inflation, unemployment
Typical question How much does this firm produce? Is the country growing this year?

๐Ÿ“– Source: OpenStax Micro 3e, ยง1.2 โ€œMicroeconomics and Macroeconomicsโ€.

In this course we start with micro (Block 1) and move up to macro (Block 2). ๐Ÿง—

๐Ÿงญ Positive or Normative?

Two ways of stating something in economics:

๐Ÿ“ Positive: describes what is, and can be tested. โ€œRaising VAT reduces sales.โ€

โš–๏ธ Normative: says what ought to be, and involves value judgments. โ€œVAT should be cut.โ€

A good economist always keeps the two apart. Most of this course is positive.

๐Ÿ“– Source: OpenStax Micro 3e, ยง2.3 โ€œConfronting Objections to the Economic Approachโ€, which sets positive against normative statements.

๐Ÿงฑ Two Questions Follow

Scarcity means every choice gives something up. So the subject reduces to two questions:

Who is choosing? One person, one firm, one investor, deciding one thing. That is Part 1, and it is micro.

And when it is everyone at once? A whole economy, allocating all its resources between competing uses. That is Part 2.

Part 2 is the same problem, with more people in it. ๐Ÿ‘‡

โ“ Multiple Choice 1

Scarcity exists because:

A. Governments manage resources badly.

B. Wants exceed available resources.

C. There is not enough money in the economy.

D. There is too much specialization.

โœ… B. Scarcity is wants exceeding resources. It would exist even in a society without money.

โ“ Multiple Choice 2

Which of the following is a positive statement?

A. The government ought to subsidize public transport.

B. Inflation is too high.

C. Reducing unemployment matters more than reducing inflation.

D. A 10% rise in the price of tobacco reduces consumption by about 4%.

โœ… D. Only D claims something about what is, and the claim can be checked against data. A and C carry an explicit โ€œoughtโ€ and an explicit ranking. B looks factual but hides a value judgment in the word too: how high is too high is not something data can settle.

๐Ÿ’ฌ Discussion Question

A city council is deciding whether to close a downtown street to cars and make it a pedestrian zone.

a) Name the scarce resource at the heart of this decision.
b) Classify each statement as positive or normative: (i) โ€œPedestrianizing the street would cut retail deliveries by 12%โ€; (ii) โ€œThe council should put residents ahead of driversโ€; (iii) โ€œThe scheme costs 4 million euros.โ€
c) Is this a micro or a macro question? One line of justification.

โœ… Solution

a) The street itself: a fixed quantity of space with competing uses (cars, pedestrians, deliveries, parking). Space is scarce in exactly the sense of this part, and no amount of money makes the street wider.

b) (i) positive, a testable claim about what would happen. (ii) normative: โ€œshouldโ€, plus a ranking of whose interests count. (iii) positive, a number that can be checked against the accounts.

c) Micro. One agent, one decision, one small market for one piece of space. The macro version would ask about output or employment in the whole economy, not in one street.

Part 1 ยท How One Agent Chooses

๐Ÿ’ถ How Much Would You Pay for a 10 Euro Note?

A โ‚ฌ10 note is for sale. What is the most you would hand over for it? ๐Ÿค”

โ‚ฌ11? No.ย You would be down โ‚ฌ1 the moment you paid. โŒ

โ‚ฌ9.99? Yes, and you would be one cent better off. โœ…

Willingness to pay, or reservation price: the most you would pay, the point where buying and not buying feel the same. Here it is exactly โ‚ฌ10.

๐Ÿ’ฐ Benefit, Cost and Surplus

Every choice has a benefit \(B\), what it is worth to you, and a cost \(C\), what you hand over.

\[S = B - C\]

Surplus: what the choice leaves you with once you have paid for it.

Buy the note at โ‚ฌ9.99 and \(S = 0.01\). Pay โ‚ฌ11 and \(S = -1\). Act only while \(S > 0\).

๐Ÿ“ Surplus Is the Measuring Rod

That exercise turned โ€œis this worth doing?โ€ into a number.

One option, one scalar. And two options can be compared, because scalars can.

๐Ÿ“Ž Keep the object in mind. In session 3 we compute this same number for every buyer in a market and add them up, and the sum becomes an area under the demand curve. Same quantity, aggregated. ๐Ÿ”

โš–๏ธ Now Two Options, and Only One Choice

Scarcity, again: taking one means giving up the other.

Option 1 leaves you \(B_1 - C_1\). Option 2 leaves you \(B_2 - C_2\).

Being rational means one thing here: take the option with the larger surplus.

So you take option 1 exactly when \[B_1 - C_1 > B_2 - C_2\]

That Inequality Is the Opportunity Cost

Move \(C_1\) across, and change nothing else:

\[B_1 - C_1 > B_2 - C_2 \qquad \Longleftrightarrow \qquad B_1 > \underbrace{C_1 + (B_2 - C_2)}_{\text{opportunity cost of option 1}}\]

Read the right hand side. What option 1 truly costs is what you pay for it, plus the surplus you gave up by not taking the best alternative.

Opportunity cost: your own cost, plus the surplus of the best alternative you turned down.

So the whole rule is benefit > opportunity cost, and it holds for exactly one option: the best one.

๐Ÿ“– Source: OpenStax Micro 3e, ยง2.1, โ€œThe Concept of Opportunity Costโ€. Mind the word: some texts keep it for the given-up surplus alone. Here it is the full economic cost, what you pay plus what you forgo.

๐Ÿงฎ Check It on Numbers

Your summer: a paid internship, or a summer school costing โ‚ฌ1,200.

Option Benefit Cost Surplus
Internship 2,000 0 2,000
Summer school 3,000 1,200 1,800

Internship: opportunity cost \(= 0 + 1800 = 1800\), and \(2000 > 1800\). Rational. โœ…

Summer school: opportunity cost \(= 1200 + 2000 = 3200\), and \(3000 < 3200\). Not rational. โŒ

Note the summer school has the larger benefit and still loses.

โš–๏ธ Everything Has an Opportunity Cost

There is no free lunch. ๐Ÿฝ๏ธ

An hour of studying is an hour you are neither working nor resting.

A thousand euros in a deposit account is a thousand euros not invested elsewhere. At 3% a year, keeping it there rather than in the alternative costs โ‚ฌ30 a year, whether or not anyone sends you a bill. ๐Ÿ’ธ

This is why accounting cost and economic cost differ. The accountant records what was paid; the economist adds what was forgone.

๐Ÿงจ Beware of Sunk Costs

You have already spent โ‚ฌ8 on a cinema ticket. Halfway through, you realize you hate the film.

Stay or leave?

The โ‚ฌ8 is not coming back, whatever you do.

Sunk cost: a cost already incurred and unrecoverable.

The rational decision: ignore the sunk cost, look only at the future. If you hate the film, leave. ๐ŸŽฌ

๐Ÿ“– Source: OpenStax Micro 3e, ยง2.1, โ€œSunk Costsโ€. The book tells it as Selena, who pays 8 dollars for a film and knows after 30 minutes that it is terrible.

๐Ÿงฎ Sunk Costs, Formally

This is a property of the maximization.

At the interval the choice is over what happens next, and the โ‚ฌ8 sits in every branch:

\[\max_{a \,\in\, \{\text{stay},\, \text{leave}\}} \; \big[\, B(a) - C(a) - 8 \,\big]\]

An additive constant does not move an argmax:

\[\arg\max_{a} \big[\, f(a) - k \,\big] \;=\; \arg\max_{a} f(a)\]

So the ticket price cannot change the decision. ๐ŸŽŸ๏ธ

โž• Marginal Thinking

Big decisions are rarely โ€œall or nothingโ€. They are โ€œa bit more or a bit lessโ€.

You do not decide โ€œstudy or do not studyโ€. You decide whether one more hour is worth it.

You compare the marginal benefit of that hour with its marginal cost.

The golden rule: keep doing something as long as the marginal benefit is greater than the marginal cost.

๐Ÿ“– Source: OpenStax Micro 3e, ยง2.1, โ€œMarginal Decision-Making and Diminishing Marginal Utilityโ€, which is where the book explains why choices are made at the margin rather than all or nothing.

๐Ÿงฎ This Is a First Order Condition

Let \(B(q)\) be the total benefit of doing \(q\) and \(C(q)\) the total cost. The problem is

\[\max_{q} \; B(q) - C(q)\]

Differentiating and setting to zero: \(B'(q) = C'(q)\).

That is, MB = MC. The โ€œgolden ruleโ€ of economics is the first order condition you already know.

๐Ÿ“‰ The Optimum Is Where the Margins Cross

MB falls, MC rises, and they cross at q* = 4 hours.

๐Ÿ”— One Problem, Two Faces

Both halves of this part are the same problem, \(\max_{x \in X} \; B(x) - C(x)\), read at two resolutions:

Choice set \(X\) Optimality condition
Which one? \(\{1, 2\}\), discrete \(B_1 - C_1 \;\ge\; B_2 - C_2\)
How much? an interval, continuous \(B'(q) = C'(q)\)

The discrete condition compares totals, in euros. The continuous one compares marginals, in euros per hour. On an interval the rival to \(q\) is \(q + \Delta q\): divide the surplus difference by \(\Delta q\), then let \(\Delta q \to 0\), and the comparison becomes \(B'(q)\) against \(C'(q)\).

๐ŸŽฏ Incentives Move the Margins

An incentive is anything that shifts \(MB\) or \(MC\). Shift either curve and \(q^{*}\) moves, because \(q^{*}\) is defined by where they cross.

Fuel duty rises: the \(MC\) of driving shifts up, the crossing moves left. People drive less and buy more efficient cars. ๐Ÿš—

A scholarship tied to grades raises the \(MB\) of study: the crossing moves right. ๐ŸŽ“

Predicting behavior is comparative statics on that crossing.

โ“ Multiple Choice 3

You may take option 1 or option 2, never both, and option 1 is the rational choice. The opportunity cost of option 1 is:

A. The cost \(C_1\) you actually pay for it.

B. The benefit \(B_2\) of the option you turned down.

C. The surplus \(B_2 - C_2\) you gave up.

D. \(C_1 + (B_2 - C_2)\): what you pay, plus the surplus you gave up.

โœ… D. Rationality is \(B_1 - C_1 > B_2 - C_2\), which is \(B_1 > C_1 + (B_2 - C_2)\). Option C is only the implicit half; the money you hand over is a cost too.

โ“ Multiple Choice 4

The sunk cost of a decision:

A. Should weigh heavily in the decision.

B. Is irrelevant to the rational decision.

C. Is the same thing as opportunity cost.

D. Grows over time.

โœ… B. It is no longer recoverable, so it enters every branch of the problem as the same constant, and constants do not move an argmax. Only benefits and costs still ahead of you count.

๐Ÿงฎ Numerical Question

Studying \(q\) hours brings a total benefit \(B(q) = 90q - 7.5q^{2}\) and carries a total cost \(C(q) = 30q + 7.5q^{2}\) (euros, \(q\) in hours).

a) Derive the marginal benefit and the marginal cost.
b) Find the optimal number of hours \(q^{*}\).
c) What net benefit does the student get at \(q^{*}\)?

โœ… Solution

a) Differentiate the totals: \[MB(q) = B'(q) = 90 - 15q, \qquad MC(q) = C'(q) = 30 + 15q\]

b) Set \(MB = MC\): \(90 - 15q = 30 + 15q \Rightarrow 60 = 30q \Rightarrow q^{*} = 2\) hours, where \(MB = MC = 60\) euros per hour.

c) \(B(2) - C(2) = (180 - 30) - (60 + 30) = 150 - 90 = 60\) euros. It really is a maximum: \(B'' - C'' = -15 - 15 < 0\). โœ…

Part 2 ยท How a Society Chooses

๐Ÿงฉ Nobody Produces What They Consume

Part 1 gave one agent a rule. Now put many of them in the same economy.

Imagine having to grow your own wheat, build your own house and repair your own phone. Impossible.

Nobody lives like that. Why not? Adam Smithโ€™s answer (1776): the division of labor. ๐Ÿญ

๐Ÿญ The Pin Factory

Smith observed a pin factory. Making a pin involves about 18 distinct tasks.

One worker alone: maybe 20 pins a day.

Ten workers, each specialized in one task: 48,000 pins a day. ๐Ÿคฏ

That is 4,800 per worker, against 20. How?

๐Ÿ“– Source: OpenStax Micro 3e, ยง1.1, โ€œThe Division of and Specialization of Laborโ€. Smithโ€™s own account is in The Wealth of Nations (1776), Book I, ch.ย 1.

๐Ÿ“ˆ Why Specialization Produces More

Smith gave three reasons:

  1. ๐ŸŽฏ Advantage: each person focuses on what they do best.
  2. โšก Practice: repeating a task makes it faster and better.
  3. ๐Ÿ“ฆ Economies of scale: producing at scale lowers the average cost of each unit.

๐Ÿ“– Source: OpenStax Micro 3e, ยง1.1, โ€œWhy the Division of Labor Increases Productionโ€, where the three reasons are set out one by one.

๐Ÿ”„ Specialization Requires Exchange

If I specialize in just one thing, how do I get everything else?

I trade. I use what I earn from my work to buy what others have produced.

Specialization and the market always come together. You cannot build a phone, but you can buy one. ๐Ÿ“ฑ

Smithโ€™s own limit: the division of labor is limited by the extent of the market. A specialist needs enough buyers to be worth being a specialist. ๐Ÿ“

๐Ÿ“– Source: OpenStax Micro 3e, ยง1.1, โ€œTrade and Marketsโ€. The limit itself is Smithโ€™s own, and it is the title of The Wealth of Nations (1776), Book I, ch.ย 3.

๐Ÿค” But Who Specializes in What?

Smith says specialization raises output. He does not say who should do which job.

Suppose two people can each do both jobs. How do we assign them?

The answer is Part 1, applied to production. Putting someone on a job costs the output they would have produced elsewhere: an opportunity cost.

So the rule is: give a job to whoever gives up least to do it. ๐Ÿ‘‡

๐Ÿ“ Two Producers, Two Opportunity Costs

Ana and Bruno each work a full day, on bread ๐Ÿž or software ๐Ÿ’ป:

Worker Bread only Software only Opportunity cost of 1 software
Ana 12 6 2 bread
Bruno 6 4 1.5 bread

Ana is better at both jobs: 12 against 6, and 6 against 4. She has the absolute advantage everywhere.

And yet Bruno should write the software, because he gives up only 1.5 loaves for each unit while Ana gives up 2. Lower opportunity cost, so he goes first.

Comparative advantage: producing something at a lower opportunity cost than someone else.

๐Ÿ“‰ Pool Them: the Frontier Bends

Both on bread: 18 loaves. Both on software: 10 units. In between, Bruno switches first.

๐Ÿ”Ž Reading the Kink

Efficiency has an order: put the cheapest producer on the job first.

Up to 4 units of software, Bruno does it, and each costs 1.5 loaves. That is the flat stretch.

Past 4, Bruno is fully occupied and only Ana is left. Each further unit now costs 2 loaves. The line gets steeper.

So the frontier bends because the cheap capacity runs out first. ๐Ÿ“

๐Ÿ“ Many Producers: a Smooth Frontier

Two producers gave one kink. A hundred give ninety-nine, and the corners vanish.

๐Ÿ”Ž Reading the Frontier

Production possibilities frontier (PPF): what an economy can produce with all its resources fully and efficiently used.

๐Ÿ”ต On the curve (A): all resources are used. This is efficient.

๐Ÿ”ด Inside the curve (B): waste, idle resources. This is inefficient.

๐ŸŸข Outside the curve (C): desirable, but unattainable with todayโ€™s resources and technology.

Keep the two words apart: inside is a waste, outside is a limit.

๐Ÿ“– Source: OpenStax Micro 3e, ยง2.2 โ€œThe Production Possibilities Frontier and Social Choicesโ€, which draws the same frontier for a society choosing between healthcare and education.

๐Ÿ“ The Slope Has a Name

Write the frontier as \(y = f(x)\), with \(x\) units of software and \(y\) of bread. Its slope is the economyโ€™s exchange rate between the two:

\[MRT(x) \;=\; -\,\frac{\mathrm{d}y}{\mathrm{d}x}\]

Marginal rate of transformation: how much \(y\) the economy must give up to get one more unit of \(x\).

Which is to say: the opportunity cost of software, measured in bread, for a whole economy. On the kinked frontier the \(MRT\) was 1.5, then 2. ๐Ÿ”

๐Ÿ“ˆ Concavity Is Increasing Opportunity Cost

On the kinked frontier the \(MRT\) jumped once. On a smooth one it rises continuously, and that is exactly what concavity means:

\[\frac{\mathrm{d}\,MRT}{\mathrm{d}x} > 0 \quad \Longleftrightarrow \quad \frac{\mathrm{d}^{2} y}{\mathrm{d}x^{2}} < 0 \quad \Longleftrightarrow \quad f \text{ concave}\]

The economics is the kink argument with more producers: resources are not equally suited to the two uses, and the best suited are moved first. Each further unit costs more than the last.

A straight frontier would say every resource is equally good at both jobs, so the order of switching would not matter.

๐Ÿ“– Source: OpenStax Micro 3e, ยง2.2, where the curvature is tied to the law of diminishing returns.

๐Ÿš€ Growth Means Pushing the Frontier Out

How do we get to point C, unattainable today?

With more resources (more workers, more machines) or better technology.

Economic growth shifts the frontier outward. That is the subject of Block 2. ๐ŸŒฑ

๐ŸŒ Countries Are Producers Too

Ana and Bruno were two workers. Replace them with two countries and not one step of the argument changes.

The country with the lower opportunity cost in a good has the comparative advantage in it, and should produce it. Ana was better at everything in absolute terms, and Bruno still wrote the software. ๐ŸŒ

That is the basis of international trade. And what a country gains by doing it can be read straight off the frontier we just drew. ๐Ÿ‘‡

scarcity โ†’ opportunity cost โ†’ comparative advantage โ†’ specialization โ†’ exchange. โ›“๏ธ

๐Ÿ” A Second Way Past the Frontier

Growth moved the frontier itself, and it needed new machines or new technology.

The harder question: with todayโ€™s resources and todayโ€™s technology, can a country consume a bundle its own frontier puts out of reach?

Yes, if it can trade. ๐Ÿค

The frontier limits what a country can produce. What it consumes is a separate question the moment there is somebody on the other side of a trade.

๐Ÿ“– Source: OpenStax Micro 3e, ยง19.2, โ€œProduction Possibilities and Comparative Advantageโ€, which draws this line for US and Mexican shoes and refrigerators.

๐Ÿ“ˆ Trade Along the Price Line

Back to point A: the economy makes 6 units of software and 8 thousand loaves. Suppose the world market swaps 3 thousand loaves for every 4 units of software, a price this small economy takes as given.

Each unit sold brings 0.75 back, the first and the last alike, so the bundles A opens up lie on a straight line through it.

๐Ÿ”บ The Consumption Set

Sell all 6 units of software and you hold 12.5 thousand loaves, where producing bread yourself stops at 10. The other corner: 16.7 units of software against 10.

Production never left the frontier. It is consumption that moved out to the line, and the shaded region between the two is the gains from trade.

๐Ÿค Why a Country Cannot Lose

No country is forced to trade at the price it faces.

Point A sits on the line, at zero trade (autarky). Whatever the price, the bundle the economy produced is still available to it. โœ…

And the frontier is concave, so the tangent line lies weakly above it everywhere: no bundle that was attainable before the price existed becomes unattainable now.

Why produce at A? Where the frontier is flatter than the price line, a unit of software costs the economy less bread than the market pays for it, so it should make more. That stops exactly where \(MRT\) equals the price ratio, which is where the line is tangent. ๐ŸŽฏ

Producing at A while consuming elsewhere on the line is specialization and exchange, drawn. Where the price comes from, and how two countries split these gains, is session 13. ๐Ÿ”

โ“ Multiple Choice 5

A point inside the Production Possibilities Frontier represents:

A. An efficient combination.

B. An unattainable combination.

C. A combination with wasted resources.

D. Economic growth.

โœ… C. Inside the frontier there are idle resources: inefficient production.

โ“ Multiple Choice 6

Ana produces more of both goods per day than Bruno. It follows that:

A. Ana should produce both goods, and Bruno neither.

B. There is nothing to gain from letting Bruno produce anything.

C. Ana has the comparative advantage in both goods.

D. Who produces what still depends on the opportunity costs, which these figures alone do not give.

โœ… D. Absolute advantage compares output levels; comparative advantage compares what each gives up. Ana was better at both and still handed the software to Bruno, because he sacrificed less bread for it. C is impossible: the two opportunity costs are reciprocals, so nobody can be lower in both.

๐Ÿงฎ Numerical Question

An economyโ€™s frontier is \[y = 100 - \tfrac{1}{4}x^{2}, \qquad 0 \le x \le 20\] with \(x\) units of software and \(y\) tonnes of bread.

a) How much bread at \(x = 0\)? And at \(x = 8\)?
b) Obtain the marginal rate of transformation \(MRT(x)\).
c) Roughly what does the 8th unit of software cost? And the 16th?
d) Is the frontier concave? Say what that means in economic terms.

โœ… Solution

a) \(y(0) = 100\) tonnes. \(y(8) = 100 - 64/4 = 84\) tonnes.

b) \(MRT(x) = -\,\mathrm{d}y/\mathrm{d}x = x/2\).

c) \(MRT(8) = 4\) tonnes, \(MRT(16) = 8\) tonnes. The 16th unit costs twice as much bread as the 8th. ๐Ÿ“ˆ

d) \(y'' = -1/2 < 0\), so yes, and equivalently \(MRT' = 1/2 > 0\). Economically: resources are not equally suited to both uses, so the ones moved into software first are those least productive in bread, and every further unit costs more than the last. โœ…

Wrap-Up

๐ŸŽฏ What to Take From This Session

โš–๏ธ Scarcity means resources are limited and wants are not, so every choice gives something up.

๐Ÿ’ฐ Surplus \(B - C\) turns โ€œis this worth doing?โ€ into one number, and that is what makes options comparable.

๐Ÿ’ถ Opportunity cost is what you pay plus the surplus you forgo, so the rule is benefit above opportunity cost.

โž• Choices are marginal: \(MB = MC\) is the first order condition of \(\max B(q) - C(q)\), and sunk costs drop out because constants do not move an argmax.

๐Ÿ“ The PPF is that logic for a whole economy. Its slope is the MRT, and it is concave because the best suited resources are used first.

๐ŸŒ Differences in opportunity cost are comparative advantage, which is why we specialize and exchange. Session 13 turns it into trade.

๐Ÿ‘‹ Next Session

Consumer Choice.

Today we compared surplus across a handful of options. Next we do it properly:

  1. ๐Ÿ˜Š Preferences: how we describe what you like.
  2. ๐Ÿ’ถ The budget constraint: what you can afford, and a slope that is again an opportunity cost.
  3. ๐ŸŽฏ Constrained maximization: the best affordable bundle, and the demand it produces.

See you next week. ๐Ÿ™Œ