Every choice has a price tag.
The story It's summer. You have $300 saved and about 10 free hours every weekend. You could mow lawns for neighbors (about 1 hour and $15 per lawn), fix up old bikes and resell them (1 to 4 hours each, and a full 4-hour fix-up makes about $70 profit), study for the SAT, or hang out with friends. You can't do all of it, so you have to choose.
Choosing how to use something you only have a limited amount of, like time or money.
Saying yes to one thing always means saying no to something else. When you can see what you're giving up, you make better choices.
Compare each option by its opportunity cost: the best thing you give up to get it.
Economists study these choices. Strategy analysts and consultants get paid to make them for companies.
What you're looking at: a sketch of the production possibilities frontier (PPF) for your 10 free hours, with no numbers yet. Lawns mowed go to the right and bikes fixed go up. The green curve is every way to use all 10 hours. The shaded part under it holds plans that waste time, and the space past it is impossible for now. The real chart with numbers is in the first section below.
Slide your weekend.
Watch what it costs.
Say mowing pays $15 an hour. Every hour you spend with friends is an hour you aren't mowing, so that hour isn't really free. It costs you the $15 you could have earned. That missed $15 is the hour's opportunity cost.
- Opportunity cost
- Spend 1 hour with friends and the opportunity cost is the $15 you could have made mowing. Spend 4 hours and it's 4 × $15 = $60.
From the hours you mowed
Fun, rest, the stuff that keeps you sane
The money you gave up. That's its opportunity cost.
What you're looking at: your 10 free hours as 10 boxes. Green boxes are hours spent mowing ($15 each), and orange boxes are hours with friends. The slider sets how many hours you mow, from 0 to 10. The numbers below show what you earn and what your free time costs you.
Now look at every possible weekend.
This time, picture all 10 hours going to your two jobs: mowing lawns and fixing bikes. A lawn always takes 1 hour. Bikes don't: the four bikes in your garage need different amounts of work. One just has a flat tire (1 hour), one needs a new chain (2 hours), one needs new brakes (3 hours), and one is a rusty mess that needs a full fix-up (4 hours). You'd do the quick ones first. So you could mow 10 lawns, or fix 1 bike and mow 9 lawns, or fix 2 bikes and mow 7, or fix 3 and mow 4, or fix all 4 bikes and mow none.
The green curve below shows the most of both you can finish in one weekend. It's called a production possibilities frontier, or PPF for short.
- PPF
- The green curve below. Each point on it is one way to spend all 10 hours, like 7 lawns + 2 bikes or 4 lawns + 3 bikes.
- On the curve: you use all 10 hours. Nothing is wasted.
- Inside the curve: some hours go unused. You could do more of both.
- Outside the curve: impossible with the time and tools you have now.
Tap anywhere on the chart to test a plan.
Tap the chart to try a plan.
A repair stand is a clamp that holds a bike while you work, which makes bike jobs faster. Tap the button to see what it does to the curve.
What you're looking at: the real PPF for one weekend. Lawns mowed run along the bottom (0 to 10) and bikes fixed go up the side (0 to 5). The green line is every plan that uses all 10 hours, and the shaded area under it is every plan you could do. Tap a point to test it. After you buy the repair stand, the dashed line shows where the old curve was.
Two minutes. Just listen.
Tap any line to jump to it.
Ten Free Hours
Four weekends, ten hours each. Your goals by the end: $200 toward a repair stand, 12 hours of SAT practice, and don't burn out. You won't hit everything perfectly. That's the point.
The logic, step by step.
Opportunity cost
You only count the single best option you gave up, not every option added together. Say one hour of your time could earn $15 mowing a lawn or $12 babysitting. If you spend that hour with friends instead, the hour cost you $15, the better of the two. It didn't cost $27, because you could never have mowed and babysat in the same hour.
Measuring cost in the other thing
Opportunity cost doesn't have to be in dollars. Often it's easier to ask: "To get one more of this, how much of that do I give up?"
Take the full fix-up from the story: it takes 4 hours. In those same 4 hours you could mow 4 lawns. So one bike costs you 4 lawns. As a formula:
Worked example: bikes or lawns
- Write down what each job takes. A lawn takes 1 hour and pays $15. A full bike fix-up takes 4 hours and makes about $70 profit.
- Find what one bike costs in lawns. The 4 hours a fix-up takes could have mowed 4 lawns. So one bike costs 4 lawns, which is 4 × $15 = $60 of mowing money.
- Compare that cost to what the bike pays. The bike makes $70, and you gave up $60 to fix it. So the bike is the better use of those hours, by $10.
- Watch the cost go up. Not every bike takes 4 hours. In "See it", your four bikes took 1, 2, 3 and 4 hours. The 1-hour flat tire costs only 1 lawn ($15). The 4-hour rusty one costs 4 lawns ($60). The more bikes you fix, the more lawns each extra one costs. This rising cost is why the frontier is a curve instead of a straight line.
- Decide one at a time. Don't ask "bikes or lawns?" Ask "is one more bike worth more than the lawns it replaces?" Keep going until the answer becomes no. Economists call this thinking at the margin.
- Thinking at the margin
- Instead of "bikes or lawns?", you ask about one bike at a time. One fix-up costs 4 lawns ($60) and pays $70, so that one more bike is worth it, by $10.
How many is too many? One more at a time
Thinking at the margin also tells you when to stop. Say your bike business grows: you and two friends now work in a garage. A repair stand (the clamp that holds a bike while you work on it) can be rented for $60 a month. More stands let you fix more bikes, but here's the catch: there are still only three of you, in one garage.
| Stand | Extra profit it adds per month (marginal benefit) | Rent per month (marginal cost) | Worth it? (benefit − cost) |
|---|---|---|---|
| 1st | $150 | $60 | Yes, +$90 |
| 2nd | $120 | $60 | Yes, +$60 |
| 3rd | $80 | $60 | Yes, +$20 |
| 4th | $40 | $60 | No, −$20 |
Why does each stand add less? The first stand is in use all day. With a second, two of you can work at once. By the fourth stand, there are more stands than people. It mostly sits empty, so it adds only a little. Each new stand is shared by the same three people and the same garage. Economists call this diminishing returns.
Economists have names for the two numbers you compare. What one more unit adds is its marginal benefit. What one more unit costs is its marginal cost. ("Marginal" just means "one more.")
- Marginal benefit
- What one more stand adds. The 1st stand's marginal benefit is $150. The 4th stand's is only $40.
- Marginal cost
- What one more stand costs: its $60 rent. It's the same for every stand.
- What you keep
- Marginal benefit minus marginal cost. For the 1st stand: $150 − $60 = $90. For the 4th: $40 − $60 = −$20, a loss.
- Diminishing returns
- The marginal benefit shrinks with each stand ($150, $120, $80, $40), because the same three people share them.
The rule: keep adding one more as long as its marginal benefit is bigger than its marginal cost. Stop at the first one where it isn't. Here that means 3 stands. Notice the 4th stand still adds money ($40). It just adds less than its $60 rent, so renting it would lose $20 a month.
Sunk costs
A sunk cost is time or money you've already spent and can't get back. It shouldn't change what you do next. Say you've put 3 hours into a bike, and then you find out it needs $80 of parts. Those 3 hours are gone whether you finish the bike or not. The only question now is whether finishing it will make more than the $80 and the hours still ahead. If it won't, stop, even though it feels like a waste.
- Sunk cost
- The 3 hours you already spent on the bike. They're gone either way, so they shouldn't count when you decide whether to finish it.
Why the frontier bends outward
On an exam you'll be asked why a PPF is "bowed outward": it bulges away from the corner instead of being a straight line. The short answer is that not everyone (or everything) is equally good at both jobs. Here's what that means with real numbers.
Say your business grows and two friends work the weekend with you. You'll call the team's effort "resources". Each person can spend the weekend on bikes or on lawns:
| Person | Bikes in a weekend | Lawns in a weekend | Cost of each bike |
|---|---|---|---|
| Maya, a bike whiz | 4 | 5 | 5 lawns4 bikes = 1.25 lawns |
| Leo, so-so at both | 2 | 6 | 6 lawns2 bikes = 3 lawns |
| Jordan, never held a wrench | 1 | 8 | 8 lawns1 bike = 8 lawns |
- Start with everyone mowing. 5 + 6 + 8 = 19 lawns, 0 bikes.
- You want some bikes, so who switches first? Maya, because she gives up the fewest lawns per bike. You gain 4 bikes and lose only 5 lawns: 14 lawns, 4 bikes. Cheap bikes.
- Want more bikes? Leo switches next. You gain 2 bikes but lose 6 lawns: 8 lawns, 6 bikes. Each bike now costs 3 lawns.
- Want every possible bike? Jordan has to switch. You gain just 1 bike and lose 8 lawns: 0 lawns, 7 bikes. That last bike cost 8 lawns.
Each extra bike costs more lawns than the one before, because you used up the people who are good at bikes first. Plot those four points and you get a curve that bulges outward:
What you're looking at: the team's real PPF, built from the table above. Lawns mowed run along the bottom (0 to 19) and bikes fixed go up the side (0 to 7). Each dot is one plan: everyone mowing, then Maya switching to bikes, then Leo, then Jordan. The green line joins them. The dashed straight line is what the curve would look like if all three of you were equally good at both jobs.
If all three of you were equally good at both jobs, every bike would cost the same number of lawns, and the PPF would be the straight dashed line. The bulge comes from people (and machines, land and time) being better at some jobs than others. Economists call this the law of increasing opportunity cost.
- Law of increasing opportunity cost
- Each extra bike costs more lawns than the last: Maya's bikes cost 1.25 lawns each, Leo's 3, and Jordan's 8. That rising cost is what bends the curve.
Same idea, one person. The bend also happens when you work alone. Your first bike of the weekend is an easy one. If you keep going, you get to the rusty bikes that need a full 4-hour fix-up, so each extra bike costs more lawns. Different reasons, same result: the more of one thing you make, the more each extra one costs. Exam tip: if a PPF is a straight line, every unit costs the same amount.
Comparative advantage
Having a comparative advantage means you can do something while giving up less than someone else would. Say your friend Sam can mow 2 lawns an hour, but takes 8 hours to fix a bike. In those 8 hours Sam could have mowed 16 lawns, so a bike costs Sam 16 lawns. A bike only costs you 4. So you should fix the bikes, Sam should mow the lawns, and you split the work. You both end up with more than if each of you did both jobs. This works even when one person is faster at everything. An economist named David Ricardo explained it in 1817, and it's the main reason countries trade with each other. It's on every intro economics exam.
- Comparative advantage
- A bike costs you 4 lawns but costs Sam 16 lawns, so you have the comparative advantage in bikes. Sam gives up fewer bikes per lawn, so Sam has it in lawns.
Moving on the curve vs. moving the curve
Exams love this one. Three different things can happen on a PPF, and only one of them moves the curve itself. Remember: the curve shows the most you could make with what you have. So the curve only moves when "the most you could make" changes.
What you're looking at: a sketch, not real numbers. It's a PPF with bikes going up and lawns going to the right, showing the three kinds of moves: (1) sliding along the curve, (2) a wasteful plan inside the curve (the red dot) moving up to it, and (3) the whole curve moving out to the bigger dashed curve.
- Sliding along the curve: you change your mind, not your ability. You decide to do more bikes and fewer lawns. You're picking a different spot on the same curve, and the most you could make hasn't changed. For a country, "people buy more cars and less wheat" is this case.
- Moving from inside up to the curve: you stop wasting. Say Jordan spent the weekend on the couch. Your team was inside the curve. When Jordan gets to work, you move up toward the curve. But the curve stays put, because Jordan could have worked all along. For a country, unemployment falling is this case: people who were idle start working.
- The whole curve moves out: you can now make more than was possible before. This only happens when you get more or better resources. You buy a repair stand so bikes go faster (that's the button in the chart above), you learn a new skill, or a fourth friend joins. For a country, it's new technology, more workers, more machines or better education. Economists call this economic growth.
- Economic growth
- Buying the repair stand moved your curve out, from at most 4 bikes in 10 hours to 5 bikes. Same hours, more possible.
What doesn't move it: prices. If bikes sell for less, you can still fix exactly as many in a weekend. The PPF counts how much you can make, not what it's worth.
Which point on the curve is best?
If the PPF doesn't count money, how do you choose a point? Every point on the curve uses all 10 hours, so none of them wastes anything. To pick the best one, you take a second step after drawing the curve: you bring in what each thing pays.
- List the plans on the curve. Bikes take 1, 2, 3 and then 4 hours, and every hour left over goes to lawns. That gives five plans: 0 bikes + 10 lawns, 1 bike + 9 lawns, 2 bikes + 7 lawns, 3 bikes + 4 lawns, and 4 bikes + 0 lawns.
- Put a price on each plan. A lawn pays $15 and a bike makes about $70 profit. For 2 bikes + 7 lawns: 2 × $70 = $140, plus 7 × $15 = $105, so $245 in total.
- Pick the plan that makes the most. At $70 a bike, 4 bikes + 0 lawns wins: 4 × $70 = $280.
Now change the bike profit and watch the winner move. The curve stays exactly the same, because you can still make the same things. Only the best point on it changes.
What you're looking at: the five whole-bike plans on your curve, one bar each. A longer bar means the plan makes more money, from $0 at the left to $400 at the right, at the bike profit you pick on the slider ($20 to $100). Under each total you see where it comes from: the bike money plus the lawn money. The green bar is the winner. These are the lesson's real numbers, not a sketch.
Here's the shortcut: add one more bike only if its profit beats the lawns it costs. The 1st bike costs 1 lawn ($15), the 2nd costs 2 lawns ($30), the 3rd costs 3 lawns ($45) and the 4th costs 4 lawns ($60). At $40 a bike, the 1st and 2nd bikes are worth it, but the 3rd isn't, because $40 is less than $45. So 2 bikes + 7 lawns wins with $185 (2 × $40 = $80, plus 7 × $15 = $105). That's thinking at the margin again.
Why only whole bikes? A point in the middle of the curve, like 5 lawns + 2.7 bikes, is possible, but 0.7 of a bike can't be sold. It earns $0 until it's finished. So that plan really pays for 5 lawns and 2 finished bikes: 5 × $15 = $75, plus 2 × $70 = $140, so $215. Spending those 2 unfinished hours on lawns instead would pay $30 more.
Economists have names for these two steps. Any plan on the curve has productive efficiency: nothing is wasted. The one plan that's worth the most has allocative efficiency: you're making the right mix.
- Productive efficiency
- Any plan on the curve, like 2 bikes + 7 lawns or 4 bikes + 0 lawns. All 10 hours get used.
- Allocative efficiency
- At $70 a bike, 4 bikes + 0 lawns, worth $280, the most of any plan. At $40 a bike, it's 2 bikes + 7 lawns, worth $185.
A tree runs on a budget.
A tree makes only so much sugar from sunlight each year. Every bit spent on roots can't go into leaves, and leaves can't become seeds. Trees in dry ground spend on deep roots. Trees in a crowded forest race upward for light. Neither can max out everything.
What you're looking at: an illustration, not data. One tree's yearly sugar is split three ways: leaves to catch light, roots to find water, and seeds for the future. Like your 10 hours, more for one part means less for the others.
The lesson from biology. Every living thing faces scarcity, so every living thing makes trade-offs. Ecologists even call it an "energy budget." The tree doesn't feel bad about not growing seeds in a drought year. It puts its sugar where it matters most right now. That's exactly what you're learning to do with money.
The page you'd copy down.
- Scarcity: you want more than you have time, money or energy for. That's the reason economics exists.
- Trade-off: getting more of one thing means getting less of another.
- Opportunity cost: the value of the next best alternative you give up. Only the best one counts.
- Production possibilities frontier (PPF): a curve showing the most you can make of two things with what you have. On the curve, nothing is wasted. Inside it, something is wasted. Outside it is impossible for now.
- Growth (better tools, better skills, more time) moves the frontier outward.
- Marginal thinking: compare the cost and benefit of one more unit, not all or nothing.
- Sunk costs are already gone. Ignore them when deciding what's next.
Fill in the blanks
Grab a friend or a study group.
The $1,000 city council
Your town has $1,000 left this year. Options: fix a pothole-filled road, add a bus stop, or repaint the skate park. Each person argues for one. Before you vote, everyone has to name the opportunity cost of their own pick.
Trade like Ricardo
Time each other for one minute: how many words can each of you type, and how many math problems can each of you solve? Work out who gives up less to do each task (that's comparative advantage), then split a pretend homework load so you finish fastest.
Hours showdown
Both play Ten Free Hours and compare your weekends. Did one of you chase money and the other chase SAT hours? Explain the one hour you'd move if you played again.
Just you and your choices.
These stay on this device. Nobody else sees them.
Exam-style questions.
Written the way a college exam would ask them. Each right answer on the first try is worth 10 xp.
On the job: you're the strategy analyst
A coffee shop has 40 staff hours a week to spare. A staff hour is one worker working for one hour, so 5 workers for 8 hours is 40 staff hours. The owner has three ideas, and each one would use all 40 hours, so the shop can only pick one:
- Catering service: 4 workers × 10 hours of cooking and delivery = 40 staff hours. Profit: about $1,200 a week.
- Stay open two extra evenings: 5 workers × 4 hours × 2 evenings = 40 staff hours. Profit: about $900 a week.
- Weekend pop-ups: 2 workers × 10 hours × 2 days = 40 staff hours. Profit: about $1,000 a week.
Your task: recommend one option, and state its opportunity cost in dollars. What one fact would make you change your answer?
See a model answer
Pick catering. All three use the same 40 hours, so compare profit per staff hour. Catering: $1,20040 hours = $30 an hour. Pop-ups: $1,00040 hours = $25. Evenings: $90040 hours = $22.50. Catering earns the most for each hour.
Opportunity cost: $1,000, the profit from pop-ups, the next best option. Not $1,900: you can only give up one alternative with the same hours.
What would change it: if catering needs $400 a week in van rental that isn't in the estimate, it drops to $800 and pop-ups win. Always check that every option's numbers include all of its costs.
Trade-offs come back all through the course.
What you're looking at: a map of where this lesson fits in the course. Read it left to right: what comes before, this lesson in the middle, and the later lessons that build on it.
- Before · Unit 3Budgeting
- You are hereScarcity and trade-offs
- Next · Unit 8Supply and demand
- Later · Unit 10The time value of money
- Later · Unit 11Starting a business
- Later · Unit 13Project decisions (NPV)