Lecture: Midterm Review & Exam
Lecture script · about 15–20 minutes spoken · Week 8
Opening
Picture a café owner at closing time, keys in hand, wondering whether to stay open one more hour. One more hour means a few more customers. It also means paying staff and keeping the lights on. The owner doesn't need the whole year's books to decide. The owner needs one comparison: what that hour adds against what it costs.
That's the one new idea in this lecture, and we'll get to it near the end. Most of what we do is review, because the midterm is coming.
Here's where we are. Week 1 gave you the frontier and opportunity cost. Week 2 gave you comparative advantage. Weeks 3 and 4 built demand, supply, and the running market. Week 5 measured how strongly buyers respond, Week 6 measured the gains from trade as surplus, and Week 7 ran price controls and taxes through the market.
That's a lot of notes. So I'm going to ask each model for only two things: the one graph it draws and the one calculation it asks for. We'll rerun each one on numbers you've already met, and I'll name the classic slip beside it. Then you'll meet thinking at the margin, the habit every firm week uses from Week 9 on. One honest reminder before we start: every number here is illustrative, built for this course, not measured from a real market.
1. The frontier: one curve, one slope
Think about a weekend with two jobs, studying and paid shifts. Every hour on one is an hour you can't spend on the other. The frontier draws that trade-off for a whole economy.
Remember the island. It can catch fish or gather coconuts. The production possibilities frontier is the graph of every combination of the two goods the island can make when it uses all of its resources fully and efficiently. Picture fish along the bottom and coconuts up the side. The curve runs from 105 coconuts with no fish down to 60 fish with no coconuts, and it bows outward, like the curve of a bridge seen from the side.
The calculation is the slope, read as an opportunity cost. At 30 fish, the island can gather 75 coconuts. At 40 fish, only 55. So those 10 extra fish cost 20 coconuts, which is 2 coconuts a fish.
Then sort points. The point 30 fish and 75 coconuts sits right on the curve, so it's efficient. The point 30 fish and 50 coconuts sits inside the curve. The island could have had 75 coconuts there, and it has only 50.
Pause and try this. Is the point 30 fish and 50 coconuts possible for the island, or out of reach?
Think about what "inside" means.
Here's the answer. It's possible, but wasteful, because the island could reach 75 coconuts at 30 fish and some workers must be idle or misused.
The points out of reach are the ones outside the curve, like 40 fish and 70 coconuts.
2. Comparative advantage: one ratio at a time
Two roommates split the chores, and one of them is faster at every single chore. Should that roommate do them all? Week 2 said no, and the reason was opportunity cost.
Remember the campus food stand. In an hour, Amara makes 8 smoothies or 4 sandwiches. Diego makes 3 smoothies or 3 sandwiches. Amara is faster at both, so she has the absolute advantage in both. But comparative advantage is the ability to make a good at a lower opportunity cost than another producer.
So you divide, one ratio at a time. A sandwich costs Amara 2 smoothies, because 8 divided by 4 is 2. A sandwich costs Diego 1 smoothie, because 3 divided by 3 is 1. Diego gives up less, so Diego has the comparative advantage in sandwiches, and Amara has it in smoothies.
The check that comes with it is the range. A trade helps both only at a rate between 1 and 2 smoothies per sandwich. Our pinned rate, 1.5 smoothies per sandwich, sits inside.
Pause and try this. Diego is slower at both foods. Why does he still make the sandwiches?
Compare what a sandwich costs each of them.
Here's the answer. A sandwich costs Diego 1 smoothie and costs Amara 2, so his opportunity cost is lower.
Advantage in output isn't advantage in cost. That's the whole lesson of Week 2 in one line.
3. Equilibrium: one crossing, one solve
Think about a merch table at a concert. Price the shirts too low and the line outlasts the shirts. Price them too high and boxes go home unsold. Somewhere in between, the table clears.
That clearing price is the equilibrium price. In the running market, picture two straight lines on one graph: demand sloping down to the right and supply sloping up. The calculation is to set quantity demanded equal to quantity supplied and solve. Demand is 90 minus 10 times the price. Supply is 10 times the price minus 30. Set them equal, gather the price terms on one side, and you get 20 times the price equals 120. So the price is 6 dollars, and the quantity is 30 units a day.
Now try a price below that. At 4 dollars, buyers want 50 units a day and sellers offer 10. That gap of 40 units is a shortage.
Pause and try this. At 4 dollars on the running market, who is left over: unsold units, or buyers without a unit?
Ask what the gap is made of.
Here's the answer. Buyers are left over, since 50 are wanted and only 10 are offered, so it's a shortage of 40.
Below the equilibrium price you get a shortage. Above it you get a surplus, with unsold units waiting.
4. Shifts: name the curve, the way, and the new price
Suppose paychecks in a town grow, and people want more of a normal good at every price. The good's own price didn't change first. Something else did.
That's a shift. Whenever you see one, say three things: which curve, which way, and where the new price and quantity land. Here, income changed what buyers want at every price, so demand shifts, and for a normal good it shifts right, by 20 units at every price.
Now solve again. The new demand is 110 minus 10 times the price, and supply hasn't moved. Set them equal and the price comes out at 7 dollars, with 40 units a day. So demand shifted right, and the market moved up along the supply curve from 6 dollars and 30 units to 7 dollars and 40 units.
Pause and try this. The price of the good falls and buyers buy more. Did demand shift?
Ask what changed first.
Here's the answer. No, that's a movement along the demand curve, because only the good's own price changed.
When only the price moves, you move along a curve. Everything else shifts it.
5. Elasticity: the midpoint formula and the revenue test
A transit agency wants more fare money. Should it raise fares? That depends on how strongly riders respond, and Week 5 gave that strength a number.
The price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. You compute each percentage on its midpoint, dividing the change by the average of the two values. Elasticity uses its own demand curve, Dataset B, not the running market.
On Dataset B, as the price rises from 4 to 6 dollars, quantity falls from 120 to 80. The quantity change is 40 on an average of 100, a 40 percent fall. The price change is 2 on an average of 5, a 40 percent rise. Divide them and you get minus 1.0. That's unit-elastic.
Then the revenue test. At 4 dollars, revenue is 480 dollars. At 6 dollars, it's 480 dollars again. On a unit-elastic stretch, revenue doesn't change.
Pause and try this. Dataset B's line has the same slope everywhere. Does that mean its elasticity is the same everywhere?
Think about percentages, not units.
Here's the answer. No, the slope stays at minus 20 units per dollar, but elasticity is a ratio of percentages and changes along the line.
So a steep-looking line isn't the same thing as inelastic demand.
6. Surplus: two triangles
Say you'd have paid 30 dollars for a used jacket and you got it for 18. You walked away 12 dollars better off. Week 6 added up gains like that for every buyer and every seller.
Consumer surplus is the area below the demand curve and above the price. Producer surplus is the area above the supply curve and below the price. Picture the running market's crossing at 6 dollars and 30 units. Above the price line sits one triangle, reaching up to where demand starts at 9 dollars. Below the price line sits another, reaching down to where supply starts at 3 dollars.
Each triangle has a base of 30 units. The top one is 3 dollars tall, from 9 down to 6, so consumer surplus is half of 30 times 3, or 45 dollars a day. The bottom one is 3 dollars tall too, from 6 down to 3, so producer surplus is also 45. Together that's 90 dollars a day.
Pause and try this. A classmate multiplies 30 by 3 and gets 90 for consumer surplus. What's the slip?
Picture the shape of the area.
Here's the answer. The area is a triangle, not a rectangle, so it needs the one half in front, which gives 45.
7. Controls and taxes: the gap, the wedge, the lost triangle
A city caps a price, or a state adds a tax to every unit sold. Week 7 ran both through the running market and asked what disappears.
Start with a ceiling at 4 dollars. It binds, because 4 is below 6. Buyers want 50 and sellers offer 10, so there's a shortage of 40, and only 10 units trade. The trades between the 10th unit and the 30th never happen. That lost value is the deadweight loss, the total surplus that disappears because the quantity traded moves away from the efficient quantity. Here it's 40 dollars a day.
Now a tax of 2 dollars a unit, collected from sellers. Supply shifts up by 2 dollars at every quantity. Buyers now pay 7 dollars, sellers keep 5, and 20 units trade. The government collects 2 dollars on each of 20 units, which is 40 dollars a day. The lost triangle is smaller: half of 2 dollars times the 10 lost units, or 10 dollars a day. And each side bears 1 dollar of the tax, only because the two curves are equally steep here.
Pause and try this. Someone says the tax's loss is 2 dollars times 20 units, so 40 dollars. What did they compute?
Ask where that money goes.
Here's the answer. They computed the revenue, which goes to the government as a transfer; the loss is only the 10-dollar triangle.
And remember who bears a tax follows responsiveness, not who writes the check.
8. Thinking at the margin: the café's extra hours
Back to the café owner with the keys. The question isn't "Is this a good business?" It's "Is the next hour worth it?" That's thinking at the margin: deciding a choice one extra unit at a time, instead of judging the whole total at once.
Two words come with it. The marginal benefit is the extra benefit from one more unit of an activity, here the extra sales from one more hour. The extra cost of that same hour is its marginal cost, here the staff and power. Week 9 builds marginal cost from a full cost table. For now, you only need the cost of one more hour.
The rule is the marginal-benefit and marginal-cost rule: do one more unit while its extra benefit is at least its extra cost, and stop at the first unit whose extra cost is larger.
Here's the café's evening. The 1st extra hour brings in 60 dollars, the 2nd 45, the 3rd 30, the 4th 20, and the 5th 10. Each hour costs 25. The 1st hour beats 25, the 2nd beats 25, and the 3rd beats 25. The 4th brings in 20 against 25, so it fails. The café opens 3 extra hours. Its net gain, the extra benefit minus the extra cost, is 35, then 20, then 5, for 60 dollars a night.
Pause and try this. The 4th hour still brings in 20 dollars. Why not open it?
Compare that 20 with the hour's cost.
Here's the answer. It costs 25 and brings in only 20, so it would make the café 5 dollars worse off, and the net gain would drop to 55.
You've seen this rule before without its name. The used-bicycle market made trades while each one was worth at least what it cost, and it stopped at three.
9. Sunk costs: what to leave out
Imagine you bought a nonrefundable ticket to a play, and on the night you feel sick. The ticket money is gone whether you go or stay home. The only question left is which evening you'd enjoy more from here.
That spent money has a name. A sunk cost is money or time already spent that cannot be recovered whatever you decide next. Because it's the same under every option, it doesn't change which option is best.
Think about the café's rent. It was paid before the evening began, and closing early won't bring it back. It's the same whether the café opens 0 extra hours or 5. So it can't change the comparison for any single hour, and the answer stays at 3 extra hours.
Pause and try this. Suppose the café's rent had been much higher. Would it open a different number of extra hours?
Ask whether rent changes any hour's comparison.
Here's the answer. No, the rent is the same at every number of hours, so each hour's benefit and cost are unchanged, and it still opens 3.
Here's one caveat. The rent still counts when you add up how a whole year went. It drops out only of the decision about the next hour. And that's the bridge: from Week 9 on, a firm decides how much to make by asking what one more unit adds against what it costs.
Closing
Let me pull it together. The frontier's slope is an opportunity cost, 2 coconuts a fish from 30 to 40, and an inside point is wasteful, not impossible. Comparative advantage goes to the lower opportunity cost, so Diego makes sandwiches. The running market clears at 6 dollars and 30 units, with a shortage of 40 at 4 dollars. A shift needs its curve, its direction, and its new price and quantity, like 7 dollars and 40 units. Elasticity is minus 1.0 from 4 to 6 dollars on Dataset B, with revenue steady at 480. The two surplus triangles are 45 each. A ceiling at 4 dollars loses 40, and the 2-dollar tax loses 10 while raising 40. And the margin rule opens the café 3 extra hours, with the rent left out.
Next in this module, look through the slide deck, then the Readings and Resources page, and then work the practice set and the discussion before the midterm. The midterm covers Weeks 1 to 7. Next week, in Week 9, Production & Costs, the margin question moves inside the firm.
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