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MICROECONOMICSWhen two curves move at once
A fuel levy hits the boiler room and a health campaign hits the produce aisle in the same season. One of price and quantity is certain, the other genuinely isn't — and knowing which is which is most of introductory microeconomics.
Textbook supply and demand problems are usually polite about it. Something happens, one curve moves, the new equilibrium sits neatly up and to the right, and everybody goes home.
Real markets are not polite. Things happen at the same time, on both sides of the market, and they do not agree about which direction prices should go. This is where students start guessing — and it is also where the model is most worth having, because the model can tell you exactly how much you are entitled to conclude and exactly where you have to stop.
The situation
Picture the greenhouse tomato growers of southwestern Ontario. Between them they have found an equilibrium: a price that clears the market, a quantity that sells. Put real numbers on it so we can check our reasoning later — $4.00 a kilo, 40 tonnes a week.
Then two things land in the same season.
A fuel levy raises the price of the natural gas that heats every greenhouse through the cold months. And a national healthy-eating campaign, backed by a long run of television advertising, puts fresh vegetables in front of households that had not been buying many.
One event arrived through the boiler room. The other arrived through the produce aisle. Neither one is a change in the price of a tomato, which is the whole point: both of them move a curve.
The habit that makes this easy
There is one question that resolves almost every shift problem, and it has to be asked separately for each event:
Hold the price fixed. At that unchanged price, does this event change how much people want, or how much producers are willing to make?
The price has to be held fixed, because that is what distinguishes a shift from a movement. A supply curve is a list of promises — at this price I'd grow this much, at that price I'd grow that much — drawn up under a fixed set of costs. Change the price of heating gas and every promise on the list is rewritten. The curve has not been traversed. It has been replaced.
The same logic runs on the demand side. More buyers in the market, buyers expecting prices to climb, buyers whose complementary goods just got cheaper — none of those are a change in the tomato price, so each one rewrites the demand schedule rather than sliding along it.
Apply the question to the levy: it raises the cost of growing every kilo, so at any given price the growers are willing to supply less. Supply shifts left. Apply it to the campaign: at any given price, more households now want fresh tomatoes. Demand shifts right.
Write both answers down before you draw anything. Students who draw first and reason afterward tend to draw whatever looks familiar.
Now the interesting part
Here is the move that separates people who have understood the model from people who have memorised four diagrams.
Make yourself a small table. Two rows, one per event. Two columns: what this shift alone does to price, and what it alone does to quantity.
| Event | Which curve, which way | Effect on price, alone | Effect on quantity, alone |
|---|---|---|---|
| Fuel levy on greenhouse heating | Supply shifts left | Up ↑ | Down ↓ |
| National healthy-eating campaign | Demand shifts right | Up ↑ | Up ↑ |
| Columns agree? | Yes — price rises | No — ambiguous |
Fill it in. Then read the columns.
Where both rows agree, you have certainty. Both shifts push that variable the same way, so the combined effect pushes it that way too, regardless of which shift is bigger. You can state the direction flatly. Here, both a leftward supply shift and a rightward demand shift raise price — so price definitely rises.
Where the rows disagree, you have genuine ambiguity. One shift pushes up, the other pushes down, and which wins depends entirely on the relative magnitudes — information you do not have. The leftward supply shift cuts quantity; the rightward demand shift raises it. So quantity could go either way, and the honest answer is a range, not a point.
In any two-shift problem, this is the shape of the answer: one variable you can call, one you cannot. Which is which depends on the directions, and the table is how you find out without guessing.
The Curve Playground has the same pair of shifts preloaded — supply left, demand right — and keeps the original S₁, D₁ and E₁ on screen beside the new ones, so you can read the shift rather than imagine it. It runs on its own scale, so the numbers differ from the figures above; the shape is the point. Drag either curve to see which variable holds its direction and which flips.
Open the double-shift market →That ambiguity is not a gap in the model. It is the model being precise about the limits of what the evidence supports. An economist who says "price definitely rises, quantity could go either way, and here is why" has said something far more useful than one who picks a direction for both and sounds confident. Most of applied economics is the discipline of refusing to sign a number you cannot sign.
Then the government turns up
Suppose the demand effect turns out to be the larger one, as in Figure 1. Tomatoes are now noticeably dearer than they were last winter, shoppers are unhappy, and somebody proposes a cap at the old price — $4.00 a kilo.
It is a popular idea, and it is worth tracing carefully rather than dismissing.
The cap is drawn on the new market — the one with the shifted curves — because that is the market that exists now. At the capped price, read two quantities: across to the new supply curve for how much gets grown, across to the new demand curve for how much people want. The gap between them is a shortage.
And here is the part that surprises people: the quantity actually grown under the cap is lower than it was before either event happened. Not lower than the new equilibrium quantity — lower than the original. The cap is set at the old price, but it is sitting on a new supply curve, and the levy means the growers are no longer willing to produce 40 tonnes at $4.00. They will produce 30.
Drawing the ceiling on the original diagram. A cap at the old price is not binding on the old market — it was the equilibrium there, so it does nothing. The whole effect comes from the cap meeting curves that have since moved.
So the policy delivers a lower price to whoever manages to fill a basket, and fewer tomatoes for everyone else to fight over.
And they do fight over it, because price is no longer doing the rationing. Something always rations a scarce good. Remove the price mechanism and the job falls to empty shelves by mid-morning, to queues, to grocers quietly reserving stock for their best accounts, or to smaller and poorer-quality fruit at the same headline price. None of these distribute tomatoes to the people who value them most, and none of them address what actually happened — which was that heating got dearer and more households wanted vegetables.
The cap treats the price as the problem. The price was the messenger.
A different market, the same shape of problem: two shocks in one season, then a cap pegged to the old price. Read the evidence, name the culprit, and check your reasoning against the verdict.
Open the case file →The other half: how much does quantity actually respond?
Everything above is about direction. The companion question is magnitude, and that is elasticity's department.
The quickest practical tool is the total revenue test, and it requires no formula at all. Multiply price by quantity before the change, and again after. Then compare:
- Price and revenue moved in opposite directions → demand is elastic over that range. Quantity responded proportionally more than price did.
- Price and revenue moved in the same direction → demand is inelastic. Quantity barely flinched.
- Revenue didn't move → unit elastic, the knife edge between them.
A grocer drops the price of bagged salad from $5.00 to $4.00 and weekly sales rise from 1,800 to 2,520 bags:
| Price | Quantity | Total revenue | |
|---|---|---|---|
| Before | $5.00 | 1,800 | $9,000 |
| After | $4.00 | 2,520 | $10,080 |
| Direction | Down ↓ | Up ↑ | Up ↑ |
Price down, revenue up — opposite directions, so demand is elastic over this range. That is the whole test, and it is genuinely how a shop owner should think about a price change. "I dropped the price and made more money" is an elasticity finding. The coefficient just puts a number on something the till already told you.
The total revenue test reads a movement along one demand curve — the grocer changed the price and nothing else changed. It does not work on the tomato market above, where price and quantity both moved because the curves shifted. There, the before-and-after points sit on two different demand curves, so their price–quantity ratio measures nothing about elasticity. Before reaching for the test, check that demand stayed put.
One further trap worth naming: do not try to eyeball elasticity by comparing the raw changes. A drop of $1.00 against a rise of 720 bags is a comparison of dollars to salad, which means nothing. Elasticity is proportional by construction, which is exactly why it is unit-free and why it travels across markets.
When the goods are related
Cross elasticity asks a different question: when this good's price moves, what happens to the quantity demanded of that one?
EC = (% change in Qd of one good) ÷ (% change in P of the other good)
The magnitude tells you how tightly the two are linked. The sign tells you what kind of link it is, and the sign is where the economics lives.
| Sign of EC | What happens | Relationship | Example |
|---|---|---|---|
| Positive + | One gets dearer, people buy more of the other | Substitutes | Pre-cut veg price +10%, bagged salad sales +5% → +0.5 |
| Negative − | One gets dearer, people buy less of the other | Complements | Bagged salad price +15%, dressing sales −6% → −0.4 |
| About zero | Nothing much happens | Unrelated | Bagged salad price +15%, dish sponge sales flat → ≈ 0 |
A positive coefficient means the quantities move with the price — one gets dearer, people buy more of the other. They are competing for the same want. A negative coefficient means they move against it. They are consumed together, so dampening demand for one drags the other down with it.
A negative income elasticity means something entirely different — an inferior good, one people buy less of as they get richer. Same sign, different formula, different question. Check which variable is in the denominator before you name the relationship.
And because the relationship is just a ratio, it runs backwards as a prediction. Rearranged:
% change in Qd = EC × % change in P
Which is how a grocer discovers that a price increase on bagged salad is not a decision about salad. If the dressings on the next shelf are complements with EC = −0.4, then raising the salad price 15% costs the shop 0.4 × 15 = 6% of its dressing sales as well. The goods were never independent; the coefficient just made the dependence legible before the monthly numbers did.
The through-line
Three tools, one habit.
Hold price fixed and ask what moved. Check whether your two effects agree or disagree before you commit to a direction. And when you want magnitude rather than direction, work in proportions, because proportions are the only thing that compares across units.
Markets rarely hand you one clean change at a time. What the model offers is not a way to make the ambiguity disappear — it is a way to say precisely how much of the outcome you know, and precisely which part you don't.
Five questions to test yourself
Work each one through before opening the answer. These are the specific places where understanding and recognition come apart.
01The two-shift table, from scratch
A drought raises the price of cocoa beans, and at the same time a widely shared study reports health benefits from dark chocolate. Build the two-row table for the dark chocolate market and state what you can and cannot conclude.
Answer
The drought raises an input cost, so at any given price producers will make less: supply shifts left — alone, price up, quantity down. The study changes tastes, so at any given price more people want chocolate: demand shifts right — alone, price up, quantity up.
The price column agrees, so price definitely rises. The quantity column disagrees, so quantity is ambiguous: it rises if the demand shift is larger, falls if the supply shift is larger, and is unchanged in the knife-edge case. Without magnitudes you cannot say which, and claiming one is the error.
Note that this is the same structural problem as the tomato market — same two directions, so the same answer shape. Recognising that is the skill.
02When the other variable is the certain one
A new factory technique cuts the cost of making laptops, and in the same quarter a recession cuts household incomes (laptops are a normal good). Which of price and quantity can you call?
Answer
Cheaper production: supply shifts right — alone, price down, quantity up. Falling income for a normal good: demand shifts left — alone, price down, quantity down.
Now the price column agrees: price definitely falls. The quantity column disagrees, so quantity is ambiguous.
It is worth seeing a case where quantity is the certain one. Supply right plus demand right gives a definite rise in quantity and an ambiguous price. The rule is never "price is the certain one" — it is "read the columns."
03The ceiling arithmetic
On the shifted tomato market, quantity supplied is Qs = −50 + 20P and quantity demanded is Qd = 140 − 20P, with P in dollars per kilo and Q in tonnes. The original equilibrium, before either event, was $4.00 and 40 tonnes. A ceiling is set at $4.00. Find the quantity traded, the shortage, and compare the quantity traded with the original 40.
Answer
First confirm the cap binds. Free-market equilibrium: 140 − 20P = −50 + 20P → 190 = 40P → P = $4.75. The cap at $4.00 is below that, so it binds.
At P = 4: Qs = −50 + 80 = 30 tonnes; Qd = 140 − 80 = 60 tonnes.
The quantity traded is whichever side is smaller — you cannot buy tomatoes nobody grew — so 30 tonnes. The shortage is 60 − 30 = 30 tonnes.
And 30 is below the original 40. The cap restores the old price but not the old quantity, because the levy moved the supply curve underneath it. Anyone arguing the cap returns the market to how things were last winter has restored one number and lost the other.
04Two revenue tests, one of them a trap
(a) A campus café raises coffee from $2.40 to $2.75 and weekly cups fall from 1,400 to 1,310. Elastic or inelastic? (b) In the tomato market, the outcome went from $4.00 × 40 tonnes to $4.75 × 45 tonnes. Apply the total revenue test and explain what goes wrong.
Answer
(a) Before: 2.40 × 1,400 = $3,360. After: 2.75 × 1,310 = $3,602.50. Price rose and revenue rose — same direction — so demand is inelastic over this range. Quantity moved proportionally less than price did. (The coefficient confirms it: roughly −6.6% ÷ +13.6% ≈ −0.49.)
(b) Revenue went from $160,000 to $213,750 a week — up, alongside a price rise, which the test would read as inelastic. That conclusion is meaningless. The test requires a movement along one demand curve, and here demand itself shifted: the two points sit on D₀ and D₁, two different curves. Quantity rose because the campaign brought new buyers in, not because the higher price drew them in.
The check to run first is always the same one from the top of this post: did anything other than price change? If yes, you are looking at a shift, and the revenue test does not apply.
05Sign, name, prediction
A city raises bus fares 15% and rides taken on a ride-share service rise 6%. (a) Compute the cross elasticity and name the relationship. (b) Predict the effect on ride-share rides of a 25% fare rise. (c) The ride-share company also finds a negative income elasticity for its service. What does that mean — and why is it not a contradiction?
Answer
(a) EC = +6% ÷ +15% = +0.4. Positive, so bus travel and ride-share are substitutes — dearer buses push people toward the alternative. The magnitude 0.4 says the link is real but mild; they are not close substitutes.
(b) % change in Qd = EC × % change in P = 0.4 × 25 = +10%. This assumes the coefficient is stable over that larger range, which is exactly the assumption to flag out loud.
(c) A negative income elasticity makes it an inferior good — people use it less as their incomes rise, perhaps switching to owning a car. That is a statement about the response to income, not to another good's price. Different denominator, different question, so no contradiction. Negative signs mean nothing until you know which elasticity you are reading.
A short checklist before you answer a shift question
- Each event classified before any drawing — demand or supply, left or right.
- The "hold price fixed" test actually applied, not assumed. If the event is a price change, it is a movement, not a shift.
- A two-row table written out, with both columns filled in for each shift alone.
- Only the agreeing column stated as a direction. The disagreeing one stated as ambiguous, with the condition that would settle it.
- Any price control drawn on the post-shift curves, and the traded quantity read off the short side.
- Elasticity claims checked for a shift first — the revenue test only reads movements along a fixed demand curve.
- Cross elasticity named by its sign, and the denominator checked so income elasticity isn't mistaken for it.
Reading a two-shift diagram is one thing; dragging supply and demand until the ambiguity flips direction is another.
Open the Market Lab →