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When two curves move at once

A tax hits the factory and a sold-out event hits the showroom in the same spring. One of price and quantity is certain, the other genuinely isn't — and knowing which is which is most of introductory microeconomics.

Dr. Sarva Jeganathan · 25 October 2026 · about 14 minutes

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 a workshop on Vancouver Island that builds high-end mountain bikes. It has found its equilibrium: a price that clears the market, a quantity that sells. Put real numbers on it so we can check our reasoning later — $3,000 a frame, 40 frames a month.

Then two things land in the same spring.

A new tax is applied to aluminum and carbon fibre — the raw materials the frames are made of. And an international cycling competition comes to the Island, putting local trails and, by association, local bikes in front of a global audience.

One event arrived through the loading dock. The other arrived through the showroom door. Neither one is a change in the price of a bike, 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:

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 make this many, at that price I'd make that many — drawn up under a fixed set of costs. Change the cost of carbon fibre 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 bike price, so each one rewrites the demand schedule rather than sliding along it.

Apply the question to the tax: it raises the cost of making every frame, so at any given price the workshop is willing to make fewer. Supply shifts left. Apply it to the competition: at any given price, more people now want one of these bikes. 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.

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.

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. Prices are now noticeably higher than they were in the winter, local buyers are unhappy, and somebody proposes a cap at the old price — $3,000.

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 made, 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 produced 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 input tax means the workshop is no longer willing to make 40 frames at $3,000. It will make 32.

So the policy delivers a lower price to whoever manages to buy a bike, and fewer bikes 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 waiting lists, to relationships with the shop owner, to a resale market the shop cannot control, or to quietly worse components at the same headline price. None of these distribute bikes to the people who value them most, and none of them address what actually happened — which was that frames got more expensive to build and more people wanted one.

The cap treats the price as the problem. The price was the messenger.

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 bookstore drops its magazine price from $7.50 to $6.00 and monthly sales rise from 2,000 to 2,750:

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.

One further trap worth naming: do not try to eyeball elasticity by comparing the raw changes. A drop of $1.50 against a rise of 750 units is a comparison of dollars to magazines, 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?

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.

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.

And because the relationship is just a ratio, it runs backwards as a prediction. Rearranged:

Which is how a bookstore discovers that a price increase on magazines is not a decision about magazines. If the protein bars by the till are complements with E_C = −0.3, then raising the magazine price 20% costs the shop 0.3 × 20 = 6% of its protein bar 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.

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.

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