15 The Moves Before the Price
Every parameter in the last four chapters was a decision somebody made
The last part treated competition as a fight about price. Two firms, two prices, one equilibrium, and everything else held still while they argued.
That was the right place to start, because price is where rivalry finally settles and it is the variable both firms can change on a Tuesday. It is also the last thing that happens. By the time two firms are adjusting prices against each other, most of what decides the outcome has already been decided.
Look back at what that analysis needed before it could produce a single number: an appeal, a price sensitivity, two directions of switching, a unit cost. Six parameters, taken as given. Not one of them was given. Each is the residue of a decision somebody made, usually years earlier, usually without thinking of it as a competitive move at all.
The Parameters Were Decisions
This is worth being concrete about, because the abstraction hides how ordinary these decisions are.
| Decision | What it moves |
|---|---|
| Reach — advertising, distribution, listings, being findable | a — how many people know about you and can buy |
| Distinctiveness — features, design, service, brand | b and the two d's — how readily people leave over price |
| Segment — who you decide to sell to | all of them — a different population has different sensitivities |
| Make or buy, process, automation | c — what one unit costs to deliver |
| Size of the commitment — space, equipment, headcount | f — the bar volume has to clear |
| Exclusivity — contracts, shelf space, integration | the d's — how easily a rival reaches your customers |
Read that table in the direction founders actually experience it. Nobody sits down to choose a substitution coefficient. They decide whether to sign the exclusive supply deal, whether to add the feature, whether to lease the bigger space, whether to sell to students or to families. The coefficient is what those decisions look like from the outside, months later, when somebody estimates a demand system.
Which means the six parameters are not facts about your market. They are the accumulated shape of your own past decisions, and the ones you have not made yet are still open.
Equilibrium as a Profit Engine
That reframing turns the machinery of the last part into something you can point at a decision.
You have a procedure that takes six parameters and returns an equilibrium: two prices, two quantities, two profits. Feed it one set of parameters and it tells you what happens. Feed it a different set and it tells you what would happen instead. The procedure does not care where the parameters came from.
So a structural decision can be evaluated the same way a price can:
- Say what the decision does to the parameters.
- Recompute the equilibrium.
- Compare the profit to what you would have had.
Step one is the hard step and it is the only one that needs judgment. Steps two and three are arithmetic, and the competition app or any competent AI will do them while you wait.
That is the whole method of this part. What makes it worth a part rather than a paragraph is that the answers it produces are frequently not the ones anybody expected.
Running the Engine Once
Return to Smart Cookie and Hogi Yogi, whose estimated demand system the chapter on advantage already put on the table.
Hogi Yogi is the frustrated firm. It has the cost advantage, twenty-five cents a unit, and it is losing anyway — charging $1.02 against Smart Cookie’s $1.53, and earning $0.96 per person per month against $1.33. Suppose an advertising agency offers it a campaign: for $0.50 per person per month, the campaign will add one more unit of consumption per person per month.
That is a real offer with a real price, and it is exactly the kind of decision the table above describes. It buys reach, so it moves \(\mathsf{a_{hy}}\) and nothing else. The products do not change, so distinctiveness is untouched. Costs per sandwich do not change.
Before deciding, notice how easy it is to answer badly. The campaign adds a unit at $0.50 per person, and Hogi Yogi’s contribution is about fifty cents a unit, so the extra unit roughly pays for the campaign and no more. A close call, probably worth it. That reasoning treats the demand curve as a thing that sits still while you add units to it.
It does not sit still, because prices move once the curve does. Recompute the equilibrium with \(\mathsf{a_{hy}}\) raised by one and everything else unchanged:
| Smart Cookie price | Hogi Yogi price | Smart Cookie profit | Hogi Yogi profit1 | |
|---|---|---|---|---|
| Before | $1.53 | $1.02 | $1.33 | $0.96 |
| After Hogi Yogi advertises | $1.74 | $1.18 | $2.11 | $1.14 |
| Change | $0.21 | $0.16 | $0.79 | $0.17 |
| 1 Hogi Yogi's profit is net of the $0.50 campaign. Per person per month. | ||||
Hogi Yogi should buy the campaign. Its profit goes from $0.96 to $1.14, a gain of seventeen cents on a fifty-cent investment. Thin, and positive, and the naive arithmetic was in the right neighborhood.
Now look at the column it was not watching. Smart Cookie’s profit rises from $1.33 to $2.11. Smart Cookie did not advertise, did not change its product, did not change its price deliberately, and did not spend a cent. It gained seventy-nine cents, which is more than four times what Hogi Yogi got for paying.
And the gap between the two firms, the thing Hogi Yogi was actually trying to close, goes from thirty-six cents to ninety-eight cents. It nearly tripled.
Why the Spillover Runs That Way
That result is not a quirk of these numbers. It follows directly from the asymmetry the differentiation chapter made the center of the argument.
The campaign puts more people in the market for an ice cream sandwich. Those people then face two prices. And this pair of firms has wildly lopsided switching: when Hogi Yogi’s price rises, 5.57 units of demand move toward Smart Cookie, while a rise in Smart Cookie’s price sends only 0.55 back the other way.
So expanding the pool hands the differentiated firm most of the expansion. Worse for Hogi Yogi, the extra demand lets it raise price from $1.02 to $1.18, and every cent of that rise pushes customers toward the rival, whose own best response is to raise price too, from $1.53 to $1.74. Both firms end up charging more and selling more, and the one with the loyal customers captures most of it.
The lesson is not that Hogi Yogi should skip the campaign. It should buy it; seventy-eight cents is seventy-eight cents. The lesson is that a move that improves your position and a move that closes a gap are different moves, and reach is the first kind. Buying reach in a market where you are the substitutable firm subsidizes the firm you are trying to catch.
Closing that gap would require moving \(\mathsf{b}\) or the \(\mathsf{d}\)s — making Hogi Yogi’s own customers less willing to leave. That is a different and more expensive campaign, and no amount of the cheap kind adds up to it.
Why This Has to Be Solved Backwards
Notice the order in which that analysis had to happen.
The decision is the advertising, and it comes first in time. Hogi Yogi signs with the agency, and only afterwards does anyone set a price. But it was impossible to evaluate the decision without first working out what prices would follow it. The second-stage answer had to be computed before the first-stage question could be asked.
That is backward induction, and it is the only way a staged decision can be evaluated. Solve the end first, then use its answer to choose at the beginning.
Backward induction — solving a staged decision from the last stage forward. You cannot judge a move until you know how the game finishes, so you compute the finish first and reason back to the move.
It also explains what the naive arithmetic was missing. One unit at fifty cents of contribution against fifty cents of cost is a first-stage calculation that never solved the second stage, and it assumed the price would stay at $1.02. The price did not stay at $1.02, which is why the campaign was worth rather more to Hogi Yogi than the back-of-envelope suggested, and worth far more than that to Smart Cookie.
What the Engine Cannot Tell You Yet
There is one assumption still buried in all of this, and it is large.
Hogi Yogi was offered the campaign. Smart Cookie was not — or was offered it and did not take it, or had not heard of the agency. The entire analysis above assumes the rival stands still while you act.
That is the assumption the chapter on price competition dismantled at length, and there is no reason it should survive here. Advertising agencies sell to whoever will buy. If the campaign is available to Hogi Yogi it is almost certainly available to Smart Cookie, and Smart Cookie can do the same arithmetic.
Which means the honest version of the question is not what happens if we advertise. It is what happens if we advertise and they do too, or we do and they do not, or they do and we do not, or neither of us does. Four outcomes, each requiring its own equilibrium, and a decision that depends on which one you expect.
That is a game, in the technical sense, and it is the subject of the next chapter. The useful part is that you already have everything needed to build it: the engine that turns parameters into profit, run once for each combination.
Ask yourself — which parameter would this actually move?
Take the largest non-price decision currently in front of you. New feature, new channel, new equipment, a hire, an exclusive deal, a campaign.
Now answer one question about it, in the vocabulary of the last four chapters. Does it change how many people know about you, how willing your customers are to stay when you raise price, how readily people move between you and a rival, or what a unit costs you?
Most decisions move exactly one. If yours seems to move all four, you have described an ambition rather than a decision, and it is worth pushing until you can say which.
Then the harder question, and the one this chapter exists for. If it moves reach, and your rival is the more differentiated firm, ask honestly who captures the customers you are about to create.
The move: A structural decision is evaluated by recomputing the equilibrium it produces, not by adding up its direct effects. The direct effects assume prices hold still, and prices are the one thing guaranteed to move.
Hogi Yogi’s frustration was well founded and its instinct was not wrong. Advertising did help. What it could not do was change the thing that made it the weaker firm, and the reason is visible in the parameters: reach is available to anyone with a budget, while the loyalty that lets Smart Cookie hold a fifty-cent premium was built over years and is not for sale by the month.