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Quantitative Foundations: Elasticity & Margins
Course contents

Module · Thinking at the margin

What it really costs

Lesson 2 of 5 · 6 min

What does one more cost? asked what changes if you say yes. This one asks the harder half of the same question: changes compared to what?

The cost of the road not taken

You have $30,000 and two ways to spend it. Marketing wants it for ads. Sales wants it for a new hire.

Both are good. Only one is best.

Ad campaign

Returns over the year
$54,000
Profit
+$24,000

New salesperson

Returns over the year
$64,000
Profit
+$34,000

Run the campaign and the books will say you made $24,000. The books are right and the decision is still wrong, because the campaign did not cost $30,000 — it cost $30,000 and the $34,000 you could have had instead. Measured against the alternative you gave up, running the ads lost $10,000.

Opportunity cost: the value of the best thing you did not do. It never appears in an account, and it decides whether a profitable choice was a good one.

This is why "it made money" is a weak defence of anything. Almost every option makes money. The question is whether it made the most money available at the time — and answering it means putting the options in the same unit, per dollar, over the same period.

Why the second one is always worth less

You are buying leads. The first $10,000 of advertising reaches the people already looking for you. The next $10,000 has to reach people who are harder to find, and so on outward.

Diminishing returns: more spend still buys more leads, but each one costs more than the last.

$10,000

Leads
400
Extra leads for the last $10,000
400
Cost of each extra lead
$25

$20,000

Leads
700
Extra leads for the last $10,000
300
Cost of each extra lead
$33

$30,000

Leads
900
Extra leads for the last $10,000
200
Cost of each extra lead
$50

$40,000

Leads
1,020
Extra leads for the last $10,000
120
Cost of each extra lead
$83

$50,000

Leads
1,080
Extra leads for the last $10,000
60
Cost of each extra lead
$167

Nothing here is broken. Spending more genuinely does bring more leads at every level. The question is where to stop, and that needs one more number: a lead is worth $60 to you.

Now read the last column against $60. At $30,000 the next batch of leads costs $50 each — cheaper than they are worth, so buy them. At $40,000 they cost $83 each — more than they are worth, so don't. Stop at $30,000.

Watch what average cost says here. At $40,000 you have 1,020 leads, which is $39 each against a lead worth $60 — a healthy-looking number that invites you to spend more. But that last $10,000 bought 120 leads worth $7,200. It lost $2,800. The average was still improving while the decision had already turned bad.

Same lesson as last time, one level up: averages describe, margins decide.

The money that is already gone

You have spent $200,000 over eighteen months building something. It needs $50,000 more to finish. Someone asks whether to continue, and the room says: we have already put in $200,000, we can't stop now.

That sentence has the logic backwards. The only question is:

  • Will the $50,000 still to spend earn more than $50,000?
  • Is there anything better to do with $50,000?

The $200,000 does not appear in either question, because no decision available to you now can get it back. It is sunk — the same status the $6,000 of fixed cost had in the last lesson, except that this one is buried in time rather than in a monthly total, which makes it far harder to ignore.

The uncomfortable version: if a competitor offered you the half-finished project for free today, would you spend $50,000 to complete it? If no, then finishing your own is also a no, and the $200,000 is the only difference between the two situations.

Three questions, one habit

Compared to what?

To catch
opportunity cost — a profitable choice that beat nothing

What did the last one buy?

To catch
diminishing returns — spending past the point it pays

Would I start this today?

To catch
sunk cost — throwing good money after committed money

Next: the other half of every pricing decision. We have been asking what things cost us. Now we ask what customers do when the price moves.