Case Study 2: The Marginal Cost Curve

🔬 Deep Dive. The most quantitative material in Part I. We compute the complete cost curve for one wedding from 100 to 200 guests, identify every discontinuity, and derive the practical rules that follow. If you build one artifact from this book before Chapter 6, build this one.

Tier 3 — Illustrative. Wildrye Farm's specifications and all pricing are constructed for teaching, at a mid-cost US market level. Re-derive locally before use.

The Setup

Wildrye Farm, September, the Reyes–Whitfield wedding. A raw site: barn, lawn, gravel lot, and almost nothing else.

The constraints that create steps:

The unit costs:

The Curve

📊 Total cost from 100 to 200 guests

$ | ● 62k| ●····· | ●·····●····· 58k| ┃ | ●·····┛ ← 168: tent 50′ 54k| ●····· | ┃ 50k| ●·····┛ ← 151: restrooms | ●····· + generator 46k| ●····· + shuttle | 42k|● +──┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬── 100 110 120 130 140 150 160 170 180 190 200

Alt-text: A cost curve rising from about $42,000 at 100 guests to about $63,000 at 200 guests. The line slopes upward steadily with small sawtooth jumps every eight guests (new tables), punctuated by two large vertical jumps: one at 151 guests and a larger one at 168 guests. The slope between jumps is roughly constant.

The curve is not a line. It is a staircase with a slope, and the two large risers are the whole point.

Every Threshold, 100 to 200

⚡ The complete step map

Guest #	Event	Cost
97	Tent 30′ → 40′	+$1,800
101	Restroom trailer ≤100 → ≤150	+$700
104	13th table	+$147
112	14th table	+$147
120	15th table	+$147
121	Dance floor 12×12 → 16×16	+$220
121	6th server	+$260
128	16th table	+$147
136	17th table	+$147
144	18th table	+$147
145	7th server	+$260
151	Restroom trailer ≤150 → ≤200	+$1,200
151	Generator 25kW → 45kW	+$800
151	4th shuttle run (70% × 151 = 106 riders ÷ 32)	+$420
152	19th table	+$147
160	20th table	+$147
161	2nd bartender	+$310
161	8th server	+$260
168	Tent 40′ → 50′	+$2,500
168	21st table	+$147
176	22nd table	+$147
181	Dance floor 16×16 → 20×20	+$280
181	2nd bar station	+$420
184	23rd table	+$147
185	9th server	+$260
192	24th table	+$147
193	5th shuttle run	+$420
200	25th table	+$147

The two clusters that matter:

At 151: restroom bracket + generator + shuttle = $2,420 in a single guest. At 168: tent frame = $2,500 in a single guest (plus a table).

Guest 150 costs $158.52. Guest 151 costs **$2,578.52. Guest 152 costs $305.52. Guest 167 costs $158.52. Guest 168 costs $2,805.52.**

The Marginal Cost Curve

📊 Marginal cost of each guest, 100–200

$2600| ╷ ╷ | │ │ $2000| │ │ ← 151 and 168 | │ │ $1400| │ │ | │ │ $800| ╷ │ │ | │ │ │ $400| │ ╷ ╷ ╷ │ ╷ ╷ ╷ ╷ ╷ ╷ │ ╷ ╷ ╷ ╷ ← tables, servers | │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ $160|▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔ ← the floor +──┬────┬────┬────┬────┬────┬────┬────┬── 100 120 140 160 180 200

Alt-text: A spike chart of marginal cost per guest. Most guests sit on a flat floor of about $160. Small spikes of $150 to $550 occur regularly where tables and servers are added. Two very tall spikes exceed $2,500 — at guest 151 and guest 168.

Ninety-two of the hundred guests in this range cost $158.52.** Six cost between $305 and $580. **Two cost more than $2,500.

That distribution is why the average is useless. The mean marginal cost across 100–200 is about $228, and there is not a single guest in the range who actually costs $228.

The Rules That Follow

Rule 1: Find the plateaus and camp on them

The cheapest places to sit are just below a cluster.

Practical consequence. A couple hovering at 148 should be told, plainly: "You have three free names. Adding a fourth costs $2,578."

That sentence is worth more than any other single thing you can say about their guest list, and it is available only to a planner who built the map.

Rule 2: Cut to a threshold, never past it

A client at 154 who needs to save money should cut to 150, not to 145. Cutting four names saves $2,420 + $317 = **$2,737.** Cutting nine saves $3,530 — an additional five names for $793, which is $159 each.

The first four names are worth $684 apiece. The next five are worth $159 apiece.

Tell the client that. "The first four names save you two thousand seven hundred dollars. Every name after that saves a hundred and sixty. So cut four, and then stop unless you need a lot more."

Rule 3: The invitation count and the planning count are different numbers

At 84% forecast attendance:

A couple inviting 180 is planning a wedding whose cost depends on a forecast being right to within one person. That is an unacceptable position, and it is invisible to anyone who has not built the map.

The correct advice at 180 invited: either commit to the larger infrastructure now and budget for it, or bring the invitation count to 172, where a forecast error of ±6% still lands under the step.

Rule 4: Size step items to the plausible high, variable items to the forecast

Because the two error directions cost differently:

• Step items (tent, restrooms, generator, shuttle, dance floor) are booked early, cannot be changed late, and fail publicly. Size them to the high end of the plausible attendance range.
• Variable items (food, place settings, chairs, favors) are set at the guarantee, ten to fourteen days out, when you actually know. Size them to the confirmed count plus 2–3%.

A planner who sizes the tent to the forecast and the food to the invitation count has it exactly backwards, and both errors are expensive.

🔍 Why Does This Work? Because the two categories have different reversibility, not different uncertainty. Both are uncertain. But a 40′ tent booked in month four cannot become a 50′ tent in week two — the inventory is gone — whereas food can be adjusted right up to the guarantee. When you cannot change your mind, buy the version that survives being wrong. When you can, wait.

This principle recurs throughout the book. It is why the rain plan is built in month six (Chapter 28), why the venue's access window is negotiated at booking (Chapter 10), and why the timeline's buffers go in the places that cannot absorb a slip (Chapter 25).

The Full Cost Table

💰 Total cost at selected counts

Guests	Variable	Steps	Fixed	Total	Per guest (avg)	Marginal
100	$15,852 | $9,300	$16,170 | **$41,322**	$413 | $158
110	$17,437 | $9,447	$16,170 | **$43,054**	$391 | $158
120	$19,022 | $9,594	$16,170 | **$44,786**	$373 | $158
130	$20,608 | $10,221	$16,170 | **$46,999**	$362 | $158
140	$22,193 | $10,368	$16,170 | **$48,731**	$348 | $158
150	$23,778 | $10,775	$16,170 | **$50,723**	$338 | **$2,578**
160	$25,363 | $13,342	$16,170 | **$54,875**	$343 | $158
170	$26,948 | $16,559	$16,170 | **$59,677**	$351 | $158
180	$28,534 | $16,706	$16,170 | **$61,410**	$341 | $158
190	$30,119 | $17,553	$16,170 | **$63,842**	$336 | $158
200	$31,704 | $17,847	$16,170 | **$65,721**	$329 | $158

Read the "per guest (avg)" column. It falls from $413 to $329 as the count rises, because fixed costs spread. This is why "cost per guest goes down as you add people" is a true statement that is nonetheless useless for any decision — it describes the average, and no individual guest ever costs the average.

The Reyes–Whitfield budget is $42,000.** At $41,322, they can afford 100 guests**, not 140. That is the finding this whole case exists to produce, and it is the conversation Chapter 6 has to have.

What This Means for the Progressive Project

Alicia and Sam invited "around 140." At 140 the modeled cost is $48,731** against a $42,000 budget — $6,731 over**, before anything goes wrong and before any contingency.

Three honest paths:

1. Reduce to ~112 guests. Total $43,890. Still $1,890 over, closable with modest trims. Requires cutting 28 names.

**2. Hold 140 and find $6,731.** Cut fixed costs — a cheaper photographer, no videographer, a DJ instead of the band that is not yet booked — plus reduce the variable spend per head from $158 to about $140 by simplifying the menu and the bar. Possible. Produces a noticeably plainer wedding for 140.

3. Hold 140 and raise the budget. Sam's parents' $6,000 was earmarked "for the party." A second ask is a real option and belongs to the couple, not to you.

Whichever they choose, they must choose it in month two. All three paths are open now. In month nine, path 1 costs a kitchen-table crisis, path 2 is foreclosed because the vendors are booked, and path 3 is an emergency ask rather than a considered one.

Discussion Questions

1. Rule 2 says the first four names cut are worth $684 each and the next five are worth $159 each. Is telling a client that manipulative — steering them toward exactly four cuts — or is it simply accurate information? Where is the line?

2. The average cost per guest falls from $413 to $329 across the range. Construct the sales pitch a venue could build from that fact, and then explain what it conceals.

3. Rule 4 distinguishes step items from variable items by reversibility rather than uncertainty. Find a third category in this wedding that fits neither cleanly, and say how you would treat it.

4. At 180 invited, the wedding's cost depends on a forecast being right to within one person. Would you tell the client that in those words? What is the risk of doing so, and of not?

5. The case concludes that the Reyes–Whitfield budget supports 100 guests, not 140. Chapter 1 established that they invited "around 140" and Chapter 3 established that Rosa Reyes's extended family is large and largely non-negotiable. Is path 1 actually available to them? If not, does that change which of the three paths you would recommend, and how you would present it?

Mini-Project

Build this for a real venue.

Pick one venue in your market. Obtain: table configuration and capacity, staffing ratios, restroom provision, tent or capacity brackets, transport requirements, and power. Get real rental pricing for tables, linens, restroom trailers, and generators.

Produce:

1. The complete step map from 60% to 150% of the venue's typical guest count
2. The marginal cost curve — a table or chart showing what each guest costs
3. The plateau list — the three or four counts that are the cheapest places to sit
4. A one-page client version that a couple could read in ninety seconds and use to answer "can we add four more?" without calling you

Then do the thing that turns this from an exercise into an asset: repeat it for your three most-used venues. A planner who can answer the marginal-cost question instantly, for the venues they work at most, has a capability almost nobody else in their market has — and it takes about three hours per venue, once.

References

Tier 3 — Illustrative. All specifications, unit costs, and totals are constructed for teaching at a mid-cost US market level. Staffing ratios (1 server per 20–25 for family style, 1 bartender per 75–85) and restroom and tent bracketing reflect common industry practice (Tier 2) but vary substantially by supplier, region, and event style. Re-derive every number locally.

Related chapters: Cost decomposition and steps — Chapter 5 §5.2–§5.3. Budget construction from this curve — Chapter 6. Tent, generator, and restroom specification — Chapter 13. Bar staffing and consumption — Chapter 15. Catering staffing ratios and the guarantee — Chapter 14. Shuttle sizing — Chapter 29. Reversibility as a planning principle — Chapters 10, 25, and 28.