Pricing with limited capacity

Break-even volume at two prices set against capacity, the lowest price a full month can support, the price a full month needs for a stated profit, and the room a viable price leaves.

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

You will set the break-even volume of a price against the most the business can make, find the lowest price at which a full month covers the fixed costs and the price a full month needs for a stated profit, write a full month's profit as a rule in the price, and measure how much room a viable price leaves.

2. What you already have

You can find a break-even volume: fixed costs divided by contribution a unit. The last two lessons showed every business has a ceiling on what it can make. This lesson puts the two numbers side by side, and from them builds two prices no earlier lesson could give: the lowest price at which a completely full month covers the fixed costs, and the price a full month needs to earn a stated profit. Both are limits, not recommendations, and the lesson keeps the difference clear.

3. Words this lesson uses

4. A break-even point you cannot reach

Corner Bean's lunch service has 6000 dollars a month of fixed costs — the cook, the extra hours, the kitchen's share of the rent — and each plate costs 3 to make. The kitchen can make at most 1500 plates a month.

At 6 dollars a plate, each contributes 3, and breaking even takes 6000 ÷ 3 = 2000 plates. That is 500 more than the kitchen can make. The line can stretch round the block and the price still loses money every month, because the plates that would cover the fixed costs cannot be cooked.

At 8 dollars, each contributes 5, and break-even is 1200 plates: inside capacity, with 300 plates of room.

$$\text{capacity floor price} = \text{variable cost} + \frac{\text{fixed costs}}{\text{capacity}}$$

For the lunches it is 3 + 6000 ÷ 1500 = 7. Any price below 7 fails even in a full month. Any price above it can work, if enough customers will pay it.

Term	What it means
Capacity	The most units the business can make in a month.
Viable price	A price whose break-even volume fits within capacity.
Capacity floor price	The lowest price at which a completely full month just covers the fixed costs.
Room	Capacity less the break-even volume: how far a month can fall short and still cover its costs.
Target price	The price at which a full month earns a stated profit.

Another way: steps

Collect the fixed costs, the variable cost a unit and the capacity.
For a price, find the contribution and the break-even volume.
Set the break-even volume against capacity: viable or not.
Find the floor: variable cost plus fixed costs over capacity.
For a profit target, share fixed costs plus profit over capacity.

Another way: table

Corner Bean's lunch plates: 6000 fixed, 3 a plate, at most 1500 a month.

Price	Contribution a plate	Plates to break even	Within 1500?
6	3	2000	No
7	4	1500	Only when completely full
8	5	1200	Yes, with 300 to spare

The middle row is the floor.

5. The method, step by step, and how to check it

Measure capacity honestly. The most units the business can make in a normal month, with its current people, equipment and hours — not in a record month when everything went right.

Find the break-even volume for each price. Fixed costs over contribution a unit. Keep the exact figure; round it up only when comparing with capacity, because a part-unit is never sold.

Compare with capacity. A break-even volume above capacity means the price cannot work. One below it is viable, and the gap between them is the room.

Find the floor. The variable cost plus the fixed costs shared over capacity. Every viable price is above it.

For a profit target, share the fixed costs and the profit wanted over capacity and add the variable cost.

Check the floor by working a full month at that price: capacity times the contribution should equal the fixed costs exactly. Check a viable price by working the month at its break-even volume: contribution times that volume should equal the fixed costs.

6. Viable is not the same as best

The floor says which prices can work. It does not say which one will. At 8 dollars Alexa might sell 1300 plates or 900; that depends on customers, and no costing sheet knows. So the floor is a filter, used first: strike out every price below it, then think about demand for the prices that are left.

The room between break-even and capacity is worth reading too. At 8 dollars the café can fall 300 plates short of full and still cover the month. A price that breaks even at 1450 of 1500 plates is viable on paper and leaves no room for a wet week.

7. Raise the price or raise the capacity

When a business is full and its price is below the floor, it has two ways out, and they cost very different amounts.

Raise the price. Every unit contributes more and break-even falls. If customers will pay it, this costs nothing but the conversation, and the line at the old price is a sign that many will.

Raise the capacity. More units to spread the fixed costs over lowers the floor. But more capacity usually brings more fixed cost — a second cook, a bigger kitchen — and the floor only falls if the capacity rises faster than the fixed costs do. A café that doubles its kitchen and its fixed costs together has the same floor it had before.

So the first question for a full business with a low price is whether the price can rise. A long line is often the market saying that it can. Only if it cannot is the more expensive route — more capacity — worth working out, and then with the extra fixed costs included in the new floor.

8. Capacity that changes with the season

Capacity is not always the same all year. A garden's packing hours are long in summer and short in winter; a café with outdoor seats has more capacity from May to September; a repair shop may add a Saturday in December. The floor price moves with it: fewer units to share the fixed costs over means a higher floor.

A single year-round price has to clear the floor in the months when capacity is lowest, or those months lose money however full they are. Some businesses solve this with seasonal prices — a winter veg box that costs more than a summer one — and others by keeping enough profit from the high season to carry the low one. Either way, working out the floor month by month shows which months need help.

9. Pricing below the floor on purpose

There are times an owner prices below the floor knowingly: an opening month to fill a new studio, a quiet January offer, a product sold cheaply to bring customers in for others. None of these is wrong, as long as the arithmetic of this lesson is done first and the cost is named.

Say how much it costs. A month at a price below the floor loses money even when full; the loss is the gap between the floor and the price, times the units sold. An opening offer that costs 1,200 over a month is an investment of 1,200 in finding customers, and should be judged like one.

Say when it ends. An introductory price with no end date becomes the price customers expect, and raising it later is harder than starting higher.

Say what it is meant to bring. A cheap product that draws customers who then buy full-price items is judged on the whole basket, not on the one item. If the basket covers the floor, the cheap item has done its job; if customers buy only the cheap item, it has not.

Written down in three lines — the cost, the end date and what it should bring — a deliberate price below the floor is a plan. Without them it is the same loss as an accidental one, and usually lasts longer.

10. In the world: a yoga studio's class price

A yoga studio has fixed costs of 7,200 dollars a month: rent, the instructors' salaries and the booking system. Its room holds 20 mats, and it runs 60 classes a month, so its capacity is 1,200 class places. Each place costs about 1 dollar in towels, laundry and the card fee.

The owner has been charging 6 a class to fill the room, and the room is full. Contribution is 5 a place, so break-even is 7,200 ÷ 5 = 1,440 places — 240 more than the room holds. The studio has been losing about 240 × 5 = 1,200 a month, however full it looks.

The floor is 1 + 7,200 ÷ 1,200 = 7. She wants a profit of 1,800 a month from a full studio, which needs 1 + (7,200 + 1,800) ÷ 1,200 = 8.50. She sets classes at 9, or 80 a month for a ten-class pass that works out at 8. At 9, break-even is 900 places, leaving 300 places of room; at 8, it is about 1,029, leaving 171.

She also looks at capacity. A second room would add 1,200 places and about 4,000 a month of fixed costs, lowering the floor to 1 + 11,200 ÷ 2,400 ≈ 5.67. That is worth doing only if the waiting list is long enough to fill both rooms at the new prices; for now, the price rise comes first.

11. In the world: why budget airlines fill every seat

Airlines work with a fixed capacity on each flight and very high fixed costs. Budget airlines keep their floor price low by flying fuller planes more often, which spreads the fixed costs of each aircraft over more seats each day. The capacity side of the floor-price formula is the one they work on hardest, because it lets them charge less than rivals and still clear the floor.

12. Where this goes wrong

Capacity never matters to price. It decides whether a break-even volume can be reached at all.

A low price makes it up on volume. Only on volume the business can make; past capacity, extra demand is just a longer line.

Any price above variable cost is fine when you are busy. It must also cover the fixed costs within capacity.

The floor price is the right price. It is the lowest that can work, with no room for a bad month.

A break-even volume of 112.5 means 112 will do. Half a screen replacement is never sold. The month covers its fixed costs on the 113th, so a volume that is not whole is rounded up before it is set against capacity.

More capacity always lowers the floor. Only if it rises faster than the fixed costs that come with it.

13. Long Row Gardens' veg boxes

14. Fixit Mobile's screens

15. Corner Bean doubles its lunch kitchen

16. Your turn: fixed costs 1600, variable cost 18, capacity 100

17. Guided practice

Fixit Mobile has fixed costs of $3600$ dollars a month for its screen replacements. Each one costs $30$ dollars to make, and the most it can make in a month is $120$. The owner is choosing between $62$ and $70$ dollars. For each price, fill in the contribution a unit and the monthly volume that breaks even, written exactly.

18. Guided practice

Complete the worked solution: a kitchen has fixed costs of $912$ dollars a month. A meal costs $10$ to make and sells for $18$, and the kitchen can make at most $134$ a month. Is the price viable, and what does a full month earn?

19. Guided practice

Corner Bean has fixed costs of $6000$ dollars a month for its lunch plates. Each one costs $3$ dollars to make, and the most it can make in a month is $1500$. A price of $6$ dollars would bring more customers than it can serve. Can that price cover the month's fixed costs?

20. Practice

Fixit Mobile has fixed costs of $1600$ dollars a month for its battery swaps. Each one costs $18$ dollars to make, and the most it can make in a month is $100$. What is the lowest price, in dollars, at which selling every unit it can make would just cover the fixed costs?

21. Practice

Fixit Mobile has fixed costs of $3600$ dollars a month for its screen replacements. Each one costs $30$ dollars to make, and the most it can make in a month is $120$. Write the month's profit in dollars as a rule in $p$, the price, if it sells all $120$.

22. Practice

A catering kitchen has fixed costs of $1026$ dollars a month and can make at most $171$ platters. A platter costs $11$ dollars to make. The owner wants a profit of $513$ dollars from a full month. What price must a platter sell for, in dollars?

23. Somewhere new

A burger stall pays $700$ dollars for its pitch at a one-day festival. Ingredients cost $2$ dollars a burger, and the griddle can cook at most $200$ burgers in the day. Mark the lowest price at which selling every burger it can cook would just cover the pitch.

24. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

25. Test question

Long Row Gardens has fixed costs of $1800$ dollars a month for its veg boxes. Each one costs $9$ dollars to make, and the most it can make in a month is $150$. It sets the price at $24$ dollars. How many units a month could it fall short of capacity and still cover its fixed costs?

26. What you can do now

You can tell whether a price can cover the month within capacity, find the floor below which none can, and price a full month for a profit. Tell someone why a line round the block cannot rescue a price below that floor. Next: whether a discount earns back what it gives away.

	Contribution a unit	Units to break even
At $62$ dollars
At $70$ dollars