How to Calculate a Limit Price
A limit price equals the entrant's minimum average total cost minus a small undercut margin, low enough that entry would lose money and still above the incumbent's own cost.
The Limit Pricing formula
Calculator
Enter the entrant's cost, the incumbent's cost and both quantities to get the limit price and what deterrence costs.
Cost per unit a newcomer would face at the scale it could start at.
How far below the entrant's cost the incumbent sets its price.
The established firm's own cost per unit at its current scale.
A low price moves more units, which softens the profit sacrifice.
What the firm would charge if entry were impossible.
Fewer units, because the higher price prices some buyers out.
Charging $11 leaves a newcomer unable to cover its own cost per unit.
- Profit at the limit price
- $600,000
- Profit with no entry threat
- $845,000
- Profit given up to deter entry
- $245,000
- Entrant's margin per unit
- −$1
- Does the strategy hold?
- Entry deterred, incumbent still profitable
The incumbent's margin times the units it moves at the lower price comes to $600,000.
Charging what it likes and selling less would earn $845,000 instead.
Holding the low price costs $245,000 per period, which only pays if entry would take away more than that.
A newcomer selling at this price would make −$1 on every unit, which is the whole point of setting it there.
The price has to sit between the two firms' costs: below the entrant's so entry loses money, above the incumbent's so deterrence does not.
How to calculate Limit Pricing, step by step
- 1Find the entrant's minimum average total cost. Work out what a newcomer would pay per unit at the scale it could realistically start at, which is usually higher than the incumbent's because it starts small.
- 2Set the price a little under that figure. The limit price is the entrant's cost minus a small margin, so a newcomer selling at the going price would lose money on every unit it made.
- 3Check the incumbent still covers its own cost. The limit price has to stay above the incumbent's average total cost. If it does not, the firm is paying more to deter entry than entry would have cost it.
- 4Work out profit at the limit price. Profit equals the limit price minus the incumbent's cost per unit, times the quantity it sells at that lower price.
- 5Compare with profit at the unconstrained price. The difference is what deterrence costs each period. It is worth paying only if entry would take away more than that over the years the rival would stay.
Worked example: Limit Pricing
An incumbent produces at $5 a unit while a newcomer starting small would face $12. Pricing $1 under that cost puts the limit price at $11, and at $11 the firm sells 100,000 units for (11 − 5) × 100,000 = $600,000. Left alone it would charge $18 and sell 65,000 units for (18 − 5) × 65,000 = $845,000, so deterrence costs 845,000 − 600,000 = $245,000 a year. A newcomer selling at $11 against its own $12 cost loses $1 a unit, so it stays out, and the incumbent still clears $6 on everything it sells.
Limit Pricing questions
What is the difference between limit pricing and predatory pricing?
A limit price stays above the incumbent's own average total cost and aims at firms that have not entered yet, so the firm gives up profit but keeps earning. Predatory pricing goes below cost to force out a rival already in the market, which means accepting an outright loss and counting on raising prices afterward.
Does the incumbent lose money at the limit price?
No. The limit price sits between the two firms' costs, so it covers the incumbent's cost per unit while falling short of the entrant's. The firm sacrifices the higher profit it could have made at the unconstrained price, not its solvency.
What if the entrant has the same costs as the incumbent?
Then the strategy collapses. Any price low enough to make entry unprofitable would also be below the incumbent's own cost, so it would be losing money to keep a rival out. Limit pricing needs a genuine cost advantage, usually from economies of scale or an established volume a newcomer cannot match at first.
How do you tell whether the limit price is worth holding?
Compare the profit given up each period against the profit entry would take away permanently. In the example the firm sacrifices $245,000 a year, so the low price pays as long as a rival's arrival would have cost it more than that every year it stayed.
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