In short: When output is the binding constraint, a price increase adds contribution at no volume cost for as long as demand at the new price still exceeds what you can make, so the estimate you need is the market clearing price rather than an elasticity. Allocation rations too, and it gets paid for in order inflation, which Lee, Padmanabhan and Whang named in 1997 as one of the four causes of the bullwhip effect. The expensive part of the price route arrives afterwards, when a customer who qualified an alternative supplier during the shortage carries on buying from them. Run that payback before the argument, and check your notice periods before you run anything.
The plant can make 700 tonnes this quarter and the order book says 1,000. The supply review has been going forty minutes and the room has settled into two camps. Sales wants a fair share cut so nobody can accuse them of picking winners. The commercial director wants twelve percent on the price, on the grounds that anything you have to ration is underpriced. Neither camp has a number behind its own side.
What scarcity does to the pricing question
In ordinary conditions a price increase is a bet against volume. You give up units to gain margin per unit, and the exercise turns on an elasticity that is difficult to estimate at pack and channel level, which is C1's subject.
A binding supply constraint changes the shape of that trade. You cannot sell more than 700 tonnes whatever you charge, so the volume given up by raising price is zero, all the way down to the point where demand at the new price falls below 700 tonnes. Past that point every further increase turns away units you could have sold, and under scarcity those units carry full contribution.
Put the arithmetic on the table. List price 4,200 a tonne, variable cost 2,600, contribution 1,600. Allocate 700 tonnes at list and the quarter delivers 1.12 million of contribution. Move to 4,704, a twelve percent increase, and the same 700 tonnes delivers 1.47 million. That is 353 thousand more from the same tonnes, the same customers and plant. Twelve percent on price produces about a third more contribution, because all of it lands on the margin.
The condition attached gets skipped in the meeting. It holds only while demand at 4,704 still exceeds 700 tonnes, so the quantity to estimate is the price at which demand falls to exactly what you can make. That single point matters more than the shape of the demand curve anywhere else.
Allocation rations too, and it has a price of its own
The choice usually gets framed as moving price against doing nothing, which is wrong. Allocation is a rationing mechanism with costs of its own, paid in a currency that never appears in the quarter's margin.
Proportional allocation, where every customer receives the same percentage of what they asked for, gives each buyer a reason to ask for more than they need. Lee, Padmanabhan and Whang described this in Management Science in 1997 as the rationing game, one of the four causes of the bullwhip effect they identified, and a buyer works it out in seconds. If you will receive seventy percent of your order, order forty percent more than you want. Once several accounts have done that the order book has stopped measuring demand, the allocation percentage falls further, and the incentive strengthens.
Allocation on historical purchases, sometimes called turn and earn, was analysed by Cachon and Lariviere in Management Science in 1999. It removes the incentive to inflate the current order and replaces it with an incentive to buy ahead in normal periods to build entitlement for the next shortage. That version is quieter and expensive, since it pushes stock into the channel for reasons unconnected to consumption.
Allocation therefore carries two charges: a corrupted demand signal while it runs and a corrupted history afterwards. Stripping the inflation out later depends on whether your system recorded requested quantity separately from allocated quantity, and most do not, which leaves the period as censored history of the kind D1 deals with.
The two mechanisms select different customers
Price rations by willingness to pay and allocation rations by past purchases, so the two pick out different buyers. That difference matters more than the contribution arithmetic does.
Willingness to pay in an industrial shortage comes from the value of your input inside the buyer's own process, from whether that buyer is short downstream as well, and from whether they intend to consume the material at all. The last group is the problem. In a genuine shortage the highest bidder is often a trader with no line to feed, and the tonnes you sold at a premium return as competing supply once the shortage clears, priced between what they paid and your list. The arbitrage that follows belongs to PP3, and a shortage is where most of it gets created. Allocation on history picks buyers who bought before, a crude proxy for who buys afterwards and a weak one in a growing category.
So the version worth running combines the two. Hold a base tranche allocated on history, at list, for the accounts you intend to keep, and price the marginal tranche. Two thirds and one third is a common split with nothing special about it. What the split buys is a contained experiment, since the price at which that tranche clears is the only clearing price observation you are going to get.
Fairness is a constraint with measurements behind it
Kahneman, Knetsch and Thaler set the reference point in the American Economic Review in 1986, working from telephone surveys. A hardware store raises the price of snow shovels from 15 dollars to 20 the morning after a snowstorm, and eighty two percent of respondents rated the action unfair. The same work produced the principle they called dual entitlement: a firm is entitled to its reference profit and a customer to their reference price, so an increase that defends a margin against a cost rise reads as acceptable while an increase that captures a demand shift does not.
That maps onto instruments you already have. A surcharge tied to a named external index sits on the acceptable side of dual entitlement. A premium justified by scarcity sits on the other side, and gets described in those terms to your competitors, your customer's procurement team and a regulator.
Anderson and Simester measured the aftermath in the Quarterly Journal of Economics in 2010, using field experiments run with a catalogue retailer. Customers who had previously bought an item at a lower price and then encountered a higher one reduced their later purchases from the firm, and the effect reached beyond the transaction where the increase happened. Customer antagonism has a size and a decay period, which puts it in the same comparison as the contribution gain.
There is also a legal floor. California Penal Code section 396 caps increases at ten percent above the pre-emergency price for a defined list of goods during a declared state of emergency, and New York General Business Law section 396-r prohibits unconscionably excessive prices during an abnormal market disruption without naming a percentage. Most industrial inputs sit outside these statutes, and the definitions of covered goods are broader than they look.
Moving net price without moving the reference price
The reference price is the expensive thing to damage, and four instruments change what a customer pays this quarter while leaving it intact. All of them avoid the straight list increase justified by strong demand, which gets quoted back at you and is the hardest to reverse.
Withdraw discount rather than raise list. Most industrial net prices are a list less a stack of discounts, and removing two points of a growth discount the customer is not currently earning moves net price without touching the number they anchor on. It also reverses without an announcement.
Surcharge against a named index, with the exit condition written down. Alloy surcharges in stainless steel and bunker adjustment factors in container shipping both work this way, and both survive scrutiny because the driver is external, published and symmetric. Write the removal trigger at the same time as the surcharge, since a surcharge with no stated exit becomes a permanent increase the first time the index falls and you keep it.
Price the lead time instead of the product. Charge a premium for a slot inside the current lead time and hold list for anything ordered at standard lead time. This rations by urgency and leaves the customer a way to avoid the premium that does not involve leaving.
Tender the marginal tranche. Contain the move to supply above everyone's base allocation, so the reference price for the base survives and a clearing price observation arrives as a by-product.
The cost that lands after the shortage
The case against a price move is usually made as a relationship statement, which is why it loses to a contribution number. The mechanism underneath it converts into arithmetic.
A buyer facing twelve percent on a constrained input starts a project to qualify an alternative source, because your increase is the event that finally makes their internal business case. Qualification takes months and costs the buyer real money, and it does not get undone when your price comes back down. The supplier they qualified holds a share of that volume permanently, and many procurement functions keep the second source running afterwards as policy.
Run the two against each other. The increase holds for two quarters and delivers 353 thousand a quarter, so 706 thousand in total. One customer taking 120 tonnes a quarter qualifies an alternative and moves forty percent of their volume across for good. That is 48 tonnes a quarter at 1,600 of contribution, 76.8 thousand a quarter, continuing. The price move pays for that single loss in a little over nine quarters and is negative from then on.
Nine quarters is the number to argue about, and the payback lengthens as the switchable share rises. The same increase is defensible on a qualified aerospace fastener with a two year approval cycle and poor on a commodity resin with four interchangeable producers. So the input to estimate is the share of each account's volume that could move to a qualified alternative inside a year, which your key account managers can produce in an afternoon and which matters more than the elasticity does.
When allocation is the better answer
Four conditions make the price route wrong before any of the arithmetic runs.
Where price is fixed by contract for the duration of the shortage, which covers a great deal of industrial supply, the only real discussion is about allocation. Check this first, because supply reviews regularly spend an hour arguing about a lever nobody holds.
Where the product is regulated or the buyer cannot decline, price rationing attracts attention that costs more than the contribution it earns. Pharmaceutical supply is the clear case, and the allocation problem there has its own literature (H6).
Where the shortage is your fault. A customer who is short because your line went down, then asked to pay more for the reduced supply, remembers that sequence for years, and no surcharge wording survives it.
Where the relationship runs much longer than the shortage. Two quarters of scarcity inside a five year agreement is a small event, and the discounted value of the remaining term dominates the contribution a price move can earn. Do the comparison rather than asserting it, since the direction reverses once the shortage is expected to last years.
Where this stops
The central estimate in all of this is the clearing price, and you cannot observe it. Under allocation there are no transactions near it, your order book is inflated by the regime you are trying to replace, and demand is censored at whatever you allocated. Tendering a marginal tranche is the only clean way to get an observation, and it yields one point rather than a curve.
An execution limit decides the question more often than the economics do. Most business to business price changes require contract notice, commonly thirty to ninety days, and key accounts frequently hold price protection or meet competition clauses that delay or cap the move. A two quarter shortage against ninety days of notice leaves one quarter of effect, and the relationship cost is incurred in full.
The qualification hazard behind the payback figure is a judgement rather than a measurement. You will not know which customers started a project until they have finished one, and accounts that announce they are starting one are often signalling. The arithmetic earns its place by forcing that estimate into the open.
Pull the top ten customers on your three most supply limited items and check the notice period and price protection clause in each contract, which tells you whether price is available to you at all before anybody argues about using it.