Take the coffee market again with simple numbers, owned up to as a toy. What buyers want, at each price: Qd = 120 + d − 2P, where P is the price in euros per kilo, Qd the quantity demanded in kilos per day, and d a shift of demand — d rises if coffee becomes fashionable, if incomes rise, if the price of tea climbs. What sellers offer: Qs = 3(P − c), where c is the production cost per kilo. Read that second line: as long as the price does not cover the cost, nobody sells (Qs = 0 when P = c); beyond that, every extra euro of price brings out 3 kilos. One point of method that catches everybody: here we write quantities AS A FUNCTION of price, whereas the usual diagram puts price on the vertical axis and quantity on the horizontal one. Same relation, axes swapped.

The equilibrium price is the one that equalises the two quantities. Set Qd = Qs: 120 + d − 2P = 3(P − c), i.e. 120 + d − 2P = 3P − 3c. Gather the P terms on one side: 120 + d + 3c = 5P, hence **P\* = (120 + d + 3c)/5**. Substituting into either line, the quantity traded is Q\* = (360 + 3d − 6c)/5. Take the base case, d = 0 and c = 10: P\* = (120 + 30)/5 = €30/kg, and Q\* = (360 − 60)/5 = 60 kg. Always check, it takes one line: Qd = 120 − 2×30 = 60 and Qs = 3(30 − 10) = 60. The two coincide — it really is an equilibrium.

Knowing that a price rises is not worth much; knowing by how much is. The formula says it at a glance. The cost c is divided by 5 then multiplied by 3: **if the cost rises by one euro, the price rises only by €0.60**. Put another way, out of every euro of cost increase, 60 cents are passed on to the buyer and 40 stay with the seller, who eats into the margin — because raising the price further would cost too many customers. That sharing has a name: the INCIDENCE of a shock, that is, the way its burden splits between buyer and seller — 60/40 here. It depends on how sensitive each side is to price: the side that can most easily walk away bears the smaller share (course “Price elasticity and tax incidence”). In the same way, a shift d of demand translates into d/5 on the price: +50 kg of demand yields only +€10. Keep the principle: in this model, a shock is never passed on in full. (The word “never” calls for a caveat, and an instructive one: if buyers could not do without the product at all — a life-saving medicine — they would accept any price and the whole extra cost would be passed on to them. So the sharing depends entirely on who can walk away.)

What remains is the leap the title promises. Stay with our toy coffee and the drought: the cost goes from 10 to €20, the price from 30 to €36, i.e. +20%. To know what that does to the price INDEX, you must weight it by the place of coffee in the budget: if that product is 0.5% of household spending, the index rises only by 0.005 × 20% = 0.1 point. (Real coffee did far more in 2024; we shall put a figure on it in the solving step — but the method is exactly this one.) A spectacular surge, an almost nil effect on the cost of living. That is how any newspaper headline about an exploding price should be read. For the INDEX to take off, you need on the contrary a cause that touches every market at once: a rise in energy that enters every cost, a general rise in wages, aggregate demand that is too strong, or more money in circulation (courses “The causes of inflation” and “Shocks and AS-AD equilibrium”). Click each term: