Supply & Demand Equilibrium Calculator

Market equilibrium is the price at which the quantity buyers want equals the quantity sellers will supply, so nothing is left over on either side. With linear curves the algebra is short: demand is Q = a + bP with b negative, supply is Q = c + dP with d positive, and setting them equal gives P = (a - c) divided by (d - b). The calculator solves that and reports the price, the quantity traded at it, and the demand and supply quantities separately so the two can be checked against each other.

The loaded figures work through in one line. Demand of Q = 1000 - 5P and supply of Q = 200 + 3P give P = (1000 - 200) divided by (3 + 5), which is 800 over 8, or 100. At that price demand is 1000 - 5(100) = 500 and supply is 200 + 3(100) = 500. The two match, which is what equilibrium means. Move either curve and the point moves with it: adding 200 to the demand intercept takes the price to 125 and the quantity to 575, while adding 200 to the supply intercept takes the price down to 75 and the quantity up to 625.

That last pair is worth sitting with, because it contradicts a common misreading. Equilibrium is not the price that produces the largest quantity traded. Shifting supply outward raised the traded quantity from 500 to 625 while the price fell, so the equilibrium quantity is whatever the two curves happen to produce rather than a maximum a seller can aim for. Equilibrium describes where a competitive market settles, not where a firm's profit is highest, which is a different calculation involving marginal revenue and marginal cost. A firm with pricing power will generally hold quantity below this point and charge more.

A worked example

Demand of Q = 1000 - 5P against supply of Q = 200 + 3P gives an equilibrium price of 100 and an equilibrium quantity of 500 units. Both curves return 500 at that price, which is the check the tool displays as separate demand and supply rows.

The result card carries one redundancy worth knowing about. Equilibrium Quantity and Demand at Eq are computed from the same expression and always show the same figure; Supply at Eq is calculated independently from the supply curve, so it is the row that actually confirms the two sides agree. If those two ever differed, the inputs would not describe a single crossing point.

What moves the number most

The slopes move the price far more than the intercepts do, which is the opposite of what the shape of the formula suggests at a glance. A one-unit change in either intercept moves the equilibrium price by 0.125, since the intercept difference is divided by the slope gap of 8. A one-unit change in either slope moves it by 12.5, a hundred times as much, because the slope sits in the denominator. Steepening demand from -5 to -50 drops the equilibrium price from 100 to 15.09; flattening it to -0.5 raises the price to 228.57.

Measured proportionally the picture is closer but still ordered the same way. A 1% increase in the demand intercept raises the price 1.25%, a 1% steepening of the demand slope lowers it 0.62%, a 1% rise in the supply intercept lowers it 0.25%, and a 1% steepening of supply lowers it 0.37%. The demand side dominates in both readings, which is why estimating the demand curve carefully matters more than refining the supply figures.

The formula behind this

Setting demand equal to supply gives a + bP = c + dP. Collecting terms produces P = (a - c) divided by (d - b), and substituting that price back into either curve gives the equilibrium quantity.

One boundary is worth noting. The formula returns a price whether or not it is economically meaningful: if the supply intercept exceeds the demand intercept, the arithmetic produces a negative equilibrium price. Entering a supply intercept of 1200 against a demand intercept of 1000 returns -25, and the tool flags the market as not clearing, though it still reports a quantity for that price. A negative result means the curves cross outside the region where a market exists, not that the calculation failed.