Q.The total (industry) demand and supply functions for a commodity sold in a perfectly competitive market are given as Qd = 200 − 4P and Qs = −40 + 6P, where P is price (in ₹) and Q is quantity (in units). Find the equilibrium price and equilibrium quantity, and verify your answer.

Market equilibrium under perfect competition is simply the price at which the two independently stated functions give the same quantity.

Both functions independently return the same quantity at this price, which is exactly what confirms equilibrium.

Equilibrium in a perfectly competitive market occurs where the quantity demanded exactly equals the quantity supplied, so the first step is to set the two given functions equal to each other and solve for price.

Collecting the price terms on one side and the constants on the other,

So the equilibrium price is ₹24.

To find the equilibrium quantity, this price is substituted back into either function — and, as a dual-solve check that the algebra is correct, it should be substituted into both, since the two independently computed answers must agree if the value of P found is correct. From the demand function,

and from the supply function,

Both calculations independently give 104 units, confirming that P = ₹24 and Q = 104 units together satisfy the equilibrium condition Qd = Qs.

Economically, this means that at any price above ₹24, the quantity sellers wish to supply would exceed the quantity buyers wish to buy (a surplus), pushing price back down toward ₹24; at any price below ₹24, quantity demanded would exceed quantity supplied (a shortage), pushing price back up toward ₹24. Only at P = ₹24 does the plan of every buyer match the plan of every seller exactly, with no tendency for price to move further — which is exactly what makes it the equilibrium.

This can also be solved graphically: plotting Qd = 200 − 4P and Qs = −40 + 6P on the same price–quantity axes, the two straight lines intersect at exactly the point (P = 24, Q = 104) found algebraically above — the graphical and algebraic methods must always agree.

A common slip is combining the P terms incorrectly — always move all P terms to one side and all constant terms to the other before dividing, and double-check by substituting the answer into both original functions, not just one.