The demand and supply functions of commodity x are given as follows: Qd = 20- 2p, Qs = 6p - 12 where p =…

Analyze the question: Equilibrium price is the price at which quantity demanded equals quantity supplied (Qd = Qs).

Concept: At equilibrium, the market clears, so we set the demand function equal to the supply function and solve for p.

Solution:

Qd = Qs

20 − 2p = 6p − 12

Collect the p terms on one side and the numbers on the other:

20 + 12 = 6p + 2p

32 = 8p

p = 32 ÷ 8 = 4

Check by substitution:

• Qd = 20 − 2(4) = 20 − 8 = 12
• Qs = 6(4) − 12 = 24 − 12 = 12

Both are equal at 12 units, so the equilibrium price is N4 and the equilibrium quantity is 12.

Why the other options fail:

• N8: Qd = 20 − 16 = 4, but Qs = 48 − 12 = 36, so there is a large surplus.
• N2: Qd = 16, but Qs = 0, so there is a shortage.
• N10: Qd = 0, but Qs = 48, so there is a surplus.

Exam tip: For any "find equilibrium" question with linear functions, always set Qd = Qs. If you are short on time, plug the options back into both equations. The correct price is the one that gives the same quantity for both. Always double-check by substitution, since it takes only a few seconds.