The demand function for a good is $Q_d=100-2P$ and the supply function is $Q_s=20+3P$. Find the equilibrium price and equilibrium quantity, and verify your answer by substituting back into both original equations.

Question

Accepted Answer

Market equilibrium requires $Q_d=Q_s$:
$$100-2P=20+3P$$

Collecting P-terms on one side:
$$100-20=3P+2P \Rightarrow 80=5P \Rightarrow P=16$$

Substituting $P=16$ into the demand function:
$$Q_d=100-2(16)=100-32=68$$

**Verification (dual check):** substituting $P=16$ into the SUPPLY function independently:
$$Q_s=20+3(16)=20+48=68$$

Since $Q_d=68$ and $Q_s=68$ agree exactly, both original equations are satisfied by $(P,Q)=(16,68)$, confirming the solution is correct.
> [!ANSWER]
> Equilibrium price = Rs. 16 per unit; equilibrium quantity = 68 units — verified by substituting back into both the demand and supply equations, which each independently give Q=68 at P=16.

Q.The demand function for a good is $Q_d=100-2P$ and the supply function is $Q_s=20+3P$ . Find the equilibrium price and equilibrium quantity, and verify your answer by substituting back into both original equations.

Concept understanding — Linear Equations and Market Equilibrium

Q.The demand function for a good is Qd=100−2PQ_d=100-2PQd​=100−2P and the supply function is Qs=20+3PQ_s=20+3PQs​=20+3P. Find the equilibrium price and equilibrium quantity, and verify your answer by substituting back into both original equations.

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Q.The demand function for a good is $Q_d=100-2P$ and the supply function is $Q_s=20+3P$ . Find the equilibrium price and equilibrium quantity, and verify your answer by substituting back into both original equations.

Unlock everything free for 14 days