Given demand $Q_d=200-0.2P$ and supply $Q_s=-50+0.3P$, what are the equilibrium price and quantity?

### Why this is right At equilibrium, set quantity demanded equal to quantity supplied. Solving $200-0.2P=-50+0.3P$ gives $P=500$; substituting this price into either function gives $Q=100$. ### The concept Equilibrium is the price and quantity at which buyers' planned purchases equal sellers' planned sales. If the market price differs from equilibrium, the resulting excess demand or excess supply creates pressure for adjustment. ### The other options - **$P=100$, $Q=500$**: this reverses the equilibrium price and quantity and does not satisfy both equations. - **$P=250$, $Q=150$**: substituting $P=250$ gives demand of 150 but supply of 25, so the quantities are not equal. - **$P=500$, $Q=150$**: at $P=500$, demand and supply both equal 100, not 150. ### Worked numbers - **Given**: $Q_d=200-0.2P$ and $Q_s=-50+0.3P$. - **Find**: equilibrium price and quantity. - **Formula**: At equilibrium, $Q_d=Q_s$. - **Solve**: 1. $200-0.2P=-50+0.3P$. 2. $250=0.5P$, so $P=500$. 3. $Q=200-0.2(500)=100$. - **Answer**: $P=500$ and $Q=100$. - **Check**: Supply also gives $-50+0.3(500)=100$. ### Remember Find price by equating demand and supply, then substitute to find quantity.