If QD482 3P and QS 490 59P What is the total surplus in t

If Q_D=482 - 3P and Q_S = -490 + 59P

What is the total surplus in this market?

(ROUND TO TWO DECIMAL PLACES)

Solution

At Q_d=0, the P₁=482/3=160.66 and at Q_s=0, P₂=490/59=8.30

At equilibrium, Q_d=Q_s, so,

482-3P=-490+59P

62P=972 => P=15.67

At P=15.67, the equilibrium qty is = 435 units

The total surplus is the combination of the consumer and the producer surplus. Consumer surplus is the surplus amount above the equilibrium price but below the demand curve and producer surplus is the surplus amount below the equilibrium price and above the supply curve.

Therefore the total surplus becomes = 1/2*435*(160.66-8.30)= 33138.3 (Approx Ans)