Question

Suppose the following demand and supply function:

Q^d = 750 – 25P

Q^s = -300 + 20 P

      i.         Find equilibrium price and quantity

    ii.         Find consumer and producer surplus

Answer 1

i. At equilibrium:

$Q_s=Q_s \\ -300 +20P=750 -25P \\ 20P+25P = 750 +300 \\ 45P = 1050 \\ P_{eq} = \frac{1050}{45}=23.33 \\ Q_{eq} = -300 +20 \times 23.33 \\ = -300 + 466.66 \\ = 166.66$

ii.

$Q_d = 750 -25P$

If $Q_d = 0, P_d = 30$

Consumer surplus $= \frac{1}{2}(P_d-P_{eq})Q_{eq}$

$= \frac{1}{2} \times(30-23.33)166.66 = 555.611 \\ Q_s = -300 + 20P$

If $Q_s = 0, P_s=15$

Producer surplus $= \frac{1}{2}(P_{eq} -P_s)Q_{eq}$

$= \frac{1}{2}(23.33-15)166.66 = 693.889$