Question

Qd = 90 – 6P

Qs = - 20 + 4P

Calculate consumer surplus and producer surplus at the equilibrium price?

Answer 1

$Q_d= 90- 6P$

$Q_s= -20+4P$

At Equilibrium, $Q_d= Q_s$

$90-6p= -20+4P$

$10P= 110$

P= 11

$Q^*=90- 6(11)= 24$

Y intercept P$_{max}= Q=0$ for demand curve

0=90-6P

P$_{max}$ = 15

Y intercept for supply curve, P$_{min}$ = When Q= 0

0= -20+4P

P= 5

$Consumer surplus= \frac {1}{2}\times Q_d \times \Delta P$

$\frac{1}{2}\times 24 \times (15-11)$

= 48

Producer Surplus= $\frac{1}{2}\times 24 \times (11-5)$

$= 72$