Question

Suppose the market demand for a good is described by the equation P = 80 - 2Q. If a change in market supply results in price decreasing from P0 = $60 to P1 = $50, then the resulting change in consumer surplus is:

Answer 1

Calculate Q (consumer surplus) when P = 60

$60=80-2Q$ ⇒ Subtract 60 from both sides
$60-60=80-2Q-60$
$0=20-2Q$ ⇒ Add 2Q to both sides
$0+2Q = 20-2Q+2Q$
$2Q=20$ ⇒ Divide both sides by 2
$\frac{2Q}{2} = \frac{20}{2}$
$Q=10$

--------------------------------------------------------------------------------------------------------------

Calculate Q when P = 50

$50=80-2Q$
$50-50=80-2Q-50$
$0=30-2Q{/tex] [tex]0+2Q=30-2Q+2Q$
$2Q=30$
$Q=15$

--------------------------------------------------------------------------------------------------------------

As the value of P decreasing, the value of Q increases from 10 to 15