a) QXd = 300 - 2PX.
Inverse demand curve (PX = - QXd) => 2PX = 300 - QXd => 2PX/2 = 300/2 - QXd/2 ) => PX = 150 - QXd/2
b) In calculating consumer surplus, knowing maximum willingness to pay (WTP) is first (Price when Quantity demanded is 0)
PX = 150 - QXd/2
At Q = 0, P = 150
At Px = $45,
QXd = 300 - 2*45
QXd = 300 - 90
QXd = 210
Consumer surplus is the area of the triangle whose base = Quantity demanded and height is the difference between price and WTP
CS = 1/2 * 210 * (150 - 45)
CS = 22050/2
CS = 11025
c) At Px = $30
QXd = 300 - 2*30
QXd = 300 - 60
QXd = 240
CS = 1/2 * 240 * (150 - 30)
CS = 1/2 * 240 * 120
CS = 28800/2
CS = 14400
d. As the price of a good falls, Consumer surplus increases because of increase in distance between WTP and price.