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Homework answers / question archive / The demand curve for product X is given by QXd = 300 - 2PX
The demand curve for product X is given by QXd = 300 - 2PX.
a. Find the inverse demand curve. PX = - QXd Instructions: Round your answer to the nearest penny (2 decimal places).
b. How much consumer surplus do consumers receive when Px = $45? $
c. How much consumer surplus do consumers receive when Px = $30? $
d. In general, what happens to the level of consumer surplus as the price of a good falls?
Answer:
QXd = 300 - 2PX
a) Inverse demand curve, 2PX = 300 - QXd and , PX = 150 - QXd/2
b) For calculating consumer surplus we must know maximum willingness to pay (WTP) i.e. Price when Quantity demanded is zero.
PX = 150 - QXd/2
At Q = 0, P = 150
At Px = $45,
QXd = 300 - 2 x 45
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 x 210 x (150 - 45) => 105 x 105
CS = 11025
c) At Px = $30
QXd = 300 - 2 x 30
QXd = 240
CS = 1/2 x 240 x (150 - 30) => 120 x 120
CS = 14400
d. As the price of a good falls, Consumer surplus increases because of increase in distance betwwen WTP and price.
