Question

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 1

Q_Xd = 300 - 2P_X

a) Inverse demand curve_, 2P_{X =} 300 - Q_{Xd and ,} P_{X =} 150 - Q_Xd/2

b) For calculating consumer surplus we must know maximum willingness to pay (WTP) i.e. Price when Quantity demanded is zero.

P_{X =} 150 - Q_Xd/2

At Q = 0, P = 150

At P_x = $45,

Q_Xd = 300 - 2 x 45

Q_Xd = 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

Q_Xd = 300 - 2 x 30

Q_Xd = 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.