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The demand curve for product X is given by QXd = 300 - 2PX.

a. Find the inverse demand curve. Instruction: Enter all values as integers, or if needed, a decimal rounded to one decimal place. PX = - QXd

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? The level of consumer surplus as the price of a good falls.

Sagot :

Tundexi

Answer:

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.

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