The demand curve for product X is given by Q X d = 500 - 4P X . a. Find the inve
ID: 1134868 • Letter: T
Question
The demand curve for product X is given by QXd = 500 - 4PX.
a. Find the inverse demand curve.
Instruction: Enter all values as integers, or if needed, as a decimal.
PX = ( ) - ( ) QXd
Instructions: Enter your responses to the nearest penny (two decimal places).
b. How much consumer surplus do consumers receive when Px = $50?
$
c. How much consumer surplus do consumers receive when Px = $35?
$
d. In general, what happens to the level of consumer surplus as the price of a good falls?
The level of consumer surplus (Click to select) doesn't change increases decreases as the price of a good falls.
Explanation / Answer
(a)
QXd = 500 - 4PX
QXd - 500 = -4PX
4PX = 500 - QXd
PX = (500 - QXd)/4
PX = 125 - 0.25QXd
Thus,
PX = 125 - 0.25QXd
(b)
QXd = 500 - 4PX
Calculate the PX when QXd is zero -
QXd = 500 - 4PX
0 = 500 - 4PX
4PX = 500
PX = 500/4 = 125
Caculate QXd when PX is $50 -
QXd = 500 - 4PX = 500 - (4*50) = 500 - 200 = 300
Calculate the consumer surplus -
CS = 1/2 * (PX when QXd is zero - PX) * QXd
CS = 1/2 * (125 - 50) * 300 = $11,250
Thus,
The consumer surplus that consumers receive when PX = $50 is $11,250
(c)
QXd = 500 - 4PX
Calculate the PX when QXd is zero -
QXd = 500 - 4PX
0 = 500 - 4PX
4PX = 500
PX = 500/4 = 125
Caculate QXd when PX is $35 -
QXd = 500 - 4PX = 500 - (4*35) = 500 - 140 = 360
Calculate the consumer surplus -
CS = 1/2 * (PX when QXd is zero - PX) * QXd
CS = 1/2 * (125 - 35) * 360 = $16,200
Thus,
The consumer surplus that consumers receive when PX = $35 is $16,200
(d)
The level of consumer surplus increases as the price of a good falls.
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