Which of the following is NOT true for a monopoly? A monopoly sometimes makes a
ID: 1098698 • Letter: W
Question
Which of the following is NOT true for a monopoly?
A monopoly sometimes makes a positive profit in the long run.
A price ceiling on a monopoly is always desirable.
Price does not equal marginal cost unless price is regulated.
None of the above statements are true.
The demand curve for product X is given by QXd = 520 - 5PX.
a. Find the inverse demand curve.
PX = - QXd
b. How much consumer surplus do consumers receive when Px = $45?
$
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?
A monopoly sometimes makes a positive profit in the long run.
A price ceiling on a monopoly is always desirable.
Price does not equal marginal cost unless price is regulated.
None of the above statements are true.
The demand curve for product X is given by QXd = 520 - 5PX.
a. Find the inverse demand curve.
PX = - QXd
b. How much consumer surplus do consumers receive when Px = $45?
$
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?
Explanation / Answer
1.None of the above
2.
(a) Find the inverse demand curve?
Px= 104-0.2Qx
(b) Px = $45
The area bounded by the demand curve and a horizontal line at the market price equals the amount of surplus that consumers get at that price. In order to compute the consumer surplus (CS) in this price it is useful to first invert the demand function as follows:
Q=520-5P
5p=520-Q
p=104-0.2Q
Next, substitute P=45 and solve for the quantity demanded at that price as follows:
45=104-0.2Q
0.2Q=59
Q=295 units demanded at the price $45/unit.
Surplus in this case is area of triangle S=ah/2
Consumer surplus is triangle limited from above by demand curve, from left by Y axis and below by price.
Px=45
Qdx=520-45=475
Px(0)=520
?P=520-45= 475
S=Q*?P/2=45*475/2=10687.5
Surplus is 10687.5
(c)Px = $35
The area bounded by the demand curve and a horizontal line at the market price equals the amount of surplus that consumers get at that price. In order to compute the consumer surplus (CS) in this price it is useful to first invert the demand function as follows:
Q=520-5P
5p=520-Q
p=104-0.2Q
Next, substitute P=35 and solve for the quantity demanded at that price as follows:
35=104-0.2Q
0.2Q=69
Q=345 units demanded at the price $35/unit.
Surplus in this case is area of triangle S=ah/2
Consumer surplus is triangle limited from above by demand curve, from left by Y axis and below by price.
Px=35
Qdx=520-35=485
Px(0)=520
?P=520-35=485
S=Q*?P/2=35*485/2=8488.5
Surplus is 8488.5
(d) In general, what happens to the level of consumer surplus as the price of a good falls?
Level of consumer surplus increases.
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