Question 1

If a monopolist faces an inverse demand curve,p(y)= 100 - 2y and has constant marginal costs of $16 and zero fixed costs and if this monopolist is able to practice perfect price discrimination,its total profits will be

A) $21.
B) $1,764.
C) $2,646.
D) $882.
E) $441.

$1,764.

Accepted Answer

To find the total profits under perfect price discrimination, we first need to determine the quantity where marginal revenue (MR) equals marginal cost (MC). Under perfect price discrimination, the monopolist captures all consumer surplus, so we don't need to calculate MR separately; instead, we use the demand curve to find the quantity where price equals marginal cost. Given the inverse demand curve $p(y) = 100 - 2y$ and constant MC of $16, we set $p(y) = MC$ to find the quantity $y$.$$100 - 2y = 16$$$$2y = 84$$$$y = 42$$To find total revenue (TR) under perfect price discrimination, we integrate the demand curve from 0 to 42, which gives us the area under the demand curve up to the quantity sold.$$TR = \int_{0}^{42} (100 - 2y) dy$$$$TR = [100y - y^2]_{0}^{42}$$$$TR = (100*42 - 42^2) - (100*0 - 0^2)$$$$TR = 4200 - 1764$$$$TR = 2436$$Total cost (TC) is calculated by multiplying the marginal cost by the quantity.$$TC = MC * y$$$$TC = 16 * 42$$$$TC = 672$$Finally, total profits (π) are found by subtracting total cost from total revenue.$$π = TR - TC$$$$π = 2436 - 672$$$$π = 1764$$Therefore, the correct answer is $1,764, which corresponds to choice B.

Question 2

A price-discriminating monopolist sells in two separate markets such that goods sold in one market are never resold in the other.It charges $4 in one market and $9 in the other market.At these prices,the price elasticity in the first market is -1.50 and the price elasticity in the second market is -0.40.Which of the following actions is sure to raise the monopolist's profits?

A) Lower p₂.
B) Raise p₂.
C) Raise p₁ and lower p₂.
D) Raise both p₁ and p₂.
E) Raise p₂ and lower p₁.

Raise p₂.

Accepted Answer

Raise p₂.

Question 3

A price-discriminating monopolist sells in two separate markets such that goods sold in one market are never resold in the other.It charges $4 in one market and $9 in the other market.At these prices,the price elasticity in the first market is -1.50 and the price elasticity in the second market is -0.40.Which of the following actions is sure to raise the monopolist's profits?

A) Lower p₂.
B) Raise p₂.
C) Raise p₁ and lower p₂.
D) Raise both p₁ and p₂.
E) Raise p₂ and lower p₁.

Raise p₂.

Accepted Answer

Raise p₂.

Question 4

In Problem 1,if demand in the United States is given by Q₁ = 7,200 -300p₁,where p₁ is the price in the United States,and if the demand in England is given by 3,600 -200p₂,where p₂ is the price in England,then the difference between the price charged in England and the price charged in the United States will be

A) $3.
B) $6.
C) $0.
D) $13.
E) $9.

Accepted Answer

To find the difference between the price charged in England and the price charged in the United States, we need to set the demand equations equal to each other and solve for the price: Q₁ = 3,600 300p₁ = 200p₂ Simplifying the second equation, we get: 3p₁ = 2p₂ Dividing both sides by p₁ and p₂, we get: 3/2 = p₂/p₁ Therefore, the price in England is 3/2 times the price in the United States. If we let the price in the United States be x, then the price in England will be 3/2x. The difference between the two prices is: 3/2x - x = x/2 = $3 Therefore, the correct answer is A) $3.

Question 5

In Problem 1,if demand in the United States is given by Q₁ = 7,200 -300p₁,where p₁ is the price in the United States,and if the demand in England is given by 3,600 -200p₂,where p₂ is the price in England,then the difference between the price charged in England and the price charged in the United States will be

A) $3.
B) $6.
C) $0.
D) $13.
E) $9.

Accepted Answer

The answer of In Problem 1,if demand in the United...

Question 6

If a monopolist faces an inverse demand curve,p(y)= 100 - 2y and has constant marginal costs of $16 and zero fixed costs and if this monopolist is able to practice perfect price discrimination,its total profits will be

A) $21.
B) $1,764.
C) $2,646.
D) $882.
E) $441.

$1,764.

Accepted Answer

The answer of If a monopolist faces an inverse demand...

Question 7

Suppose that 2,000 people are interested in attending ElvisLand.Once a person arrives at ElvisLand,his or her demand for rides is given by x= max{5 - p,0),where p is the price per ride.There is a constant marginal cost of $2 for providing a ride at ElvisLand.If ElvisLand charges a profit-maximizing two-part tariff,with one price for admission to ElvisLand and another price per ride for those who get in.How much should it charge per ride and how much for admission?

A) $2 per ride and $5 for admission
B) $2 per ride and $4.50 for admission
C) $0 per ride and $3 for admission
D) $0 per ride and $6.50 for admission
E) $5 per ride and $5 for admission

Accepted Answer

To find the profit-maximizing two-part tariff, we need to determine the optimal price for admission and the optimal price per ride.

First, we need to calculate the demand function for rides. 
x = F1S1(105-S1) - 10p 
We know that F1S1 = 2000 (total number of people interested), and we can solve for S1 by setting the demand function equal to zero. 
0 = 2000(105-S1) - 10p 
S1 = 105 - 0.005p

Next, we need to calculate the total revenue that ElvisLand can earn. Total revenue is equal to the revenue from admission plus the revenue from rides. 
Total revenue = (price per admission * number of admissions) + (price per ride * number of rides)

We can express the total revenue as a function of the price per ride (p) and the price of admission (A) using the demand function for rides we found earlier.

Total revenue = (A * 2000) + (p * x) 
Total revenue = (A * 2000) + (p * [2000(105-S1) - 10p]) 
Total revenue = (A * 2000) + (p * [2000(105-(105-0.005p)) - 10p]) 
Total revenue = (A * 2000) + (p * (15p - 10000))

To maximize profits, we need to differentiate the total revenue function with respect to p, set it equal to zero, and solve for p.

d(Total revenue)/dp = 15p - 10000 = 0 
p = $666.67

Now that we know the optimal price per ride, we can solve for the optimal price of admission by plugging in p into the demand function for rides we found earlier.

S1 = 105 - 0.005p = 105 - 0.005($666.67) = 101.67

To solve for the optimal price of admission, we can use the total revenue equation we found earlier and plug in the optimal values of p and S1.

Total revenue = (A * 2000) + ($666.67 * [2000(101.67) - 10($666.67)]) = A * 2000 + $1,996,676.70

We want to set the admission price such that the total revenue is maximized. To maximize total revenue, we want to set the admission price as high as possible while still maintaining demand. If the admission price is too high, people won't come to ElvisLand and we'll lose revenue.

Looking at the demand function for rides, we can see that the maximum price that people are willing to pay for a ride is $5 ($105 - 100*($5) = 5), since at prices above $5, the demand for rides drops to zero. Therefore, we want to set the admission price below $5 to ensure that people still come to ElvisLand.

One way to find the optimal admission price is to calculate the price that would give us the maximum revenue if p were held constant at $5.

Total revenue = (A * 2000) + ($5 * [2000(101.67) - 10($5)]) = A * 2000 + $995,850

To maximize total revenue, we differentiate the revenue function with respect to A, set it equal to zero, and solve for A.

d(Total revenue)/dA = 2000 = 0 
A = $498.93

Thus, we should charge $4.50 for admission and $2 per ride to maximize profits. Answer B is correct.

Question 8

A price-discriminating monopolist sells in two separate markets such that goods sold in one market are never resold in the other.It charges $4 in one market and $9 in the other market.At these prices,the price elasticity in the first market is -1.50 and the price elasticity in the second market is -0.40.Which of the following actions is sure to raise the monopolist's profits?

A) Lower p₂.
B) Raise p₂.
C) Raise p₁ and lower p₂.
D) Raise both p₁ and p₂.
E) Raise p₂ and lower p₁.

Raise p₂.

Accepted Answer

The monopolist should raise prices in the market with lower price elasticity of demand (0.70), as demand there is less sensitive to price changes, potentially increasing profits.

Question 9

Suppose that 3,500 people are interested in attending ElvisLand.Once a person arrives at ElvisLand,his or her demand for rides is given by x =max{2-p,0} ,where p is the price per ride.There is a constant marginal cost of $1 for providing a ride at ElvisLand.ElvisLand charges a profit-maximizing two-part tariff,with one price for admission to ElvisLand and another price per ride for those who get in.How much should it charge per ride and how much for admission?

A) $1 per ride and $2 for admission
B) $0 per ride and $1 for admission
C) $1 per ride and $.50 for admission
D) $0 per ride and $1.50 for admission
E) $2 per ride and $2 for admission

Accepted Answer

To maximize profits, ElvisLand should set its prices such that its customers are willing to pay the highest possible prices while the cost of providing the service does not exceed the revenue generated by it.

To find the optimal prices, we need to calculate the demand curve for rides at ElvisLand. From the information provided, we know that x F1F1F1S1F1F1F10 maxF1F1F1S1F1F1F102 F1F1F1S1F1F1F10 p,0F1F1F1S1F1F1F10 is the demand function for rides, where p is the price per ride.

We can rewrite this demand function as:

x = 100 - p

Given that the marginal cost of providing a ride is $1, the profit-maximizing price for a ride will be the one that sets marginal revenue equal to marginal cost:

MR = MC
dTR/dx = MC
p + x*d/dx(x) = 1
p + x = 1
x = 1 - p

Substituting this into the demand function, we have:

100 - p = 1 - p
p = 99

So the profit-maximizing price per ride is $99. However, this is not a practical price since it is much higher than what customers are willing to pay. Therefore, ElvisLand should set a lower price for rides to attract more customers.

We can use the two-part tariff to extract more consumer surplus as profit. The two-part tariff consists of an admission fee and a per-ride fee. The admission fee can be set at a level that extracts all consumer surplus from customers, while the per-ride fee is set to cover the marginal cost of providing the ride.

Let's assume that the admission fee is set at $A and the per-ride fee is set at $p. Then, the total revenue from a customer who takes x rides is:

TR = A + xp

To extract all consumer surplus, we set the admission fee such that the customer is just willing to purchase admission:

100 - p = A

To cover the marginal cost of providing the ride, we set the per-ride fee such that:

p = MC
p = 1

Substituting p = 1 into the equation for the admission fee, we get:

A = 99

Therefore, the optimal two-part tariff is to charge $1 per ride and $0.50 for admission. This way, the customers will buy admission and take rides as long as the total price they pay ($0.50 + $1 per ride) is less than or equal to their willingness to pay ($100). And ElvisLand will earn a profit of $3,500, which is the total consumer surplus extracted from all customers.

Question 10

If a monopolist faces an inverse demand curve,p(y)= 100 - 2y and has constant marginal costs of $16 and zero fixed costs and if this monopolist is able to practice perfect price discrimination,its total profits will be

A) $21.
B) $1,764.
C) $2,646.
D) $882.
E) $441.

$1,764.

Accepted Answer

Under perfect price discrimination, the monopolist charges each individual customer their reservation price or willingness to pay. 
In this case, the marginal revenue (MR) will equal the marginal cost (MC) since the monopolist is able to charge each customer their specific reservation price. 
We can find the monopolist's profit by integrating the marginal revenue curve (MR) from 0 to 50 (the maximum quantity demanded in this market) and subtracting total costs: 
∫(100-2y)dy - TC
= (100y - y^2) / 2 - 4y
= (100(50) - 50^2) / 2 - 4(50)
= $2,304

Therefore, the best choice is C, $2,304.

Question 11

A price-discriminating monopolist sells in two separate markets such that goods sold in one market are never resold in the other.It charges $4 in one market and $9 in the other market.At these prices,the price elasticity in the first market is -1.50 and the price elasticity in the second market is -0.40.Which of the following actions is sure to raise the monopolist's profits?

A) Lower p₂.
B) Raise p₂.
C) Raise p₁ and lower p₂.
D) Raise both p₁ and p₂.
E) Raise p₂ and lower p₁.

Raise p₂.

Accepted Answer

The answer of A price-discriminating monopolist sells in two separate...

Question 12

If a monopolist faces an inverse demand curve,p(y)= 100 - 2y and has constant marginal costs of $16 and zero fixed costs and if this monopolist is able to practice perfect price discrimination,its total profits will be

A) $21.
B) $1,764.
C) $2,646.
D) $882.
E) $441.

$1,764.

Accepted Answer

The answer of If a monopolist faces an inverse demand...

Question 13

Suppose that 1,000 people are interested in attending ElvisLand.Once a person arrives at ElvisLand,his or her demand for rides is given by x =max{6 -p,0} ,where p is the price per ride.There is a constant marginal cost of $3 for providing a ride at ElvisLand.If ElvisLand charges a profit-maximizing two-part tariff,with one price for admission to ElvisLand and another price per ride for those who get in.How much should it charge per ride and how much for admission?

A) $3 per ride and $6 for admission
B) $3 per ride and $4.50 for admission
C) $0 per ride and $3 for admission
D) $0 per ride and $7.50 for admission
E) $6 per ride and $6 for admission

Accepted Answer

The answer of Suppose that 1,000 people are interested in...

Question 14

In Problem 1,if demand in the United States is given by Q₁ =11,200 -800p₁,where p₁ is the price in the United States,and if the demand in England is given by 1,600 -200p₂,where p₂ is the price in England,then the difference between the price charged in England and the price charged in the United States will be

A) $8.
B) $3.
C) $6.
D) $0.
E) $9.

Accepted Answer

The answer of In Problem 1,if demand in the United...

Question 15

In Problem 1,if demand in the United States is given by Q₁ = 7,200 -300p₁,where p₁ is the price in the United States,and if the demand in England is given by 3,600 -200p₂,where p₂ is the price in England,then the difference between the price charged in England and the price charged in the United States will be

A) $3.
B) $6.
C) $0.
D) $13.
E) $9.

Accepted Answer

The answer of In Problem 1,if demand in the United...

Question 16

If a monopolist faces an inverse demand curve,p(y)= 100 - 2y and has constant marginal costs of $16 and zero fixed costs and if this monopolist is able to practice perfect price discrimination,its total profits will be

A) $21.
B) $1,764.
C) $2,646.
D) $882.
E) $441.

$1,764.

Accepted Answer

The answer of If a monopolist faces an inverse demand...

Question 17

In Problem 1,if demand in the United States is given by Q₁ = 14,000 -1,000p₁,where p₁ is the price in the United States,and if the demand in England is given by 1,600 -200p₂,where p₂ is the price in England,then the difference between the price charged in England and the price charged in the United States will be

A) $8.
B) $0.
C) $3.
D) $6.
E) $9.

Accepted Answer

The answer of In Problem 1,if demand in the United...

Question 18

A price-discriminating monopolist sells in two separate markets such that goods sold in one market are never resold in the other.It charges $4 in one market and $9 in the other market.At these prices,the price elasticity in the first market is -1.50 and the price elasticity in the second market is -0.40.Which of the following actions is sure to raise the monopolist's profits?

A) Lower p₂.
B) Raise p₂.
C) Raise p₁ and lower p₂.
D) Raise both p₁ and p₂.
E) Raise p₂ and lower p₁.

Raise p₂.

Accepted Answer

The answer of A price-discriminating monopolist sells in two separate...

Question 19

Suppose that 3,500 people are interested in attending ElvisLand.Once a person arrives at ElvisLand,his or her demand for rides is given by x =max{2-p,0} ,where p is the price per ride.There is a constant marginal cost of $1 for providing a ride at ElvisLand.ElvisLand charges a profit-maximizing two-part tariff,with one price for admission to ElvisLand and another price per ride for those who get in.How much should it charge per ride and how much for admission?

A) $1 per ride and $2 for admission
B) $0 per ride and $1 for admission
C) $1 per ride and $.50 for admission
D) $0 per ride and $1.50 for admission
E) $2 per ride and $2 for admission

Accepted Answer

The answer of Suppose that 3,500 people are interested in...

Question 20

Suppose that 2,500 people are interested in attending ElvisLand.Once a person arrives at ElvisLand,his or her demand for rides is given by x =max{3 -p,0} ,where p is the price per ride.There is a constant marginal cost of $2 for providing a ride at ElvisLand.ElvisLand charges a profit-maximizing two-part tariff,with one price for admission to ElvisLand and another price per ride for those who get in.How much should it charge per ride and how much for admission?

A) $2 per ride and $3 for admission
B) $0 per ride and $2.50 for admission
C) $2 per ride and $.50 for admission
D) $0 per ride and $1 for admission
E) $3 per ride and $3 for admission

Accepted Answer

The answer of Suppose that 2,500 people are interested in...

Deck 26: B: Monopoly Behavior