3 very hard problem sets to learn Flashcards
Mock Consider the decisions of Virgin Galactic as it opens an exclusive line between Earth and the Moon. If Virgin Galactic is the sole airline operating this line, it acts like a monopolist in this market. The demand for flights to the Moon is segmented into two groups. Business travellers, who often have to buy last minute tickets, have a fully inelastic demand of 30 for any price between zero and 120 and zero demand for any price above 120. Families going on vacation, who can plan ahead, have a demand given by ๐ = 120 โ ๐. Although Richard Branson (the founder of Virgin Galactic) had to pay billions of pounds to build the Virgin Galactic ship, by using renewable energy he cut his marginal cost to zero.
a) Assume first that Virgin Galactic is allowed to charge different prices to these different groups (for example, it can charge a different price if you purchase the ticket a few months in advance than if you purchase the ticket last minute). Calculate the monopoly prices charged for each group, the profit of Virgin Galactic, and the total consumer surplus in the whole market.
a) what is the total surplus for Business travellers?
For the business travellers: Business travellers, have a fully inelastic demand of 30 for any price between zero and 120 and zero demand for any price above 120. That means that for any price the monopoly charges between 0 and 120 30 tickets will be bought and for any price above 120 zero will be bought. Therefore, the monopoly will charge 120 for business travellers with a: profit of 120ร30=3600
Consumer surplus of zero, as they these are paying their willingness to pay which is 120
0 + 3600 = 3600 ( total surplus)
Mock Consider the decisions of Virgin Galactic as it opens an exclusive line between Earth and the Moon. If Virgin Galactic is the sole airline operating this line, it acts like a monopolist in this market. The demand for flights to the Moon is segmented into two groups. Business travellers, who often have to buy last minute tickets, have a fully inelastic demand of 30 for any price between zero and 120 and zero demand for any price above 120. Families going on vacation, who can plan ahead, have a demand given by ๐ = 120 โ ๐. Although Richard Branson (the founder of Virgin Galactic) had to pay billions of pounds to build the Virgin Galactic ship, by using renewable energy he cut his marginal cost to zero.
a) Assume first that Virgin Galactic is allowed to charge different prices to these different groups (for example, it can charge a different price if you purchase the ticket a few months in advance than if you purchase the ticket last minute). Calculate the monopoly prices charged for each group, the profit of Virgin Galactic, and the total consumer surplus in the whole market.
a) what is the total surplus for families?
The demand is given by ๐ = 120 โ ๐ and therefore the Marginal revenue is MR=120 โ 2๐.
As Marginal cost is zero, the monopoly will produce at a point where MR=0 implying that 120 โ 2๐=0 and therefore ๐๐=60!
We get the price by plugging ๐=60 into the demand function to get ๐ = 120 โ 60=60 This will imply a profit for the Monopoly from the families of 60ร60=3600.
To get the consumer surplus we calculate the area of the triangle below the demand and above the price, which is (60ร60)/2=1800.
Mock Consider the decisions of Virgin Galactic as it opens an exclusive line between Earth and the Moon. If Virgin Galactic is the sole airline operating this line, it acts like a monopolist in this market. The demand for flights to the Moon is segmented into two groups. Business travellers, who often have to buy last minute tickets, have a fully inelastic demand of 30 for any price between zero and 120 and zero demand for any price above 120. Families going on vacation, who can plan ahead, have a demand given by ๐ = 120 โ ๐. Although Richard Branson (the founder of Virgin Galactic) had to pay billions of pounds to build the Virgin Galactic ship, by using renewable energy he cut his marginal cost to zero.
a) Assume first that Virgin Galactic is allowed to charge different prices to these different groups (for example, it can charge a different price if you purchase the ticket a few months in advance than if you purchase the ticket last minute). Calculate the monopoly prices charged for each group, the profit of Virgin Galactic, and the total consumer surplus in the whole market.
What is the total surplus?
Summary and Totals: Price for Business travellers 120, quantity purchased 30
Price for Families 60, quantity purchased 60
Total profits for the monopoly: 3600+3600=7200
Total consumer surplus: 0+1800=1800
Total Surplus: 7200+1800=9000
Mock The government is concerned about the monopoly power of Virgin Galactic. To measure the โsocial costโ of Virgin Galactic pricing strategy you calculated in (a), the government compares the total surplus you found in (a) to the total surplus that would arise if Virgin Galactic would charge prices as if it was in a competitive equilibrium.
b) As a first step to help the governmentโs calculation, compute the total demand for flights in the market.
The total demand is a horizontal summation of the quanity for each consumer group
Note that for any price above 120, there is no demand (not from business travellers and not from families).
For any price below 120 we have a demand of 30 from business travellers and 120-Q from families (as P=120-Q we have that Q=120-p).
Therefore, the demand, for any price between 0 and 120, will be
Q=30+(120-P) implying that Q=150-P or P=150-Q
And for any price above 120 the demand is zero
( if P = 120 q = 0)
Mock The government is concerned about the monopoly power of Virgin Galactic. To measure the โsocial costโ of Virgin Galactic pricing strategy you calculated in (a), the government compares the total surplus you found in (a) to the total surplus that would arise if Virgin Galactic would charge prices as if it was in a competitive equilibrium.
c) With the total demand you have calculated above, calculate the price, the producer surplus, and the consumer surplus that would arise if this was a perfectly competitive market.
In a perfectly competitive equilibrium the price is determined by the intersection of demand and supply. The supply curve is flat at level zero as the marginal cost is equal to zero. The demand was calculated above to be P=150-Q.
P=mc as mc = 0 p = 0, thus there is no profit for the producer and no ps.
Consumer surplus is the size of the area below the demand and above zero which is made of two areas:
- The consumer surplus of the business travellers which is the rectangle below 120 and above zero for 30 units of flights, 30ร120=3600
- The consumer surplus of families which is the triangle below the downward sloping part of the demand and above zero, for the flights between 30 and 150 (120 units of flights) on the X-ais, (120ร120)/2=7200
- Total consumer surplus is 7200+3600=10800 - Total surplus is 0+10800 = 10800
Mock d) To get the government measure of the โsocial costโ of Virgin Galactic pricing strategy, calculate the difference between the total surplus in the perfectly competitive market, and the total surplus you have computed in (a).
From our calculations above this will be Social cost = 10800-9000 = 1800
MOCK e) As a first step to reduce the โsocial costโ of Virgin Galactic pricing strategy, the government prevents Virgin Galactic from price discriminating by forcing Virgin Galactic to charge only one price for everyone. Calculate the new price, the new profits for Virgin Galactic and the new total surplus. Calculate the โsocial costโ of Virgin Galactic pricing strategy when it cannot price discriminate. Is this step taken by the government effective?
In this case we need to find the price the monopoly will charge when they cannot discriminate between the two groups.
The demand was calculated above to be equal to: P=150-Q for prices between 0 and 120 and for any price above 120 the demand is zero.
Surely the monopoly would not like to charge a price above 120 as the demand would be zero.
But as the demand has a โkinkโ (not a simple line ut its slope changes below and above Q=30) we need to check two options:
- Sell only to Business travellers at the price of 120, for a profit of 30ร120=3600
- Sell to both groups by choosing a price below 120
to do 2)
In this case we will equate MR to marginal cost, which is zero, so MR=0. As the demand is P=150-Q the marginal cost will equal MR=150-2Q. Equating this with zero we get MR=150-2Q=0 implying that Q=75, and the price we get from plugging this quantity int the demand which is P=150-75=75.
This leads to a profit of 75ร75=5625 (remember that the costs are zero!)
As 5625>3600 this is the option that the monopoly will choose!
So the profits of the monopoly are 5625
Total surplus is, like before, broken into two parts:
(i) The Consumer surplus of business travellers is 30ร(120-75) = 1350, as their willingness to pay is 120 and the price is 75 and they buy 30 units. (
ii) The Consumer surplus of families is (120-75)ร(75-30)/2=1012.5
So total consumer surplus is 1350+1012.5 = 2362.5
Total surplus is equal to 5625+2362.5 = 7987.5
The social cost in this case is Social Cost = 10800-7987.5 = 2812.5
Is this an effective measure? From the measure of social cost we calculated in this case and in the case in which the monopolist could discriminate we get that the measure is not effective as this cost increased! talk about surplus!!!
January 2020 paper
Consider the decisions of Virgin Galactic as it opens an exclusive line between earth and the moon. If Virgin Galactic is the sole airline operating this line, it acts like a monopolist in this market. The demand for flights to the moon is segmented into two groups. Business travellers, who often have to buy last minute tickets, have a demand function given by ๐๐ = 100 โ 2๐๐. Families going on vacation, who can plan ahead, have a demand given by ๐๐ = 100 โ ๐๐. Although Richard Branson (the founder of Virgin Galactic) had to pay billions of pounds to build the Virgin Galactic ship, by using renewable energy he cut his marginal cost to zero.
a) Assume first that Virgin Galactic is allowed to charge different prices to these different groups (for example, it can charge a different price if you purchase the ticket a few months in advance than if you purchase the ticket last minute). Calculate the monopoly prices charged for each group, the profit of Virgin Galactic, and the total consumer surplus in the whole market.
Calculate total surplus for business travellers
Profit = TR-TC
TR = 100q - 2q^2
Q = 25
(100(25) - 2(25)^2) - 0(MC=0)
1250 profit ( PS)
January 2020 paper
Consider the decisions of Virgin Galactic as it opens an exclusive line between earth and the moon. If Virgin Galactic is the sole airline operating this line, it acts like a monopolist in this market. The demand for flights to the moon is segmented into two groups. Business travellers, who often have to buy last minute tickets, have a demand function given by ๐๐ = 100 โ 2๐๐. Families going on vacation, who can plan ahead, have a demand given by ๐๐ = 100 โ ๐๐. Although Richard Branson (the founder of Virgin Galactic) had to pay billions of pounds to build the Virgin Galactic ship, by using renewable energy he cut his marginal cost to zero.
a) Assume first that Virgin Galactic is allowed to charge different prices to these different groups (for example, it can charge a different price if you purchase the ticket a few months in advance than if you purchase the ticket last minute). Calculate the monopoly prices charged for each group, the profit of Virgin Galactic, and the total consumer surplus in the whole market.
Calculate total surplus for Families travellers and complete the Q
January Paper 2020
The government is concerned about the monopoly power of Virgin Galactic. To measure the โsocial costโ of Virgin Galactic pricing strategy you calculated in (a), the government compares the total surplus you found in (a) to the total surplus that would arise if Virgin Galactic would charge prices as if it was in a competitive equilibrium.
b) As a first step to help the governmentโs calculation, compute the total demand for flights in the market
January Paper 2020
c) With the total demand you have calculated above, calculate the price, the producer surplus, and the consumer surplus that would arise if this was a perfectly competitive market. To get the government measure of the โsocial costโ of Virgin Galactic pricing strategy, calculate the difference between the total surplus in the perfectly competitive market, and the total surplus you have computed in (a).
January Paper 2020
d) As a first step to reduce the โsocial costโ of Virgin Galactic pricing strategy, the government prevents Virgin Galactic from price discriminating by forcing Virgin Galactic to charge only one price for everyone. Calculate the new price, the new profits for Virgin Galactic and the new total surplus. Calculate the โsocial costโ of Virgin Galactic pricing strategy when it cannot price discriminate. Is this step taken by the government effective?
January 2019 paper
Two partners choose effort levels e1 and e2 that determine output worth Y = 3e1 + 2e2. Suppose that each partner has a marginal cost of effort equal to her effort.
a) What is the total marginal benefit of Partner 1โs effort to the partnership? What is the total marginal benefit of Partner 2โs effort to the partnership? Explain your answer.
- Output is Y = 3e1 + 2e2
- Marginal cost of partner 1 is MC1 = e1
- Marginal cost of partner 2 is MC2 = e2.
- Then the marginal total benefit of Partner 1โs effort is given by derative = MB1 = 3, the additional output for an additional unit of Partner 1โs effort e1.
- Likewise, the marginal total benefit of Partner 2 is given by derative= MB2 = 2, the additional output for an additional unit of Partner 1โs effort e2.
January paper 2019
Two partners choose effort levels e1 and e2 that determine output worth Y = 3e1 + 2e2. Suppose that each partner has a marginal cost of effort equal to her effort.
b) What is the efficient level of effort for Partner 1? What is the efficient level of effort for Partner 2? Explain your answer
- The efficient level of effort for Partner 1 is given by the level at which marginal total benefit equals marginal total costs, i.e. MB1 = MC1, e1 = 3.
- Likewise, the efficient level of effort for Partner 2 is given by the level at which the marginal total benefit for Partner 2 equals Partner 2โs marginal cost, i.e. MB2 = MC2, e2 = 2.
January Paper 2019
Two partners choose effort levels e1 and e2 that determine output worth Y = 3e1 + 2e2. Suppose that each partner has a marginal cost of effort equal to her effort.
c) Assume that each partner owns 50% of the partnership. How much effort will Partner 1 exert? How much effort will Partner 2 exert? What is the level of output that partnership produces? Explain your answer.
