Q:
In the Colluding Refiners problem on the 2004 exam, is it possible to show MR on the graph?
A:
See the other posts on demand and marginal revenue.
Q:
Also on this problem, why is DWL $5 million rather than $10 million?
A:
I think you are right, in that the calculation should be 1/2 * ($2.50-$1.50)* 20 million. ($1.50 is the point on the supply curve at 100 million gallons.)
Thursday, December 13, 2007
Global Warming
Q:
In the Global Warming question on the 2005 exam, the answer to part d states:
"It would get 20 each from India and China and 80 from the rest of the world."
Why is this?
A:
So, the starting point is that China and India each has 120 permits and the rest of the world has 180. Furthermore, since the US pollutes 300 units, it would like to buy 120 permits if it can do so at a cost of $25 or less, since that is the minimum cost for the US to clean up. Now, China and India, if they clean up 100 units (which is the first "block" of marginal cost), each have 20 permits left over to sell. They will choose to sell these 20 permits each at a minimum price of $10 and $15 respectively, since that is what it cost to clean up rather than use them. The rest of the world, if it cleans up 100 units, still has 200 units of pollution and only 180 permits, so it needs to either buy permits or keep cleaning. The second block of cleaning has a MC of $20, and if they clean up this block then they have 80 permits to sell. They will sell the permits and clean if they can get a minimum price of $20.
In the Global Warming question on the 2005 exam, the answer to part d states:
"It would get 20 each from India and China and 80 from the rest of the world."
Why is this?
A:
So, the starting point is that China and India each has 120 permits and the rest of the world has 180. Furthermore, since the US pollutes 300 units, it would like to buy 120 permits if it can do so at a cost of $25 or less, since that is the minimum cost for the US to clean up. Now, China and India, if they clean up 100 units (which is the first "block" of marginal cost), each have 20 permits left over to sell. They will choose to sell these 20 permits each at a minimum price of $10 and $15 respectively, since that is what it cost to clean up rather than use them. The rest of the world, if it cleans up 100 units, still has 200 units of pollution and only 180 permits, so it needs to either buy permits or keep cleaning. The second block of cleaning has a MC of $20, and if they clean up this block then they have 80 permits to sell. They will sell the permits and clean if they can get a minimum price of $20.
Congestion Again
Q:
The answer to part a of the congestion problem on the 2007 exam states:
"the trips cost society the rectangle A in private costs plus the triangles B
and C in externalities"
Can you please explain?
A:
Technically, areas A, B, and C are all costs of the externality in the free market. The total cost of an externality is the per unit cost times the number of units transacted, which gives the area A+B+C.
The answer to part a of the congestion problem on the 2007 exam states:
"the trips cost society the rectangle A in private costs plus the triangles B
and C in externalities"
Can you please explain?
A:
Technically, areas A, B, and C are all costs of the externality in the free market. The total cost of an externality is the per unit cost times the number of units transacted, which gives the area A+B+C.
Shannon's Taxis
Q:
On part e of the Shannon's Taxis problem on the 2007 exam, the answer states:
They lose $1 x 1000 = $1000 of consumers surplus on the 1000 rides they take per day they take plus 1/2 x $1 x 20 = $10 on the 20 extra rides they would have taken had the price been $5 per ride instead of $6.
Why is there a 1/2 in the last part of the answer?
A:
if you draw the graph this should make sense. The $1000 is the rectangle of lost consumer surplus, and the $10 is the triangle of lost CS that comprises the upper part of the DWL triangle. Since the area of a triangle is 1/2 * base * height, you get the 1/2.
On part e of the Shannon's Taxis problem on the 2007 exam, the answer states:
They lose $1 x 1000 = $1000 of consumers surplus on the 1000 rides they take per day they take plus 1/2 x $1 x 20 = $10 on the 20 extra rides they would have taken had the price been $5 per ride instead of $6.
Why is there a 1/2 in the last part of the answer?
A:
if you draw the graph this should make sense. The $1000 is the rectangle of lost consumer surplus, and the $10 is the triangle of lost CS that comprises the upper part of the DWL triangle. Since the area of a triangle is 1/2 * base * height, you get the 1/2.
Valley of the Locusts
Q:
In part c of the Valley of the Locusts question, if the total marginal value 160> total cost 100, it is a good thing, right? Why NO?
A:
The answer to this question is no because the market solution, i.e. the answers to parts a and b state that the consumption where marginal benefit equals 160 and marginal cost is 100 won't happen. In other words, the answers to parts a and b are not welfare maximizing.
In part c of the Valley of the Locusts question, if the total marginal value 160> total cost 100, it is a good thing, right? Why NO?
A:
The answer to this question is no because the market solution, i.e. the answers to parts a and b state that the consumption where marginal benefit equals 160 and marginal cost is 100 won't happen. In other words, the answers to parts a and b are not welfare maximizing.
Internet Browsers Again
Q:
In the Internet Browsers problem on the 2006 exam, in part a, where does the $30 come from?
A:
A monopolist that is maximizing profit is going to produce at the quantity where MR=MC. In this case, MC is constant at $10. Marginal revenue has the same price intercept as demand and is twice as steep. The equation for this is MR=50-Q. So 50-Q has to equal 10 and Q is 40. The price in the demand equation such that quantity demanded is 40 is $30.
In the Internet Browsers problem on the 2006 exam, in part a, where does the $30 come from?
A:
A monopolist that is maximizing profit is going to produce at the quantity where MR=MC. In this case, MC is constant at $10. Marginal revenue has the same price intercept as demand and is twice as steep. The equation for this is MR=50-Q. So 50-Q has to equal 10 and Q is 40. The price in the demand equation such that quantity demanded is 40 is $30.
Internet Browsers
Q:
Spring 2006 practice exam, part 3, question 1a (Internet Browsers): From the information presented in the problem, how do you know there are only two firms in the market?
A:
I admit that this is a confusing question. There aren't two firms in the market, the solution to the problem merely shows that IF there were two firms in the market that, given the market demand that they face, they couldn't both be profitable. This would imply that one of them would exit, leaving a monopoly. A natural monopoly is one where MC is always below ATC. In this example, the constant MC at $10 plus the fixed cost ensures that this will be the case.
Spring 2006 practice exam, part 3, question 1a (Internet Browsers): From the information presented in the problem, how do you know there are only two firms in the market?
A:
I admit that this is a confusing question. There aren't two firms in the market, the solution to the problem merely shows that IF there were two firms in the market that, given the market demand that they face, they couldn't both be profitable. This would imply that one of them would exit, leaving a monopoly. A natural monopoly is one where MC is always below ATC. In this example, the constant MC at $10 plus the fixed cost ensures that this will be the case.
Congestion Pricing
Q:
Is the graph correct in the solution Question A-3a (Bloomberg Congestion case) of the 2007 practice exam? If so, what does the curve shown indicate?
A:
The graph is correct…the curve shown represents the demand for driving in New York…some people value driving in the city a lot, and others not so much, so we get the typical downward sloping demand curve…the supply in this case is drawn as being perfectly elastic, with the original supply curve being a dotted horizontal line at the marginal private cost of driving in the city (gas, etc.) and the marginal social cost is the higher horizontal line. Given this, the graph is just like the externality graphs that you saw in class.
Is the graph correct in the solution Question A-3a (Bloomberg Congestion case) of the 2007 practice exam? If so, what does the curve shown indicate?
A:
The graph is correct…the curve shown represents the demand for driving in New York…some people value driving in the city a lot, and others not so much, so we get the typical downward sloping demand curve…the supply in this case is drawn as being perfectly elastic, with the original supply curve being a dotted horizontal line at the marginal private cost of driving in the city (gas, etc.) and the marginal social cost is the higher horizontal line. Given this, the graph is just like the externality graphs that you saw in class.
Valley of the Locusts
Q:
I don't understand Fall 2006 Final Exam - Part 3. 2. Valley of the Locusts (e) because $25 and $75 payments don't look rational.
A:
Ok, so the quantity is 50 because that is the socially optimal quantity, and the price is still at $100. I disagree with the answer in the solutions(!). For a quantity of 50, M would be willing to pay 120-50=$70. Similarly, L would be willing to pay 80-50=$30. This $70+$30 covers the cost of the bugs and is what I would suggest. I am not sure where the $75 and $25 comes from.
I don't understand Fall 2006 Final Exam - Part 3. 2. Valley of the Locusts (e) because $25 and $75 payments don't look rational.
A:
Ok, so the quantity is 50 because that is the socially optimal quantity, and the price is still at $100. I disagree with the answer in the solutions(!). For a quantity of 50, M would be willing to pay 120-50=$70. Similarly, L would be willing to pay 80-50=$30. This $70+$30 covers the cost of the bugs and is what I would suggest. I am not sure where the $75 and $25 comes from.
Mosquito Control
Q:
I have a question about "Problem Set 10 - 1. Public Goods (Mosquito
Control)."
When I see (d), the answer says that the total benefit ro Adam and Beth is $16,667 and $33,334 respectively, but I don't understand this part. It is not the exact area under their respective marginal benefit curve - we have to calculate the trapezoid area like the followings -> 0.5 * (400 + about 60) * 166.67 for Beth.
A:
I think you are right. The answer in the solution would give a triangle that assumes the people would be paying a positive price for the good, when in the context of the problem they are getting it at a price of zero.
I have a question about "Problem Set 10 - 1. Public Goods (Mosquito
Control)."
When I see (d), the answer says that the total benefit ro Adam and Beth is $16,667 and $33,334 respectively, but I don't understand this part. It is not the exact area under their respective marginal benefit curve - we have to calculate the trapezoid area like the followings -> 0.5 * (400 + about 60) * 166.67 for Beth.
A:
I think you are right. The answer in the solution would give a triangle that assumes the people would be paying a positive price for the good, when in the context of the problem they are getting it at a price of zero.
Demand and MR Again
Q:
The question 1 in Part 3
Internet Browsers
How to draw and calculate the Marginal Revenue based on the Demand Curve??
A:
Graphically, the marginal revenue curve has the same P-axis intercept as the demand curve and is twice as steep (i.e. has a slope twice as large in absolute value). Mathematically, the easiest way to find it is to solve for P in the demand curve and then multiply the slope by 2. For example:
Qd = 40-2P
2P = 40-Qd
P = 20-Qd/2
so then MR = 20-Q, and you can go back and solve for Q.
The question 1 in Part 3
Internet Browsers
How to draw and calculate the Marginal Revenue based on the Demand Curve??
A:
Graphically, the marginal revenue curve has the same P-axis intercept as the demand curve and is twice as steep (i.e. has a slope twice as large in absolute value). Mathematically, the easiest way to find it is to solve for P in the demand curve and then multiply the slope by 2. For example:
Qd = 40-2P
2P = 40-Qd
P = 20-Qd/2
so then MR = 20-Q, and you can go back and solve for Q.
Pollution Abatement
Q:
Wondered if you might clarify the chart on p. 5 of Tony's hand-out notes for Class 22. I don't understand the "source of last ton" column, nor the relationship between the Total Costs of the individual plants and the Combined Least Cost.
A:
I will try my best to clarify. If your goal is to clean up tons of pollution at least cost, as in this problem, you can think of this as answering the questions: For whom is it cheapest to clean up the first ton? Okay, have them clean up one ton...now, given that, for whom is it cheapest to clean up the second ton? Okay, have them clean up a ton, and so on.
In this example, it is cheapest to have A clean up the first ton. Given that, the relevant costs for cleaning up the second ton are the marginal costs of the first ton for B (since it hasn't cleaned up at all yet) and the marginal cost of the second ton for A (since it has already cleaned up one ton). A is still cheaper, so it cleans up the second ton and the process repeats. Eventually it becomes cheaper for B to start cleaning up. Tou can get the total cost by just adding up the marginal costs for each ton based on which plant cleans it up.
Wondered if you might clarify the chart on p. 5 of Tony's hand-out notes for Class 22. I don't understand the "source of last ton" column, nor the relationship between the Total Costs of the individual plants and the Combined Least Cost.
A:
I will try my best to clarify. If your goal is to clean up tons of pollution at least cost, as in this problem, you can think of this as answering the questions: For whom is it cheapest to clean up the first ton? Okay, have them clean up one ton...now, given that, for whom is it cheapest to clean up the second ton? Okay, have them clean up a ton, and so on.
In this example, it is cheapest to have A clean up the first ton. Given that, the relevant costs for cleaning up the second ton are the marginal costs of the first ton for B (since it hasn't cleaned up at all yet) and the marginal cost of the second ton for A (since it has already cleaned up one ton). A is still cheaper, so it cleans up the second ton and the process repeats. Eventually it becomes cheaper for B to start cleaning up. Tou can get the total cost by just adding up the marginal costs for each ton based on which plant cleans it up.
A Logistical Point
Q:
What is the location of the exam?
A:
The information can be found in the exam memo on the course web site rather than in the announcements directly:
Last names A through F: Weiner Auditorium (Ground Floor of Taubman)
Last names G through Z: Land Hall (Belfer Building)
What is the location of the exam?
A:
The information can be found in the exam memo on the course web site rather than in the announcements directly:
Last names A through F: Weiner Auditorium (Ground Floor of Taubman)
Last names G through Z: Land Hall (Belfer Building)
MC and MR
Q:
When is D=MR and S=MC, and when are they different? Is it only in the competitive price-taker situation when they are equivalent?
A:
Supply is a truncated version of the marginal cost curve (above the shut-down condition) in a COMPETITIVE market. Demand equals marginal revenue when demand is perfectly elastic (i.e. horizontal). So the answer to your second question would be yes, unless for some bizarre reason market demand were randomly perfectly elastic.
When is D=MR and S=MC, and when are they different? Is it only in the competitive price-taker situation when they are equivalent?
A:
Supply is a truncated version of the marginal cost curve (above the shut-down condition) in a COMPETITIVE market. Demand equals marginal revenue when demand is perfectly elastic (i.e. horizontal). So the answer to your second question would be yes, unless for some bizarre reason market demand were randomly perfectly elastic.
Externalities and DWL
Q:
Class 22, top of pg 4 - example on positive production externality. The DWL triangle in this case doesn't seem to be pointing towards the Qe. I'm also unclear what the DWL represents in this case.
A:
You are correct. The DWL should be the other triangle. Luckily, in these examples both of the triangles are the same size. With a positive externality, DWL arises because there are units that the market isn't producing that would be beneficial to society, since for these units the Marginal Social Benefit outweighs the Marginal Social Cost. Think of it as foregone opportunity due to the fact that it didn't specifically benefit producers and consumers of the product.
Class 22, top of pg 4 - example on positive production externality. The DWL triangle in this case doesn't seem to be pointing towards the Qe. I'm also unclear what the DWL represents in this case.
A:
You are correct. The DWL should be the other triangle. Luckily, in these examples both of the triangles are the same size. With a positive externality, DWL arises because there are units that the market isn't producing that would be beneficial to society, since for these units the Marginal Social Benefit outweighs the Marginal Social Cost. Think of it as foregone opportunity due to the fact that it didn't specifically benefit producers and consumers of the product.
Pecuniary Externalities
Q:
Class 22 - definition of externality says that it helps or harms a third party through mechanisms other than price. Definition of percuniary externality is that it affects third party by changing prices. So is a percuniary externality an externality, since it affects through the price mechanism?
A:
Let's call it a pseudo-externality. :) From wikipedia:
A pecuniary externality is an externality which operates through prices rather than through real resource effects. For example, an influx of city-dwellers buying second homes in a rural area can drive up house prices, making it difficult for young people in the area to get onto the property ladder.
This is in contrast with technical or real externalities which have a direct resource effect on a third party. For example, pollution from a factory directly harms the environment.
Both pecuniary and real externalities can be either positive or negative.
I would argue that pecuniary externalities don't fit the technical definition of an externality because they affect people in the market in question rather than third parties.
Class 22 - definition of externality says that it helps or harms a third party through mechanisms other than price. Definition of percuniary externality is that it affects third party by changing prices. So is a percuniary externality an externality, since it affects through the price mechanism?
A:
Let's call it a pseudo-externality. :) From wikipedia:
A pecuniary externality is an externality which operates through prices rather than through real resource effects. For example, an influx of city-dwellers buying second homes in a rural area can drive up house prices, making it difficult for young people in the area to get onto the property ladder.
This is in contrast with technical or real externalities which have a direct resource effect on a third party. For example, pollution from a factory directly harms the environment.
Both pecuniary and real externalities can be either positive or negative.
I would argue that pecuniary externalities don't fit the technical definition of an externality because they affect people in the market in question rather than third parties.
Shut Down and Sunk Costs
Q:
In the notes for Class 11, it says that the "check shut down" test for short term is TR < TVC, only if all fixed costs are assumed to be sunk in short run. So if any of the fixed costs are not sunk in short run, how do we treat them? Should we assume we sell them off first, before doing the check shut down?
A:
Again, I don't think you have to worry about this, but if a fixed cost is not sunk in the short run, then you can think about explicit tradeoff that you are making:
If you choose not to produce, you lose the SUNK costs
If you choose to produce, you get some revenue and you pay the SUNK costs, the other FIXED costs and the VARIABLE costs. The only difference is that this doesn't simplify into a pretty little condition, but you take the choice that gives you more profit (or less loss).
In the notes for Class 11, it says that the "check shut down" test for short term is TR < TVC, only if all fixed costs are assumed to be sunk in short run. So if any of the fixed costs are not sunk in short run, how do we treat them? Should we assume we sell them off first, before doing the check shut down?
A:
Again, I don't think you have to worry about this, but if a fixed cost is not sunk in the short run, then you can think about explicit tradeoff that you are making:
If you choose not to produce, you lose the SUNK costs
If you choose to produce, you get some revenue and you pay the SUNK costs, the other FIXED costs and the VARIABLE costs. The only difference is that this doesn't simplify into a pretty little condition, but you take the choice that gives you more profit (or less loss).
Producer Surplus
Q:
In the notes for Class 2 and Class 3, it says that Producer Surplus as we have defined it, strictly speaking, only applies to basic factors like land, labor, capital. What is the reason for this? For the purpose of the exam, do we just assume that it applies?
A:
Yes. You don't have to worry about this. I woule explain further but would probably do more harm than good. :)
In the notes for Class 2 and Class 3, it says that Producer Surplus as we have defined it, strictly speaking, only applies to basic factors like land, labor, capital. What is the reason for this? For the purpose of the exam, do we just assume that it applies?
A:
Yes. You don't have to worry about this. I woule explain further but would probably do more harm than good. :)
Demand and Marginal Revenue
Q:
Is the MR curve always twice as steep as demand or is that specific to a particular question?
A:
Always twice as steep...but keep in mind that twice as steep as horizontal is still horizontal. Here's why:
Let's take the deamnd curve Qd = 40-2P...
so total revenue = P * Q
If we solve for P in demand we get P = 20 - Q/2
substitute in to get TR = (20-Q/2)*Q = 20Q - (Q^2)/2
now, marginal revenue is just the derivative of total revenue with respect to Q. (We don't explicitly talk about this since calculus is not a prerequisite to the course) So,
MR = D(TR)/D(q) = 20 - Q
Which is the same P intercept and twice as steep. Whee! :)
Is the MR curve always twice as steep as demand or is that specific to a particular question?
A:
Always twice as steep...but keep in mind that twice as steep as horizontal is still horizontal. Here's why:
Let's take the deamnd curve Qd = 40-2P...
so total revenue = P * Q
If we solve for P in demand we get P = 20 - Q/2
substitute in to get TR = (20-Q/2)*Q = 20Q - (Q^2)/2
now, marginal revenue is just the derivative of total revenue with respect to Q. (We don't explicitly talk about this since calculus is not a prerequisite to the course) So,
MR = D(TR)/D(q) = 20 - Q
Which is the same P intercept and twice as steep. Whee! :)
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