Some light has been shed on the 'mystery' in the previous post. The Federal Deposit Insurance Corporation, which is in charge of exactly what it sounds like, was unable to collect insurance premiums for 10 years (1996 - 2006).
From what I can tell - the news is new to me - banks are required to pay 1.15% of deposits as premiums to the FDIC. Unfortunately, the FDIC wasn't actually given any power to collect the premiums with.
As a result, while the banks were doing well, they refused to pay the premiums, and the FDIC's holdings fell to about 0.4% of insured deposits.
Once they were no longer doing well... that was a little too late to start paying.
So, YES, given this situation, a sharp drop in the reserve ratio could very well cause a bank run with no safety net.
Also, YES, this is as silly as it sounds. As a Consumerist commenter put it, "I kind of like this logic. I mean, I've paid homeowners insurance for a good long time and it hasn't caught on fire so far--so they should just be content with the money they have collected and continue to cover my risk free of charge."
Wednesday, March 11, 2009
Why doesn't the fed lower the required reserve ratio?
One of my students came up with a very interesting question.
US banks are still logjammed with toxic assets, and the US government is spending a lot of money it doesn't have bailing them out.
The same government is spending yet more money on a stimulus package.
Why doesn't it kill two birds with one stone and lower the required reserve ratio? Currently, it's at 10% for a large class of liabilities. (Full details at the link.)
For non-economists: Banks are in the business of lending money, not storing it. They want to lend as much as possible, and charge interest for it. The problem is that every now and then, depositors knock on their door and ask for their money back. In cash. At once. Because of this, banks can't lend ALL the money they receive. They need to keep some in reserve. The reserve ratio is the percentage of the money they take in that they need to keep in storage, just in case. In the US, this is 10%, by law (with some exceptions, see the link). In Canada, we haven't had a legally mandated reserve ratio since 1994. Our banks keep about 4.5% reserves.
Suppose the US lowered its mandatory reserve ratio to 5%, which is still higher than the ratio that Canadian banks chose on their own. All of a sudden, banks would have a whole bunch of extra cash on hand to work with. Well, okay, so most of it wouldn't actually be cash, but the idea's the same.
Provided you believe that giving bailout money to the banks will help them, then you should also believe that allowing the banks to dip into their piggy banks should help them.
The main exception to this that I can think of is that if the drop in reserve requirements is too quick and too large, investors could panic and cause a bank run. Because banks have most of their money tied up in loans and such, they can get into trouble if everyone asks for their money back at once. Mind, this trouble is always present...
A fall in the reserve ratio works very much like an injection of money, and will tend to boost the economy in the short run. (SOMEONE is getting that unfrozen money, after all.) In the long run, it all washes out, because eventually prices adjust to the new amount of cash. The kicker is that lowering the reserve ratio also 'powers up' later injections of money - so, if what the government wants to do IS pour money into the economy for a short-term band-aid while they figure things out, and if they're willing to put up with higher prices later on, lowering the reserve ratio would help.
So, why DOESN'T the US use the reserve ratio as a policy instrument? It's run out of wiggle room with interest rates, but there's still at least 5 percentage points of reserve ratio to play with before reaching Canada's level.
Some possibilities:
1. The most convincing one: after years of being stuck at 10%, lowering the reserve ratio may trigger financial panic and bank runs.
2. Maybe the US wants to avoid higher prices in the future - this is odd, given that recently there was a fear of deflation (falling prices).
3. The US may have other plans for its monetary policy that require tighter cash.
4. The US government doesn't bother because it doesn't think it would be effective - after all, banks are logjammed for other reasons. (Though I AM of the opinion that US banks doing their best to dodge reserve requirements by turning mortgages, which probably count against reserves, into other securities that don't, are part of what got us into this mess.)
This is a very good question that I don't have a satisfactory answer two. Comments encouraged.
As for the student, he's earned himself a bonus mark.
US banks are still logjammed with toxic assets, and the US government is spending a lot of money it doesn't have bailing them out.
The same government is spending yet more money on a stimulus package.
Why doesn't it kill two birds with one stone and lower the required reserve ratio? Currently, it's at 10% for a large class of liabilities. (Full details at the link.)
For non-economists: Banks are in the business of lending money, not storing it. They want to lend as much as possible, and charge interest for it. The problem is that every now and then, depositors knock on their door and ask for their money back. In cash. At once. Because of this, banks can't lend ALL the money they receive. They need to keep some in reserve. The reserve ratio is the percentage of the money they take in that they need to keep in storage, just in case. In the US, this is 10%, by law (with some exceptions, see the link). In Canada, we haven't had a legally mandated reserve ratio since 1994. Our banks keep about 4.5% reserves.
Suppose the US lowered its mandatory reserve ratio to 5%, which is still higher than the ratio that Canadian banks chose on their own. All of a sudden, banks would have a whole bunch of extra cash on hand to work with. Well, okay, so most of it wouldn't actually be cash, but the idea's the same.
Provided you believe that giving bailout money to the banks will help them, then you should also believe that allowing the banks to dip into their piggy banks should help them.
The main exception to this that I can think of is that if the drop in reserve requirements is too quick and too large, investors could panic and cause a bank run. Because banks have most of their money tied up in loans and such, they can get into trouble if everyone asks for their money back at once. Mind, this trouble is always present...
A fall in the reserve ratio works very much like an injection of money, and will tend to boost the economy in the short run. (SOMEONE is getting that unfrozen money, after all.) In the long run, it all washes out, because eventually prices adjust to the new amount of cash. The kicker is that lowering the reserve ratio also 'powers up' later injections of money - so, if what the government wants to do IS pour money into the economy for a short-term band-aid while they figure things out, and if they're willing to put up with higher prices later on, lowering the reserve ratio would help.
So, why DOESN'T the US use the reserve ratio as a policy instrument? It's run out of wiggle room with interest rates, but there's still at least 5 percentage points of reserve ratio to play with before reaching Canada's level.
Some possibilities:
1. The most convincing one: after years of being stuck at 10%, lowering the reserve ratio may trigger financial panic and bank runs.
2. Maybe the US wants to avoid higher prices in the future - this is odd, given that recently there was a fear of deflation (falling prices).
3. The US may have other plans for its monetary policy that require tighter cash.
4. The US government doesn't bother because it doesn't think it would be effective - after all, banks are logjammed for other reasons. (Though I AM of the opinion that US banks doing their best to dodge reserve requirements by turning mortgages, which probably count against reserves, into other securities that don't, are part of what got us into this mess.)
This is a very good question that I don't have a satisfactory answer two. Comments encouraged.
As for the student, he's earned himself a bonus mark.
Friday, February 6, 2009
Zimbabwe's self-destructing currency
Zimbabwe suffers from inflation of about 231 million percent a year. (Roughly, 5.5% a day.) There are many reasons for this, the most obvious being that the government keeps printing money. Like other goods, the value of money depends on the interaction of supply and demand. If the world is flooded with dollars, dollars fall in value.
The traditional first step toward slowing or stopping inflation is to stop printing money. Zimbabwe's central bank had a different idea... they'll keep the presses running, but the money will be printed with a built-in expiry date.
Very clever, even if didn't work.
The traditional first step toward slowing or stopping inflation is to stop printing money. Zimbabwe's central bank had a different idea... they'll keep the presses running, but the money will be printed with a built-in expiry date.
Very clever, even if didn't work.
Do banks create money?
(This is Tuesday's post, delayed due to midterms.)
There is a lingering belief among certain sections of the general public that the business of banks is to keep money safe. This belief is held alongside the knowledge that banks are in the business of lending money for profit. The money they lend is, in large part, that which they receive from their depositors.
The end result is that the sum of deposits is almost always greater than the sum of hard currency - banks 'expand' the money supply.
Often, this is explained as banks 'creating money' - while in some sense true, this is a very misleading description. Money is no more created by the banking system than water is created by freezing a lake. The density of water changes with heat, so that ice occupies a volume about 9% greater than the same mass of water at room temperature. While one could argue that this represents an increase in the 'amount' of water, to say water was created would be misleading.
Unfortunately, few articles take the time to explain in detail how the expansion of money works. This article, available free of charge from the Richmond Fed, is an exception. From its abstract:
"Beginning students of banking must grapple with a curious paradox: the banking system can multiply deposits on a given base of reserves yet none of its member banks can do so. Let the reserve-to-deposit ratio be, say, 20 percent and the system can, by making loans, create $5 of deposit money per dollar of reserves received. By contrast, the individual bank receiving that same dollar on deposit can lend out no more than 80 cents of it. How does one reconcile the banking system's ability to multiply loans and deposits with the individual bank's inability to do so?"
The article then explains the historical development of our understanding of the concept, and does it all with a minimum of algebra. Highly recommended reading.
There is a lingering belief among certain sections of the general public that the business of banks is to keep money safe. This belief is held alongside the knowledge that banks are in the business of lending money for profit. The money they lend is, in large part, that which they receive from their depositors.
The end result is that the sum of deposits is almost always greater than the sum of hard currency - banks 'expand' the money supply.
Often, this is explained as banks 'creating money' - while in some sense true, this is a very misleading description. Money is no more created by the banking system than water is created by freezing a lake. The density of water changes with heat, so that ice occupies a volume about 9% greater than the same mass of water at room temperature. While one could argue that this represents an increase in the 'amount' of water, to say water was created would be misleading.
Unfortunately, few articles take the time to explain in detail how the expansion of money works. This article, available free of charge from the Richmond Fed, is an exception. From its abstract:
"Beginning students of banking must grapple with a curious paradox: the banking system can multiply deposits on a given base of reserves yet none of its member banks can do so. Let the reserve-to-deposit ratio be, say, 20 percent and the system can, by making loans, create $5 of deposit money per dollar of reserves received. By contrast, the individual bank receiving that same dollar on deposit can lend out no more than 80 cents of it. How does one reconcile the banking system's ability to multiply loans and deposits with the individual bank's inability to do so?"
The article then explains the historical development of our understanding of the concept, and does it all with a minimum of algebra. Highly recommended reading.
Thursday, January 29, 2009
Overlapping generations... of jellyfish
So there's an immortal jellyfish...
Theologians and philosophers must be having a field day. Economists? I'm worried about whether the jellyfish pension system is fully-funded or pay-as-you-go.
Theologians and philosophers must be having a field day. Economists? I'm worried about whether the jellyfish pension system is fully-funded or pay-as-you-go.
Tuesday, January 27, 2009
A fun-to-read primer on banking and finance
19th century citizens were as bewildered and dismayed by 'modern' finance as we are. Enter Walter Bagehot, man of letters and editor of The Economist, who decided to clear up the confusion by writing a down-to-earth guide on what really goes on in the money market. His classic, 'Lombard Street', is surprisingly relevant and brisk reading today. The full text is available online.
For modern audiences, I recommend the following chapters:
1. Introductory - this chapter shows how a money market, for all its faults, can be of benefit to a country. It also explains how fractional reserve banking works.
2. A general view of Lombard Street - explains how reserves are managed by the central bank and other banks. This is done for both gold-standard and unbacked, fiat currency.
5. The mode in which the value of money is settled in Lombard Street - the title says it all. This short chapter explains how the value of money is determined in a money market, and goes into detail about exactly how much power the central bank has in this regard.
6. Why Lombard Street is often very dull, and sometimes extremely excited - this chapter explains business cycle fluctuations: booms and busts, good times and recessions. All from the point of view of the money market, of course.
The rest of the (short) book, while very interesting, relies too much on the particular circumstances of the time and country in which it was written for me to be able to recommend it as general reading.
For modern audiences, I recommend the following chapters:
1. Introductory - this chapter shows how a money market, for all its faults, can be of benefit to a country. It also explains how fractional reserve banking works.
2. A general view of Lombard Street - explains how reserves are managed by the central bank and other banks. This is done for both gold-standard and unbacked, fiat currency.
5. The mode in which the value of money is settled in Lombard Street - the title says it all. This short chapter explains how the value of money is determined in a money market, and goes into detail about exactly how much power the central bank has in this regard.
6. Why Lombard Street is often very dull, and sometimes extremely excited - this chapter explains business cycle fluctuations: booms and busts, good times and recessions. All from the point of view of the money market, of course.
The rest of the (short) book, while very interesting, relies too much on the particular circumstances of the time and country in which it was written for me to be able to recommend it as general reading.
Friday, January 23, 2009
An early beer ad
Advertising jingles are not new. Watkin's Ale is a beautiful beer ad from 1580, often played in concert by early music groups. Then, as now, sex sells: the ballad is a description of how a maiden surrendered her virtue for Watkin's Ale, finding it a fair trade.
Thursday, January 22, 2009
The economics of a simpler time - a reading list for reformers
It's not unusual for people fed up with the current world economy to suggest that we move back to a simpler time - one without easy credit, strict controls on interest rates (or their abolishment), a gold-backed currency, and without a focus on growth or rampant consumerism.
This is not an impossible dream. The option IS on the table... with a catch. Whatever benefits there may be from such a move come at a cost. If a country, culture or society is to make such a decision, it is very important to know exactly what the benefits and drawbacks of a 'simpler' system are.
As it happens, some of the finest economic minds in history lived during such an age, and left detailed analyses of their world to posterity. Anyone seeking economic reform or an overthrow of the current system will be well-served by reading what they have to say. (When doing so, keep in mind that some things HAVE changed. The 19th century did not have access to air travel, refrigeration or the internet.)
Here's my suggested reading list, with a few comments:
1. Thomas Malthus, 'Principles of Political Economy'. Reverend Malthus is best known for his essay on population, but he was a remarkably capable economist with a strong focus on sustainability, centuries ahead of his time. This is an outstanding basic economics text, covering a wide variety of subjects with humility and an enjoyable style of writing.
2. David Ricardo, 'Principles of Political Economy and Taxation' - Ricardo wrote this book under protest. Despite that, it turned out to be an important early investigation of what determines rent and taxes. Some of it is just plain wrong, but all of it is thought-provoking. Also, it's very short. It makes an excellent companion to Malthus, since the two refer to each other.
3. John Stuart Mill, 'Principles of Political Economy' - If you only read one book on economics, this should be it. Beautiful writing, clear exposition, an impressive scope... and he did it all without equations.
Some of you may wonder why Adam Smith didn't make the cut.
I quite enjoyed the Wealth of Nations - enough to re-read it several times. However, despite having some wonderful passages, as a complete text, it's mostly of historical interest. The book is too wordy for its own good, and extremely repetitive. The topics Smith covers are better dealt with in Mill and Malthus, who also correct a few of the pioneer's most obvious errors. Smith had a few specific axes to grind with respect to events that were important at the time and are now obscure, leading to very long stretches of boredom for the modern reader.
The Everyman edition of the Wealth of Nations, which I own, includes notes on the side of each paragraph summarizing its content. If you buy such a print edition, then Smith makes fantastic bathroom reading... flipping the book open to a random page and reading a paragraph or two at a time is a joy. Reading it through, though, as a cohesive work? Not so much.
This is not an impossible dream. The option IS on the table... with a catch. Whatever benefits there may be from such a move come at a cost. If a country, culture or society is to make such a decision, it is very important to know exactly what the benefits and drawbacks of a 'simpler' system are.
As it happens, some of the finest economic minds in history lived during such an age, and left detailed analyses of their world to posterity. Anyone seeking economic reform or an overthrow of the current system will be well-served by reading what they have to say. (When doing so, keep in mind that some things HAVE changed. The 19th century did not have access to air travel, refrigeration or the internet.)
Here's my suggested reading list, with a few comments:
1. Thomas Malthus, 'Principles of Political Economy'. Reverend Malthus is best known for his essay on population, but he was a remarkably capable economist with a strong focus on sustainability, centuries ahead of his time. This is an outstanding basic economics text, covering a wide variety of subjects with humility and an enjoyable style of writing.
2. David Ricardo, 'Principles of Political Economy and Taxation' - Ricardo wrote this book under protest. Despite that, it turned out to be an important early investigation of what determines rent and taxes. Some of it is just plain wrong, but all of it is thought-provoking. Also, it's very short. It makes an excellent companion to Malthus, since the two refer to each other.
3. John Stuart Mill, 'Principles of Political Economy' - If you only read one book on economics, this should be it. Beautiful writing, clear exposition, an impressive scope... and he did it all without equations.
Some of you may wonder why Adam Smith didn't make the cut.
I quite enjoyed the Wealth of Nations - enough to re-read it several times. However, despite having some wonderful passages, as a complete text, it's mostly of historical interest. The book is too wordy for its own good, and extremely repetitive. The topics Smith covers are better dealt with in Mill and Malthus, who also correct a few of the pioneer's most obvious errors. Smith had a few specific axes to grind with respect to events that were important at the time and are now obscure, leading to very long stretches of boredom for the modern reader.
The Everyman edition of the Wealth of Nations, which I own, includes notes on the side of each paragraph summarizing its content. If you buy such a print edition, then Smith makes fantastic bathroom reading... flipping the book open to a random page and reading a paragraph or two at a time is a joy. Reading it through, though, as a cohesive work? Not so much.
Tuesday, January 20, 2009
An interesting discussion abou the US economy
In October of last year, MIT rounded up five of its researchers to give a panel discussion on the state of the economy, and how it got there. The whole sold-out session is online, courtesy of MIT's TechTV.
I think it may be a bit too jargon-filled for non-economists to absorb in one sitting, but it's at just the right level for 1st and 2nd-year economics undergraduates. Thanks to Michael Picard for the link.
For non-economists, my favourite explanations of the sources of the crisis remain This American Life's two brilliant episodes, The Giant Pool of Money and Another Frightening Show about the Economy. Be warned, though, that the announcer had laryingitis during the first of the episodes.
I think it may be a bit too jargon-filled for non-economists to absorb in one sitting, but it's at just the right level for 1st and 2nd-year economics undergraduates. Thanks to Michael Picard for the link.
For non-economists, my favourite explanations of the sources of the crisis remain This American Life's two brilliant episodes, The Giant Pool of Money and Another Frightening Show about the Economy. Be warned, though, that the announcer had laryingitis during the first of the episodes.
Thursday, January 15, 2009
A barley farmer's view of the Canadian wheat board
The Canadian Wheat Board is the world's largest single seller of wheat and barley, accounting for 20% of the global market.
It was formed in response to the tremendous poverty of Western Canadian farmers during the Great Depression. Individual (small) farmers were powerless, and had to take whatever they could get for their crops. By having one entity, the CWB, sell the crops of thousands of farmers, they could obtain much better prices for their wheat and barley.
Membership is mandatory in three provinces and part of a fourth. This gives the CWB the clout it needs in global grain markets.
At least one farmer would like the Canadian Wheat Board to leave him alone. Hearing the reasons why is interesting, and of special value to economics undergraduates learning about perfect competition and monopoly.
It was formed in response to the tremendous poverty of Western Canadian farmers during the Great Depression. Individual (small) farmers were powerless, and had to take whatever they could get for their crops. By having one entity, the CWB, sell the crops of thousands of farmers, they could obtain much better prices for their wheat and barley.
Membership is mandatory in three provinces and part of a fourth. This gives the CWB the clout it needs in global grain markets.
At least one farmer would like the Canadian Wheat Board to leave him alone. Hearing the reasons why is interesting, and of special value to economics undergraduates learning about perfect competition and monopoly.
Tuesday, January 13, 2009
Some interesting features of recent US/Canada cross-border shopping
Prior to 2001, same day auto trips between the US and Canada moved in lockstep with the US dollar/Canadian dollar exchange rate. This is not terribly surprising; Canadians are famously quick to snap up exchange-rate-induced bargains. If the Canadian dollar rose in value, we'd quickly dash across the border to stock up on cheap US goods before the prices adjusted.
As Statistics Canada showed in a December 2007 report, that pattern has since broken down. If anything, same-day auto trips now look to be almost entirely independent of the exchange rate.
Why?
There are several suspects. Crossing the border is more of a hassle than it used to be, and online cross-border shopping is as easy as typing '.com' instead of '.ca' after the name of a South American river.
Here's something else to add spice to the discussion: according to the CBC, in 2007 the perception at the border was that automobile-fueled cross-border shopping was booming. According to Statistics Canada, it was not.
Was the perceived boom due to a confusion of anecdotes with data? Was there a sharp increase in unreported trips? Food for thought.
As Statistics Canada showed in a December 2007 report, that pattern has since broken down. If anything, same-day auto trips now look to be almost entirely independent of the exchange rate.
Why?
There are several suspects. Crossing the border is more of a hassle than it used to be, and online cross-border shopping is as easy as typing '.com' instead of '.ca' after the name of a South American river.
Here's something else to add spice to the discussion: according to the CBC, in 2007 the perception at the border was that automobile-fueled cross-border shopping was booming. According to Statistics Canada, it was not.
Was the perceived boom due to a confusion of anecdotes with data? Was there a sharp increase in unreported trips? Food for thought.
Thursday, January 8, 2009
Unintended consequences
After several scandals, the US has decided to mandate lead testing for all items that may come in contact with children.
As this Bookblog entry explains, the regulation was written so sloppily that it may put US-based used book stores out of business. All of them.
More information is available from The Consumerist, including further side effects.
If you have any information suggesting that this policy is not the lunacy it appears to be, please post it in the comments below.
Update: From Bookshopblog - "EDIT: as of 1/8/09 CPSC has issued an exemption for second hand dealers. New books are STILL not exempted, but step in right directionm (sic). (and no guarantee they won’t change their mind again)"
As this Bookblog entry explains, the regulation was written so sloppily that it may put US-based used book stores out of business. All of them.
More information is available from The Consumerist, including further side effects.
If you have any information suggesting that this policy is not the lunacy it appears to be, please post it in the comments below.
Update: From Bookshopblog - "EDIT: as of 1/8/09 CPSC has issued an exemption for second hand dealers. New books are STILL not exempted, but step in right directionm (sic). (and no guarantee they won’t change their mind again)"
The nature of capitalism
John Kay has some interesting views on the nature of capitalism, and suggests that some modern business types have missed the point entirely.
(Thanks to LW for the link.)
(Thanks to LW for the link.)
Wednesday, January 7, 2009
Virtual currencies can have exchange rate crises, too
A student sent me a link to a very interesting article on a virtual currency crisis.
Massively multiplayer video games, such as World of Warcraft, allow millions of gamers to participate in a virtual world, complete with a virtual economy. These economies typically have their own currencies.
The biggest difference between virtual and real currencies is that players usually mint the virtual currencies, whereas that power is reserved by government in most offline currencies. In these online games, currency is often created from nothing whenever a player accomplishes a specific task, such as defeating an enemy. The currency is valued because many desirable in-game activities and purchases require its use. Hyperinflation is kept at bay by a planned system of leakages and money sinks.
There's a catch to all this, of course. Some players play for hours on end, others for much shorter periods of time. Money sinks must be scaled to the intensive players in order to avoid hyperinflation or, for in-game items with hard-coded prices, in order to maintain scarcity.
This puts casual players at a disadvantage, and creates the opportunity for a carry trade of sorts, exchanging real-world currency for in-game currency.
The article linked to above deals with an example of this 'Real Money Trading' (RMT), and its peculiar pitfalls.
Massively multiplayer video games, such as World of Warcraft, allow millions of gamers to participate in a virtual world, complete with a virtual economy. These economies typically have their own currencies.
The biggest difference between virtual and real currencies is that players usually mint the virtual currencies, whereas that power is reserved by government in most offline currencies. In these online games, currency is often created from nothing whenever a player accomplishes a specific task, such as defeating an enemy. The currency is valued because many desirable in-game activities and purchases require its use. Hyperinflation is kept at bay by a planned system of leakages and money sinks.
There's a catch to all this, of course. Some players play for hours on end, others for much shorter periods of time. Money sinks must be scaled to the intensive players in order to avoid hyperinflation or, for in-game items with hard-coded prices, in order to maintain scarcity.
This puts casual players at a disadvantage, and creates the opportunity for a carry trade of sorts, exchanging real-world currency for in-game currency.
The article linked to above deals with an example of this 'Real Money Trading' (RMT), and its peculiar pitfalls.
Tuesday, January 6, 2009
Price, sales and music piracy
In August of 2007, Ars Technica pointed out that the impact of piracy on the music business is probably over-estimated. The demand for music at a near-zero price is, after all, much larger than the demand for music at $20 a CD.
An example: Assume a world where there is no piracy, songs cost $1 each, and the public buys 10,000 of them. Now suppose a pirate enters the market, giving away songs at $0 each, and that 30,000 people are willing to listen to free songs. Even if the number of songs sold legally stayed at 10,000, piracy could be measured as being twice the volume of sales. This would be misleading, though, since the extra 20,000 songs are not lost sales. They're evidence of a downward-sloping demand curve that continues past the price that legal suppliers are willing to charge.
An example: Assume a world where there is no piracy, songs cost $1 each, and the public buys 10,000 of them. Now suppose a pirate enters the market, giving away songs at $0 each, and that 30,000 people are willing to listen to free songs. Even if the number of songs sold legally stayed at 10,000, piracy could be measured as being twice the volume of sales. This would be misleading, though, since the extra 20,000 songs are not lost sales. They're evidence of a downward-sloping demand curve that continues past the price that legal suppliers are willing to charge.
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