Tape 99 - The economics of zero population growth

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-	Welcome, once again, as MIT Professor Paul Samuelson	0:02
	discusses the current economic scene.	0:04
	This bi-weekly series is produced	0:07
	by Instructional Dynamics Incorporated	0:09
	and was recorded April 10th, 1972.	0:11
-	One subject that is discussed very much	0:15
	these days in economics is the problem	0:17
	of zero population growth.	0:20
	It's part of the whole concern over ecology.	0:23
	Just to tick off some items in the passing news	0:28
	that are related to this,	0:31
	a group of English scientists, Natural Scientists,	0:33
	got together and put out a blueprint for survival	0:39
	and some very sweeping predictions about the dismal future	0:43
	for the world and some rather drastic	0:47
	measures of therapy are recommended,	0:51
	for example any product that doesn't	0:53
	last a great number of years	0:55
	should have a special tax on it,	0:58
	a tax in other words upon obsolescence.	0:59
	Still, another indication of the tremendous	1:04
	interest in this matter is the work	1:07
	of the so-called Club of Rome.	1:10
	I have reference to my own colleague at MIT,	1:12
	Dr. J. Forrester and one of his co-workers,	1:17
	Professor Meadows who have put out a book	1:22
	that has received a great deal of attention.	1:26
	Forrester has a book of his own	1:28
	on this subject and Meadows, with the group	1:29
	for the Club of Rome, has put out a publication	1:33
	which is very much under discussion now,	1:37
	for example, the state department has had Meadows	1:41
	addressing groups in other countries.	1:44
	It's a subject in short which is fraught with interest.	1:48
	Now, I did touch on this matter	1:50
	in one of my earlier tapes a long time ago	1:53
	but because I get so many letters on the subject	1:56
	I'd like to speak about it.	2:01
	I may say that my experience is not unique.	2:03
	My colleague, as a Newsweek columnist,	2:06
	Professor Henry Wallach, of Yale,	2:10
	devoted a column in which he was kind of cold	2:13
	towards zero population growth	2:16
	and the heavens descended on him,	2:18
	a real barrage of mail onslaughts.	2:20
	He's a brave and determined man	2:24
	and he came back with a second column,	2:27
	I haven't heard but I suppose that	2:29
	that hasn't pleased everybody.	2:31
	I propose in the beginning to give a brief history	2:35
	of population and notions about population	2:38
	because this is not something entirely new	2:41
	that we're talking about	2:44
	and it'll give us some perspective	2:45
	to go back a distance.	2:47
	Let me go back just to the end of the 18th century	2:50
	and recall for you that	2:54
	there was a school of thought in England	2:59
	that believed in progress,	3:02
	in the perfection of man,	3:04
	these were the perfectionists.	3:06
	William Godwin was the leader of that,	3:08
	very interesting man in the history of ideas	3:12
	who has not been studied enough, I think,	3:15
	and who will increasingly come under new study.	3:18
	But, for this purpose, I need only mention	3:23
	that the father of the economist Malthus	3:26
	became a follower of Godwin and he believed	3:32
	that every day, in every way,	3:36
	things were getting better and better.	3:38
	That the Earth could support any size population,	3:40
	that man was,	3:44
	after having sinned in Eden,	3:47
	having gone through travail,	3:49
	man was now finally coming out	3:51
	at the other end of the tunnel	3:54
	into perfection.	3:56
	And	3:59
	T. Robert Malthus, who was to become	4:01
	a Church of England parson and economist,	4:05
	listened to his father and, as so often happens,	4:10
	father and son did not agree in every respect,	4:13
	and in arguing with his father	4:16
	Malthus,	4:19
	Malthus,	4:21
	M-A-L-T-H-U-S,	4:23
	Malthus decided that Godwin was completely wrong	4:26
	and he sat down and wrote a book about it,	4:31
	this was in 1798.	4:33
	Of course, that's a very famous book,	4:35
	it's something that everybody	4:36
	knows about.	4:40
	I say everybody, not every modern computer	4:43
	realizes that it is going through	4:46
	some of the same paces	4:48
	that T.R. Malthus went through at that time.	4:49
	Now, what was it that Malthus said?	4:53
	Malthus said	4:56
	man	4:57
	is not becoming perfect,	4:59
	we are not moving towards Utopia.	5:01
	Quite the contrary, there are some inevitable laws	5:04
	and	5:09
	as Thomas Carlyle came to say	5:11
	these are dismal laws.	5:14
	Economics as the dismal science	5:15
	got that name from Thomas Carlyle	5:18
	and it got that name in connection	5:20
	with the dire predictions of Malthusian type	5:23
	about the law of diminishing returns	5:26
	and starvation around the corner.	5:28
	Malthus puts his arguments in the form	5:32
	of an irrefutable syllogism.	5:34
	He started out by saying that in every species	5:38
	and in mankind there is a tendency	5:42
	for population to grow at compound interest.	5:45
	If you have a hundred parents and you get	5:50
	210 offspring,	5:56
	that's one situation,	5:59
	if you have 200 parents you get twice 210 offspring,	6:01
	420, and this will happen through time.	6:05
	So, his first law is the famous law	6:09
	of the geometric progression.	6:12
	A geometric progression is like,	6:14
	1, 2, 4,	6:17
	8, 16,	6:18
	doubling every time.	6:20
	Of course, to follow such a sequence,	6:23
	geometric progression, with a positive rate of growth	6:25
	for any little length of time	6:29
	results in enormous numbers.	6:32
	I will remind you of the old story	6:34
	about how chess was discovered.	6:36
	The Sultan was so pleased by the discovery	6:39
	of this amusing game that he said to the inventor,	6:42
	name your reward, and the inventor said,	6:46
	I'm a modest man, I don't want anything.	6:48
	Sultan said, nonsense, name it, and he said,	6:50
	well if you really wanna give me something	6:53
	just put one grain of wheat	6:55
	on the first square of the chessboard	6:58
	and two grains of wheat on the second	7:00
	and just continue in this way	7:02
	until you've filled the whole chessboard.	7:04
	Well, there's not enough wheat in the world	7:06
	to	7:10
	provide that magnificent gift.	7:13
	That's the way geometric progressions grow.	7:16
	And Malthus was not the first,	7:19
	and he had a great number of followers	7:23
	who persued relentlessly the vision	7:25
	down the trail of geometric growth.	7:29
	It always fascinates classes in economics	7:34
	if you discuss the fact that all the wealth in England	7:36
	today could be traced back, as Keynes said,	7:41
	to the gold that Sir Francis Drake	7:45
	stole from the Spanish in the Golden Hind.	7:50
	If you compound that forward at 6% or 8%,	7:53
	some similar number, you will equal	7:58
	the present wealth of England.	8:01
	The American Indians sold the island of Manhattan	8:03
	for $24, so it is said, for trinkets.	8:07
	What if that $24 had have been put in the bank	8:12
	at compound interest?	8:14
	In early editions of my textbook	8:16
	I said at 6% that would equal the value	8:18
	of all the land in Manhattan today.	8:21
	Somebody wrote in to me and said,	8:26
	I think that only comes to 25 billion or 100 billion,	8:28
	and I think that you couldn't buy all the land	8:31
	in Manhattan for that price.	8:33
	So, I asked my research assistant	8:36
	to look in to the matter and she came back	8:38
	and said well, boss, if 6% won't do it try 6.5%.	8:40
	You just have to step up the rate a little bit	8:45
	and you'll get some very large numbers.	8:47
	Now,	8:51
	Malthus based his argument	8:52
	upon some casual amount of experience.	8:54
	We had in the American colonies,	8:58
	at the end of the 18th century,	9:02
	some evidence that family-size was	9:04
	eight.	9:08
	Go to old New England cemeteries	9:09
	and you'll see seven, eight women died of childbirth	9:11
	the age of 35 then the man married again.	9:14
	And, the natural rate of increase of population	9:18
	the size of the rate of growth of the geometric progression,	9:21
	Malthus estimated in a prosperous era,	9:25
	epoch, where there was no limitation	9:29
	of land and natural resources would be about	9:32
	a doubling every generation.	9:34
	Now, what is a generation?	9:36
	In college student life a generation	9:38
	can be measured in four years or eight years	9:41
	but the technical term for a generation	9:44
	is the age of a parent	9:46
	in giving birth to a child,	9:50
	and then when that child grows up and becomes a parent	9:52
	then that gap is the length of a generation.	9:56
	Of course we, as parents, have children	9:59
	over a period of time so you must	10:01
	take a certain average.	10:03
	Let's call 25 years a generation.	10:07
	A generation is longer in Sweden,	10:09
	where the women have their babies at a later age,	10:11
	then it would be in India,	10:13
	where they have their babies at a younger age.	10:14
	But a doubling of population every 25 years,	10:18
	that's the rate of compound	10:21
	interest that is a natural law according to Malthus,	10:25
	unless something prevents that from happening.	10:31
	Malthus had gone to Cambridge University.	10:36
	He learned a smattering of mathematics,	10:39
	he learned about geometric progressions.	10:41
	Unfortunately, he learned of only one	10:43
	other kind of progression.	10:45
	Aside from a geometric progression	10:48
	we're taught in high school algebra courses today	10:50
	about an arithmetic progression.	10:53
	Now an arithmetic progression,	10:55
	instead of doubling each time,	10:57
	each increment being a certain percent	11:00
	of the previous base, an arithmetic progression	11:02
	is not like compound interest,	11:05
	it's like simple interest and the steps upward	11:07
	are even steps, just like a stairway	11:10
	that always has the same size of the steps	11:13
	and it depends upon the step of the increment	11:18
	how fast an arithmetic progression will grow.	11:21
	You could have a very steep arithmetic progression	11:24
	but it still has a straight line	11:26
	if you plot it on a chart	11:27
	whereas compound interest, if you plot it on a chart,	11:29
	is always an accelerating curve	11:31
	that looks convex from	11:34
	below.	11:37
	Well, Malthus said	11:39
	America will soon be filled up with people,	11:43
	England certainly is already	11:46
	pretty much filled up with people.	11:47
	Every geometric progression must in the end	11:50
	fill up any limited amount of natural resources.	11:53
	And so, he said, the limit is going to be	11:58
	food production, essentially.	12:00
	Food production, said Malthus, and here	12:02
	we must watch his argument very closely,	12:05
	food production grows at an arithmetic progression.	12:07
	Population grows at a geometric progression.	12:13
	Every geometric progression, given enough time,	12:16
	will far exceed and infinitely exceed	12:19
	any arithmetic progression,	12:23
	no matter what the constants are.	12:24
	Therefore, said Malthus,	12:26
	there is only one destiny for mankind	12:28
	and that destiny is that	12:31
	the death rate will go up and that	12:35
	man can only come in equilibrium	12:38
	at the minimum level of subsistence.	12:40
	When you're finally through disease, and starvation,	12:43
	and malnutrition, and over crowding,	12:47
	get so large a density of population	12:50
	that the wage can be no more per man	12:53
	than barely enough to keep him alive.	12:57
	Keep him alive, by the way, and bearing	13:00
	in his family	13:04
	five, six, seven infants,	13:06
	half of whom die at birth,	13:10
	another half of whom die in infancy,	13:13
	and enough must always die	13:17
	so that each two people can only leave behind them	13:19
	two people.	13:22
	Well, I think you'll grant that,	13:24
	if that is the destiny of mankind,	13:25
	in every place, in every continent, in every time	13:28
	then economics is a dismal science.	13:33
	You mustn't, however, shoot the economist,	13:36
	he's just the messenger who brings the bad news.	13:38
	That's the way Malthus left his first edition.	13:42
	By his second and later editions	13:45
	he took pity on mankind.	13:47
	Perhaps he learned a little,	13:49
	in fact he began to study things more widely,	13:50
	and so he said there is some hope.	13:53
	What you can try to do is to change	13:56
	the geometric progression	13:59
	by late marriage.	14:02
	He advocated chastity until you get married.	14:05
	Once you were married you had a license	14:09
	to produce children,	14:12
	remember he was a Church of England clergyman,	14:14
	he was not in favor of birth control at that time,	14:16
	he says,	14:19
	"I will not comment on those nefarious French devices"	14:20
	showing us that, already,	14:24
	France was known at the end of the 18th century	14:26
	as a country which was beginning to practice	14:28
	familial limitation.	14:30
	As a matter of fact, as an aside, let me say	14:32
	that anthropologists are now pretty sure	14:33
	that in almost every culture there are certain	14:37
	mechanisms for limiting population.	14:39
	In 17th century Japan, for example,	14:42
	the population was fairly stable	14:44
	and there wasn't measure of prosperity	14:46
	but it was maintained by infanticide.	14:50
	You exposed children if you didn't want them,	14:54
	particularly if they were girl children,	14:56
	so that when a baby was born	14:58
	the neighbors never congratulated you	15:00
	until their ascertained for sure	15:02
	that you intended to keep the baby,	15:04
	otherwise you exposed the baby just as the Romans did.	15:06
	This was abortion after the fact instead of abortion early	15:10
	in the fact.	15:16
	Well, let me assure you that although	15:18
	the Malthus argument is extremely simple	15:21
	it had great potency and it had great effect	15:24
	upon the thinking of the governments of the world,	15:27
	the poor law reform of 1832	15:32
	was guided in part by the principles of Malthus,	15:35
	let's make poverty as uncomfortable as possible,	15:39
	unemployment as uncomfortable as possible,	15:41
	because if you coddle the poor they'll simply	15:44
	have more children.	15:47
	Even by the middle of the century,	15:49
	by 1848, 1850 when John Stuart Mill,	15:52
	the last really of the classical economists was writing,	15:55
	Mill was living in the midst of the Industrial Revolution,	15:59
	in the greatest period of Victorian England.	16:03
	After the	16:08
	steam engine had been invented and came in to use,	16:11
	after the railroad had begun,	16:15
	after the automatic spinning jenny,	16:17
	after the automatic loom,	16:21
	the most remarkable period of progress,	16:24
	John Stuart Mill, who was a well informed and eclectic man	16:28
	was able to write the naive words	16:32
	that it's doubtful that science and invention	16:35
	have lightened the burden of a single	16:38
	typical average man anywhere in the world.	16:41
	Showing you how little you can know your own times,	16:45
	particularly in the days when statistics	16:48
	were very hard to come by.	16:51
	Well, what did Malthus forget?	16:55
	Malthus forgot two things.	16:59
	Most importantly, there was never a good basis	17:02
	for his arithmetic progression.	17:06
	He pulled that number out of a hat.	17:09
	He said population's gonna grow	17:12
	like one, two, four, eight.	17:14
	What about food?	17:17
	If we call present food one,	17:19
	he said let's suppose you could cultivate	17:21
	England like a garden,	17:23
	you could double food production.	17:24
	That's one, two.	17:26
	But in an arithmetic progression	17:28
	if we've only gone up one at each step,	17:30
	the next time we're at three and we're already in trouble.	17:32
	Even if he became more generous	17:36
	in his arithmetic progression and let's say	17:37
	we keep the geometric progression one, two, four, eight	17:40
	but the arithmetic progression goes one, seven,	17:43
	that's a jump of six,	17:47
	and you're much better off in the second period.	17:48
	Then another jump of six is 13.	17:51
	We're beginning to not be so well off.	17:55
	But, finally we go to 19.	17:57
	We're still ahead of the food supply.	18:00
	Then we're at 25 but, by this time,	18:02
	the population's at 32.	18:06
	There's just no beating the race.	18:08
	Now, why do I labor this particular point?	18:10
	I labor it because if you read the book	18:12
	by Dr. Meadows you will see that what is speaking there	18:15
	is the authoritative voice of the computer.	18:20
	Mustn't we be impressed by the certitude and accuracy	18:25
	of anything that comes authenticated by modern science,	18:30
	and by that most wonderful tool of modern science,	18:33
	the electronic computer.	18:36
	That's how the argument goes implicitly.	18:40
	I may say, by the way, that Professor Forrester	18:44
	and Dr. Meadows do not themselves make such claims	18:47
	but no matter how many times they cross themselves	18:51
	and say we want our analysis to be judged	18:55
	upon its merits we are making guesses,	18:58
	people inevitably think if it came out of MIT	19:00
	it must have a special degree of accuracy because	19:04
	everybody knows that everything that comes out of MIT	19:08
	in the field of thermal dynamics	19:11
	is practically guaranteed	19:13
	to be an agreed upon thing by all scientists.	19:15
	Well, I think back of the days when	19:20
	there was a machine that played chess	19:25
	and all over Europe good chess players	19:28
	played against the machine and were defeated,	19:31
	and everybody thought this to be a marvel.	19:35
	This, by the way, was before the age	19:36
	of the electronic computer.	19:37
	We now know that at chess a computer	19:39
	can be programmed to play a pretty good	19:42
	game of chess, can beat a kid,	19:43
	but it can't yet beat a master.	19:46
	Maybe in Chequers, by the way,	19:48
	a machine may be the equivalent	19:49
	of practically the best that there is.	19:51
	Well, this was before that time,	19:54
	and how marvelous it was,	19:56
	but you know what they discovered?	19:57
	They discovered a little dwarf	19:58
	who would curl up, literally, inside the machine,	20:01
	I've forgotten what his name was,	20:03
	it was a fraud.	20:06
	Well, I say to you that every time a message	20:07
	comes our from a modern computer	20:11
	there is no fraud, there is no little man curled up	20:13
	inside the solid state transistors of the computer.	20:16
	But,	20:21
	behind the computer, feeding in the input to the computer	20:22
	is a man	20:26
	and he is a mortal man	20:28
	with all the imperfections of man	20:31
	and the output cannot be better than then input.	20:33
	And so, although the voice is that of the computer	20:38
	the message is essentially that of Malthus	20:42
	because, although Meadows may be right	20:45
	that the amount of resources which can be found	20:50
	by geologists in the next half-century, or the next century	20:52
	may only be double what we now have.	20:58
	Or, if he said triple let's change that to that.	21:00
	Or, whatever he said let's double that amount.	21:04
	Nevertheless, because the differential equations	21:08
	of the Forrester-Meadows model	21:11
	are of the Malthusian type	21:15
	they involve constant coefficience.	21:17
	They essentially are generalized matrix,	21:19
	non-linear, geometric progressions,	21:22
	and because there are limitations	21:26
	upon resources put in them	21:28
	the Forresters and Meadows of the world	21:30
	cannot be wrong if they simply cert the following.	21:32
	That within my model,	21:35
	if disaster does not come by the year 2000	21:37
	then it will be here by the year 2025.	21:42
	And, if I'm wrong in that, that it doesn't come by 2025	21:45
	then it will be here by the year 3000.	21:48
	It's a perfectly self-fulfilling tautology.	21:51
	Some time, under their geometric progressions,	21:56
	there wouldn't be standing room	21:58
	for all the people in the world	22:00
	and there certainly would not be resource allocations.	22:02
	The result is that when you look at these charts	22:05
	the print out of the computer,	22:10
	which show the standard of living	22:13
	of even the most advanced countries of the world,	22:15
	some time in the next	22:17
	century, reaching a peak and going down,	22:20
	you must realize that this is not science fiction	22:25
	but this is speculative social science.	22:29
	The fact that there are interviews	22:33
	in Playboy on the subject shows	22:36
	what widespread interest, the fact	22:39
	that every journal I pick up,	22:41
	that Anthony Lewis, a very sophisticated columnist	22:43
	on the op-ed page of The New York Times,	22:47
	reports back from England approvingly on this,	22:49
	still cannot belie the fact	22:54
	that water cannot rise above its own source	22:55
	and what you have here is certain assumptions.	22:58
	Now, I don't want for a moment to argue	23:02
	that the assumptions made in this case	23:06
	are wrong	23:09
	because that would take a very searching examination.	23:11
	You wanna say this,	23:15
	that if you are a sophisticated student of economics	23:18
	and of the population problem	23:21
	I do not think you will find much new	23:23
	in the Club of Rome material	23:27
	which will sharpen your knowledge on this subject,	23:29
	which will enhance your understanding.	23:32
	This is not to deny that many members of the public	23:35
	may find their understanding of the whole problem	23:38
	improved by reading	23:41
	such	23:43
	materials.	23:45
	Moreover, it's a sad thought that sometimes	23:46
	in order to sell you must oversell	23:50
	and because the problem of pollution	23:52
	is an important problem,	23:54
	because the problem of the amenities of life	23:56
	having to do with elbow room and privacy	24:01
	are important it may be that I shouldn't	24:04
	be saying what I'm saying.	24:08
	Maybe I should, so-to-speak,	24:09
	in a good cause be quiet and say	24:12
	although this isn't quite right	24:15
	and privately, with a few elder professors,	24:16
	we can agree up on this,	24:20
	there should be a conspiracy of silence because	24:21
	it's good for the people to be alerted to this matter.	24:23
	Well, I'm assuming that my audience here	24:27
	is a fairly sophisticated audience	24:31
	and that it isn't necessary for me to take that	24:32
	particular position.	24:36
	I believe that the truth can stand	24:36
	being looked at and understood	24:39
	if only we can once arrive at it.	24:41
	I have only a few minutes.	24:45
	Let me mention, in connection with zero population growth,	24:47
	that Malthus was wrong because he didn't foresee how	24:51
	powerful would be what he called is arithmetic progression	24:58
	the actual progression was more powerful	25:02
	than the geometric progression of population.	25:04
	That's why, because of modern science,	25:07
	there's been such a tremendous increase	25:09
	in the standard of life.	25:11
	Moreover, what Malthus would not	25:14
	countenance later generations came to do,	25:18
	namely, explicit birth control,	25:20
	and after 1870 you could see not only in France	25:24
	but in the vital statistics of the middle classes,	25:27
	the more affluent classes all over western Europe,	25:30
	and increasingly in the United States,	25:33
	a decrease in the birth rate.	25:35
	This became apparent to every eye after 1925	25:38
	and because people always want	25:42
	to be excited in these matters	25:43
	they go from one side of the ship,	25:45
	tipping it in one direction,	25:48
	all in an avalanche over to the other side	25:50
	tipping it in the other direction,	25:52
	and after 1925 there were a rash of books called	25:53
	The End of the Human Race,	25:59
	Sweden Faces Depopulation,	26:03
	there was very excellent work done by Edwin Cannan	26:06
	in demography showing that England's population	26:08
	would reach a maximum, by the way a maximum	26:11
	lower than the present population of England.	26:14
	The logistic studies by Dr. Raymond Pearl	26:18
	of Johns Hopkins biology department	26:23
	in which he compared human populations	26:26
	to fruit flies in a bottle and in his bottle	26:28
	every colony of fruit flies finally leveled off	26:32
	like an S-shaped curve, called the logistics curve,	26:36
	by him.	26:39
	We had calculations by A. J. Lotka and R. R. Kuczynski	26:41
	which showed that the population was indeed	26:45
	in the distant future going to decline	26:49
	if the average number of children per family	26:52
	who survived to be married, to be fertile,	26:56
	to have children, was less than two.	26:58
	So, there was ground for extrapolation	27:04
	of a coming-in to population growth.	27:07
	But, it doesn't pay to be too certain in this matter	27:12
	because, as we all know, after 1939	27:16
	there was a whole change.	27:20
	There was a baby boom and the population	27:21
	turned very much the other way.	27:24
	Well, now I leave the story in its present state	27:26
	as it's well known after 1957 you have had	27:31
	a very considerable decrease in the birth rate,	27:35
	not only in the crude birth rate,	27:39
	but, if you refine the birth rate,	27:40
	it worked with the number of births	27:42
	per mother of childbearing age	27:45
	you find that the decline is even greater.	27:48
	So, the rate of population growth is leveling off.	27:51
	We will not have zero population growth	27:55
	for a long, long time even if the tendency	27:57
	was for a declining population	28:00
	because of past baby booms.	28:02
	How shall I sum up?	28:06
	Let me sum up by saying that it's worth	28:08
	another tape some time on the whole problem	28:12
	of ecology, the whole problem of whether	28:16
	we should be against science or whether	28:20
	we should utilize science for the purpose	28:22
	of cleaning up the atmosphere	28:24
	and solving some of these other particular problems.	28:27
	But, I think, I wouldn't do duty to the subject	28:31
	and to science without saying candidly	28:35
	that the hysteria such as it's represented	28:40
	by Blueprint For Survival	28:43
	is really not substantiated,	28:46
	careful, sober analysis of the realistic facts.	28:49
-	If you have any comments or questions	28:55
	for Professor Samuelson address them to	28:56
	Instructional Dynamics Incorporated,	28:58
	166 East Superior Street,	29:00
	Chicago, Illinois, 60611.	29:03

Item Info

Title:

Tape 99 - The economics of zero population growth

Date:

1972

Contributor:

Samuelson, Paul A. (Paul Anthony), 1915-2009

Subject:

Format:

audiocassettes

Language:

English

Digital Collection:

Paul A. Samuelson papers, 1933-2010 and undated

Source Collection:

Paul A. Samuelson papers, 1933-2010

Series:

Economics Cassette Series: Paul Samuelson

Rights:

Limited Re-Use

CC BY-NC 4.0

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Identifier:

RL10082-CS-0097
ref2333_y81
samuelsonpaul
duke:325120
pstau001097
ark:/87924/r49p2wp1q
9dfb7988-0ef6-41e4-af42-db54539ea55f

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Tape 99 - The economics of zero population growth

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