Economics 373

Natural Resource Economics

Mark Witte

Northwestern University

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Long Run Population

Why is the “replacement birthrate” 2.1 children per couple?

• The replacement birthrate of approximately 2.1 children per woman (or couple) is what is thought to be needed to maintain a stable population.
• The extra 0.1 is supposed to cover
• Women who die without having children
• The imbalanced sex ratio at birth
• Approximately 105 boys are born for every 100 girls
• Probability a birth is female = 100/(105+100) = 0.488
• Boys have generally higher mortality rates than girls from 0-14
• Suppose that only 95% of women survive to have children
• Replacement fertility ( R ) given by:

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Why is the “replacement birthrate” 2.1 children per couple?

• In the numerator, the “1” refers to the woman
• The “Sex ratio at birth” is Males/Females 105/100
• Suppose that the sex ratio was 100/100 and the probability that women survived to have children was 100%
• R = (1+1)/1 = 2, to keep a stable population, we would need each woman to have two kids
• If the sex ratio favors men and there’s some chance that not all women have children, then each woman who does have children would have to have somewhat more than two

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Why is the “replacement birthrate” 2.1 children per couple?

But what if the probability that women will have children at all is lower that we think?

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We take turns with our planet’s resources

• 8 billion people are alive today
• Around 108 billion people have ever lived
• If our species survives another 50 million years at similar populations to what we have now, then that will be…

3 million billion people

• Will we get the tradeoff over time right?
• Our ancestors lived hard lives; I would not have wished them to save for my sake

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Why should we care about people in the future?

We take turns with our planet’s resources

• Adam Smith was a big fan of the Invisible Hand
• Individual choices in the face of prices and wages would lead to a well organized, efficient, wealthy society
• But for prices to work, they need to cover all the relevant costs
• A lack of property rights with open access natural resources creates negative externalities and inefficient outcomes
• It’s really weird that we often seem to be doing better with managing our non-renewable resources better than our renewable resources
• But if we burn through our scarce minerals, fish, forests, and water supplies, will future generations have the backstops they need to live good lives?

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How many humans should we aim for?

When we think about the future, how many people are we thinking about?

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What would be the optimal number?

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Philosopher Derek Parfit (1942-2017)

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Known for “Parfit’s Repugnant Conclusion.”

How important and unique are humans?

Around 108 billion people have ever lived on Earth

If our species survives another 50 million years at similar populations to what we have now, then that will be 3 million billion people

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Derek Parfit’s Repugnant Conclusion: “For any possible population of at least ten billion people, all with a very high quality of life, there must be some much larger imaginable population whose existence, if other things are equal, would be better even though its members have lives that are barely worth living.” (Derek Parfit 1984)

Derek Parfit

• Philosopher
• “Total Utilitarianism” = N*U(c)
• “Repugnant Conclusion”, “Mere addition paradox”
• How many people should we have?
• Is the goal max consumption per capita?

What’s the optimal population size?

• Jeremy Bentham (1748-1832)
• Helped found UCL (Shareholder?!)
• Founder of Utilitarianism
• Bentham’s fundamental axiom: "it is the greatest happiness of the greatest number that is the measure of right and wrong."
• “Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do, as well as to determine what we shall do. On the one hand the standard of right and wrong, on the other the chain of causes and effects, are fastened to their throne. They govern us in all we do, in all we say, in all we think….” (An Introduction to the Principles of Morals and Legislation, 1780)

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A bit more on Bentham….

• John Stuart Mill was his student and was very much influenced by him
• Bentham was a proponent of animal rights
• It was the “capacity to suffer” rather than the “capacity to reason” that should set the “insuperable line” that should determine the existence of rights
• Otherwise would babies or people who are unconscious have rights?
• And an amazing line, that I think is intended as a burn on England for being slow on this: “The French have already discovered that the blackness of the skin is no reason a human being should be abandoned without redress to the caprice of a tormentor.”
• “The question is not, Can they reason? nor, Can they talk? but, Can they suffer?”
• Early supporter of the equality of women and the acceptance of gay rights

What’s the optimal population size?

• There has been a lot of discussion of late about how the US has too many immigrants and too few births
• How do we know?
• What is the optimal number of each?
• Aren’t they sort of substitutes?
• But one is probably more useful than the other?
• How costly are immigrants?
• How much can they produce versus how many resources they consume? What are their skills? Can they speak English?
• How does that compare with raising a baby?

February 20, 2020 - Former Trump Chief of Staff

Mulvaney says U.S. is ‘desperate’ for more legal immigrants

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“We are desperate, desperate for more people,” Mr. Mulvaney told a crowd in England. “We are running out of people to fuel the economic growth.” He said the country needed “more immigrants” but wanted them in a “legal” fashion.

March 6, 2020 (two weeks later)

Maybe the US is already too crowded?

Country Population/mile² US population with that density

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US (lower 48) 104 328 million

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France 319 1 billion

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China 378 1.2 billion

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Nigeria 565 1.8 billion

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Germany 603 1.9 billion

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South Korea 1,340 4.2 billion

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India has a population of 1.44 billion

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What’s the optimal population size?

• What does Bentham’s “greatest happiness of the greatest number” mean?
• We usually take it as “greatest happiness for the greatest given number”
• We try to maximize “average utility”
• But why?
• Interesting question for population and immigration
• Consider comparisons of Mexico with Japan
• Which country is doing best in terms of the “greatest good?”

What’s the optimal population size?

• Consider comparisons of Mexico with Japan
• Which country is doing best in terms of the “greatest good?”
• Growth since 1960?
• Japan is a lot richer!
• Mexico has a lot more people!
• Do we put a weight of zero value on the lives of Japanese who never lived?

What’s the optimal population size?

• What are we maximizing?
• Classic (or average) utilitarianism: Max u(C/N)
• Total utilitarianism: Max N*u(C/N)
• Which one seems like a better goal?

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What’s the optimal population size?

• Maximize average utility or total utility?
• National welfare: W( N_t ,c_t ) = N_t*u( c_t )
• u(c_t ) utility of per capita consumption
• Suppose that there is some fixed resource R
• Fixed for the given period? Or forever?
• Are we thinking about the utility of people alive now?
• Or the utility of everyone who will ever live?
• Let’s treat the now/forever as interchangeable
• Let’s define u(c) = R/N

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So…resources matter a lot for human welfare?

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Or is this formulation stupid?

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Distribution?

What’s the optimal population size?

• National welfare: W( N_t ,c_t ) = N_t*u( c_t )
• u(c_t ) per capita consumption
• Some fixed resource R
• Let’s define u(c) = ln(R/N)
• That’s pretty standard, right?
• It shouldn’t get weird

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What’s the optimal population size?

• "Population and Welfare: The Greatest Good for the Greatest Number"
• Adhami, Bils, Jones, and Klenow, April 2025
• National welfare: W( N_t , c_t ) = N_t*u( c_t )
• u( c_t ) per capita consumption
• We don’t know R
• Suppose that we treat the value that people put on their lives as being u( c_t )

What’s the optimal population size?

• W( N_t ,c_t ) = N_t*u( c_t )
• With diminishing marginal utility of consumption, the second term heads to zero, so little social gain from high levels of consumption
• But more people add social utility linearly
• W( N_t ,c_t ) is maximized where the marginal value of one more person (the average utility) is equal to the loss of marginal utility to everyone else from having a bit less c
• u( c_t ) = N_t*u’( c_t )

What’s the optimal population size?

• National welfare: W(N_t,c_t ) = N_t*u(c_t )
• u( c_t ) = N_t*u’( c_t )
• Growing population should increase aggregate welfare because people value their own lives
• At some point this balances off negative externalities to those we share the world with
• But a lot the externalities are positive!
• This problem is hard

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What’s the optimal population size?

• From 1960 to 2019, Japan’s people grew their consumption a lot
• Mexico grew a lot of people (and some increase in consumption)

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Economists think a lot about consumption growth; much less about population

Effective Altruism

• Supposedly, the purpose of government is to help society achieve better outcomes than could be achieved by independent agents interacting voluntarily
• How did the Biden program of student debt forgiveness measure up?
• Median US household income = $80,610 in 2024

Parks and Rec

2009-2015

Effective Altruism

• What are the payoffs from various health interventions?
• Bruce Meyer, economist at UChicago
• Booo!
• But BA/MA in Econ from NU 1981
• Yea!

Effective Altruism

• Cheap ways of avoiding losing disability adjusted life years (DALYs)

Effective Altruism

Effective Altruism

Effective Altruism

Longtermism: Philosopher William MacAskill

“It feels odd, possibly even grandiose, to start thinking about the things that could happen in our lifetime that could have an impact — not just over decades, but over centuries, thousands, millions, or even billions of years.

But if we’re taking seriously that future people matter morally, and that it really doesn’t matter when harms or benefits occur, then we really should take seriously this question of whether there could be events that occur in our lifetimes that have not just long-lasting, but indefinitely persistent effects.”

Will MacAskill

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Longtermism: Philosopher William MacAskill

1. People who exist in the future deserve some degree of moral consideration.
2. The future could be very big, very long, and/or very good.
3. We can reasonably hope to influence whether people in the future exist, and how good or bad their lives are.
4. So trying to make the world better for future generations is a key priority of our time.

Intertemporal tradeoffs

“To illustrate the potential scale of the future, suppose that we only last as long as a typical mammal species, that is, around 1 million years, and assume that our population continues at its current size. In that case, there would be 80 trillion people yet to come. Future people would outnumber us 10,000 to one.”

Calculating Impact

• Scale: How much good might come from this action?
• Tractability: How many resources would it take to solve the problem? Some problems are just easier to solve than others.
• Neglectedness: If a lot of people are working on some problem, probably all the low hanging fruit will have been found. You are more likely to have an impact on something that a lot of people aren’t currently working on. Diminishing returns.
• Persistence: How long lasting will the benefits be?
• Contingency: What’s the counterfactual? Is the problem likely to be solved anyway, without your actions?
• Personal fit: Is this something that fits your skills and passions?

Do we know if we’re being unsustainable?

• Paris newspaper “Le Figaro” in 1887.
• The statesman Léon Gambetta was speaking to the novelist Alphonse Daudet.
• “Remember the words of the mason who falls from the fifth floor and to whom a tenant on the third asks: how is it?

‘Not bad so far, says the mason, but we will see at the end!’”

Next up….

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Sustainability