Module 9: Are we running out of resources?

So far in this class we have talked about:

In this module, we are going to look at non-renewable resources in the world, with the looming question:

Are we running out of them?

We will talk about:

But how do we figure out if we’re running out of a particular non-renewable resource?

Reserve-to-production ratio

One measure is the “reserve-to-production ratio” (R/P)

How long will we run out of our resources?

In the 1950-1960s, scientists worked extensively on figuring out R/P, and the picture did not look great. That picture has not recovered even till this day.

Mineral Reserve to Production
Copper 32 years
Nickel 63 years
Chromium 18 years
Silver 12 years
Zinc 26 years
Gold 16 years

And it is not only metals

Hubbert (1956): There will be a “peak oil” if we keep the current pace of growth

And Hubbert predicted a peak of oil use in 2000

Why is it a big deal?

Looking back into the evolution of human civilization, human development centered around better harvesting of surplus energy:

EROI

Energy return on investment = Energy delivered / energy cost to acquire fuels

Type of Energy Source EROI
Hunting and gathering 1.05 : 1
Agriculture for food 1.1-1.3 : 1
Coal 48 : 1
Oil 25 : 1
Wind 18 : 1
Solar PV 6 : 1
Corn ethanol 0.8-1.6 : 1

The existential crisis

Estimates suggest that our society needs at least an EROI of 10:1 to grow sustainably.

Will our civilization be able to survive/thrive when we run out of fossil fuels?

Limits to growth

In 1972, MIT scientist Donella Meadows and her group published the famous “Limits to Growth” Report for the Club of Rome. The book sold 9 million(!) copies worldwide.

They offered a neo-Malthusian prediction:

Predictions from the Limits of Growth

A quiet dissent

Economists, on the other hand, are generally more optimistic. Julian Simon, for example, argued for a drastically different picture:

The Simon-Ehrlich Wager

The looming question with the Simon-Ehrlich bet

Class Discussion:

  1. Which side will you place your own money on Simon and Ehrlich’s bet on metals (if you have to choose one, starting today and ending 10 years from today)?

  2. What are the intellectual arguments represented by Ehrlich and Simon? In your opinion, who won the intellectual debate, and why?

  3. Is there anything missing in the bet?

But, wait a minute

Physical scarcity vs. Economic scarcity

Economics is the study of how to allocate scarce resources

What is the economic scarcity of a resource?

(Hint: what Simon and Ehrlich wagered on)

(And note: this thing is close to, but not exactly the measure of scarcity. We’ll see)

What is really happening with scarcity?

Or, by looking at the reserve-to-production ratio, what can we get, and what are we missing?

A sneak peek

A stylized example

Getty Inc. controls an iron mine, with a fixed amount of supply. The company can extract and sell iron in two periods, before the world ends.

Maximize PVNB?

The dynamic efficiency rule

The present value MARGINAL net benefit (PVMNB) should be equalized across the two periods.

Some math to solve the problem

Solve the system of equations:

\(q_0 + q_1 = 20\) (Total amount of production is no more than the reserve)

\(PVMNB_0 = PVMNB_1\) (PVMNB should be equalized between two period)

Or, \(8- 0.4q_0 - 2 = (8 - 0.4q_1 - 2)/(1+r)\)

Dynamically Efficient Allocation (DEA)

Assume an interest rate of r=10%, the dynamically efficient allocation (DEA) is characterized by:

\(q_0 = 10.24\), \(q_1=9.76\), and

\(p_0 = 3.905\), \(p_1=4.095\)

Scarcity rent

Scarcity rent

For a non-renewable resource, we have the following rule:

Price = Marginal Cost + Scarcity Rent

The role of physical reserves

The role of discount rate

Hotelling’s Rule

Hotelling (1931): Rate of growth in the scarcity rent of a resource equals to the rate of return on an alternative investment

We can verify that with our two-period model:

How discount rate affects inter-temporal allocation of resources

Solve the same system of equations with different discount rates, here’s what we have:

##      r       q0        q1
## 1 0.00 10.00000 10.000000
## 2 0.01 10.04975  9.950249
## 3 0.02 10.09901  9.900990
## 4 0.05 10.24390  9.756098
## 5 0.10 10.47619  9.523810
## 6 0.20 10.90909  9.090909
## 7 0.50 12.00000  8.000000

Sustainability implications

The infinite period case

Present value marginal net benefits (PVMNB) should be equalized across all periods.

And, the marginal net benefits (MNB) in the current period is just the scarcity rent the producer receives.

Hotelling’s rule, the infinite horizon version

The scarcity rent will increase over time with a rate equal to the interest rate, or
\[SR_t = SR_0 * (1+r)^t\]

And, the price of a resource, assuming constant marginal cost, will be governed by:

\[P_t = (P_0-MC) * (1+r)^t + MC\]

Hotelling’s rule does suggest that the scarcity of a resource rising exponentially over time. But, there are strings attached to it:

Reserves

Discovery

With increasing price (and royalty) for a resource, it creates incentives for discovering new reserves, which will

Substitutes

There are always substitutes for a particular resource, but the alternatives could be

But when the price rises up to a certain point, the substitute starts to kick in. This means that

Technological development

What real tech improvement looks like

Pelletization

Environmental Concerns of Mining

Modelling environmental cost

What can we learn from variations of Hotelling’s rule?

Taking three steps back

There are two important assumptions/exceptions underlying all the above analysis. If those two conditions break, then Simon’s prediction of infinite resources will fall short.

Can you spot them?

(Hint: we have talked about both of them in this class)

  1. What is fundamentally different between drilling for oil, and harvesting fisheries?

What drives the tragedy of the commons?

Property rights

  1. What if there is no market signal for the underlying economic scarcity?

Or, what if the market signal is distorted?

Real-world scarcity

The Red Sox will take on the Yankees in the 7th game of the World Series at Fenway Park. In order to reward the loyal fans here in Boston, the Red Sox announced that they would issue the ticket to the first 10,000 fans who come to the ticket office to claim it.

What do you think is going to happen?

Scarcity

Imagine that you manage to get into the Red Sox-Yankees game, and the Red Sox win the World Series. You step out of Fenway Park and ready to go home. It is in the middle of the night, public transit has all shut down, and it is raining cats and dogs outside.

You desperately look for a cab, as do everybody else coming out of the Park. You wait, and wait, and wait, for an hour. No taxi comes to pick you up.

You open your Uber app on the phone. There is a surge pricing of 5 times here at Fenway Park. You clicked the agree button, and 5 minutes later, an Uber comes to your rescue.

What can you learn about scarcity from the above examples?

Missing or distorted market signal

Ehrlich’s second bet

After losing the first bet, Ehrlich offered Simon a second set of bets in 1994. Each of these questions worth $1000.

  1. The three years 2002–2004 will on average be warmer than 1992–1994
  2. There will be more carbon dioxide in the atmosphere in 2004 than in 1994
  3. There will be more nitrous oxide in the atmosphere in 2004 than 1994
  4. The concentration of ozone in the lower atmosphere (the troposphere) will be greater than in 1994
  5. Emissions of the air pollutant sulfur dioxide in Asia will be significantly greater in 2004 than in 1994
  6. There will be less fertile cropland per person in 2004 than in 1994
  7. There will be less agricultural soil per person in 2004 than 1994

  1. There will be on average less rice and wheat grown per person in 2002–2004 than in 1992–1994
  2. In developing nations there will be less firewood available per person in 2004 than in 1994
  3. The remaining area of virgin tropical moist forests will be significantly smaller in 2004 than in 1994
  4. The oceanic fishery harvest per person will continue its downward trend and thus in 2004 will be smaller than in 1994
  5. There will be fewer plant and animal species still extant in 2004 than in 1994
  6. More people will die of AIDS in 2004 than in 1994
  7. Between 1994 and 2004, sperm cell counts of human males will continue to decline and reproductive disorders will continue to increase
  8. The gap in wealth between the richest 10% of humanity and the poorest 10% will be greater in 2004 than in 1994

Simon just shook it off

“Let me characterize their offer as follows. I predict, and this is for real, that the average performances in the next Olympics will be better than those in the last Olympics. On average, the performances have gotten better, Olympics to Olympics, for a variety of reasons. What Ehrlich and others says is that they don’t want to bet on athletic performances, they want to bet on the conditions of the track, or the weather, or the officials, or any other such indirect measure.”

A poll

Fact-checker

  1. The three years 2002–2004 will on average be warmer than 1992–1994 (\(\checkmark\))
  2. There will be more carbon dioxide in the atmosphere in 2004 than in 1994 (\(\checkmark\))
  3. There will be more nitrous oxide in the atmosphere in 2004 than 1994 (X)
  4. The concentration of ozone in the lower atmosphere (the troposphere) will be greater than in 1994 (\(\checkmark\))
  5. Emissions of the air pollutant sulfur dioxide in Asia will be significantly greater in 2004 than in 1994 (\(\checkmark\), sulfur emission peaked in 2008 in Asia)
  6. There will be less fertile cropland per person in 2004 than in 1994 (Don’t care)
  7. There will be less agricultural soil per person in 2004 than 1994 (Don’t care)

  1. There will be on average less rice and wheat grown per person in 2002–2004 than in 1992–1994 (Don’t care)
  2. In developing nations there will be less firewood available per person in 2004 than in 1994 (Don’t care)
  3. The remaining area of virgin tropical moist forests will be significantly smaller in 2004 than in 1994 (\(\checkmark\) ?)
  4. The oceanic fishery harvest per person will continue its downward trend and thus in 2004 will be smaller than in 1994 (?)
  5. There will be fewer plant and animal species still extant in 2004 than in 1994 (\(\checkmark\))
  6. More people will die of AIDS in 2004 than in 1994 (\(\checkmark\), AIDS death peaked at 2009 though)
  7. Between 1994 and 2004, sperm cell counts of human males will continue to decline and reproductive disorders will continue to increase (\(\checkmark\), but…)
  8. The gap in wealth between the richest 10% of humanity and the poorest 10% will be greater in 2004 than in 1994 (\(\checkmark\))

Sustainability

We keep hearing about the word “sustainability”, but really what is it?

And does a dynamically efficient allocation guarantee sustainability?

Sustainability and inter-generational equity

How much should we leave for future generations? What is the appropriate rate of discounting?

Another interpretation of sustainability

Hartwick’s Rule

If we invest the entirety of the scarcity rent generated from natural resources to invest in other capitals, then the total capital of the economy will not decline over time.

Different levels of sustainability

Applying the Sustainability Criterion

Implications for Environmental Policy

Takeaways from the module