Optimal depletion of non renewable resources

Question 1

What is the resource endownment/base resource?

Answer 1

The resource endowment, or base resource, of a given resource indicates the mass of resource that is thought to exist in the Earth’s crust.

Question 2

What are the reserves of a resource?

Answer 2

The reserves of a given resource consist of quantities that are economically recoverable at current costs, prices and technology.

Question 3

What are the classifications of oil and gas reserves?

Answer 3

Undisclosed resources, potential additional resources and reserves

Question 4

What does a market demand curve represent?

Answer 4

The marginal wilingness to pay (MWTP) for additional units of that good and marginal WTP represent the marginal benefits that good brings to society.

Question 5

What is the technical constraint in an efficient depletion program?

Answer 5

The sum of the amount of oil extracte in the two periods must be equal to initial stock size.

Question 6

What is the net price per unit of oil

Answer 6

It is also known as the royalty price and is equal to P - c

Question 7

State Hotelling’s rule

Answer 7

An efficient non-renewable resource depletion programme requires the resource’s royalty value to grow over time at a constant rate equal to the market interest rate.

In other words, the discounted value of a royalty of extracting one unit of oil has to be the same at any point in time.

Question 8

In Hotelling’s rule what does the lower the cost of the resource mean?

Answer 8

The lower the cost, the deeper tha contango.
Contango: r > 0 and P(0)-c > 0

This means the gross price of oil in P(1) is higher than the gross price in P(0).

Question 9

What does contango imply?

Answer 9

Contango means that we can use this knowledge to build a basic price term structure model.
The existence of contango means that the efficient extracted quantity in period 1 will be less than that extracted in period 0.

Further to this the higher the r the higher the resource price increases and the faster the quantity decreases.

Question 10

Name the explicit and implicit assumptions of the hotelling rule

Answer 10

1. Fixed and homogenous stock of known size
2. Rates are constant over time
3. Constant marginal cost
4. At each point in time identical demand curves
5. Fixed choke price (back stop technology)
6. No technical change
7. No externality/tax/government intervention
8. Perfect competition (OPEC…)
9. Perfect information/no uncertainty

Question 11

Briefly explain why pure scarcity/stock is relevant two the two period efficient depletion model

Answer 11

• Oil in the ground is scarce and intertemporarily shiftable and therefore has a value
• Oil in the ground has value (as well as extracted oil) because it is scarce (not unlimited) and does not vanish
• In each period the value of oil in the ground is P(t) - c

Question 12

What happens if instead decisions are made by profiti maximising firms in a perfectly competitive market economy?

Answer 12

Ceteris paribus, the outcomes will be identical

Question 13

What are some factors of risk and uncertainty prevalent in optimal extraction decisions?

Answer 13

a. Stock sizes
b. Extraction costs
c. The success of R&D in substitutes to resources
d. Pay offs from discovery of new stock
e. Action of rivals

Question 14

What are the problems and implications of the Hotelling rule?

Answer 14

1/ Fixed stock of resource assumed however reserves are a function of: endowments, costs, prices and technology
2/ Stock is homogenous
3/ Costs are not constant and prices are denominated in units of utility. Barnett and Morse found that resource prices of copper, silver, iron and timber fell over time
4/ Partial monopoloy situations (OPEC)
5/ Given demand function
6/ Discount rates, population growth and technology
- There is no reason for there to be a constant discount rate over time, implies that a resource may not rise at a fixed rate
7/ Backstop technology

Question 15

Define resource scarcity

Answer 15

The availability of resources are fixed and finite at any point in time, while the wants resource use can satisfy are unlimited.

Where a market exists for a resource, the existence of any positive price is viewed as evidence of scarcity

Question 16

What is the Hartwick rule?

Answer 16

If all the rent arising from extraction of a resource along an intertemporally efficient depletion program were saved and invested in the stock of reproducible capital, K, then consumption could be maintained indefinitely.

Question 17

What is the Solow rule?

Answer 17

Save and invest so as to keep total wealth constant, where total wealth is the value of the capital stock and the value of the natural resource.

Solow further showed that this rule is equivalent to the rule of always consume an amount that is equal to the interest income on total wealth.

Question 18

What is it important to stress about the vailidity of the Hartwick solow rule?

Answer 18

That it is feasible to yield sustainbility only if a Cobb-Douglas function for resource consumption exists and that alpha is sufficiently large.

Question 19

State the Hartwick-Solow rule

Answer 19

If sustainability is feasible, it can be realised by always saving and investing in man-made capital the rent arising in the efficient depletion of the natural resource,

If saving and investment are as required for sustainability, total wealth will be constant and the sustainable consumption level will be the equivalent of the interest on that constant wealth.

To behave sustainably means keeping wealth intact by consuming just the interest income on that wealth.

Question 20

What are the problems associate with the Hartwick Solow rule?

Answer 20

1. Technology is excluded
2. Population growth is assumed constant
3. Prices are shadow prices
4. The above factors make the HS rule hard if not impossible to implement