Lecture 4: Exhaustible Resources

Question 1

Reserves (non-renewable resources)

Answer 1

Quantities economically recoverable under present costs and prices

Question 2

Resources Potential

Answer 2

Estimates of upper limits on resource extraction possibilities given current and expected technologies.

Question 3

World Reserve Base

Answer 3

Upper bound of resource stocks that is economically recoverable under ‘reasonable’ expectations of future price and tech potential

Question 4

How to frame consumption/extraction of non-renewable resources

Answer 4

• Optimal depletion of an endowment; Optional allocation of consumption across time-periods –> depends on time preferences and using a negative discount rate for future periods (implies consumption rate is more valuable today)
• Maximisation of discounted flows of net benefits

Question 5

Intertemporal Preference Curves

Answer 5

To find the optimal consumption path for exhaustible resources across time periods –> These are bendy curves allocation consumption between time periods t and t+1

Question 6

Intertemporal Production Possibilities (IPP)

Answer 6

Describing how stock in t relates to stock in t+1

Question 7

The optimal consumption path for exhaustible resources across time periods

Answer 7

Find the tangency point between IPP and preference curves
- With positive time preference, consumer chooses smoothly decreasing amount of consumption.

Question 8

Deterioration of Exhaustible Resource (at rate d) over time
[impact on optimal consumption]

Answer 8

• Negative income effect: wealth decreases as resource deteriorates –> lower stock –>consumption decreases in all time periods
• Substitution effect: Reducing productivity of conservation in time t because not consuming a unit in t will result in d units wasted
• Decreasing payoff from restraint
• Decreases slope of IPP

Question 9

Regeneration of Exhaustible Resources (at rate g) over time
[impact on optimal consumption]

Answer 9

• Positive income effect: wealth increases as resource regenerates –> higher stock –>consumption increases in all time periods
• Substitution effect: Increasing productivity of conservation in time t; Increasing payoff from restraint
• Increases slope of IPP

Question 10

Marginal User Cost

Answer 10

The opportunity cost (in terms of future consumption possibilities) of consuming another unit today.

Increasing cost because the more you use today, the higher the cost of lost future opportunity.

Question 11

What is MUC influenced by

Answer 11

Influenced from:
1. Demand in Period 1 and 2
2. IPP
3. Discount rate –> discounted demand curve.

Question 12

Marginal Extraction Curve (MEC)

Answer 12

Typically constant (k)
- Related to the production process of a non-renewable resource (while MUC is related to consumption)

Question 13

Optimal Extraction of Non-Renewable Resources Implication

Answer 13

Implies price = Marginal Cost = Sum of Marginal Extraction Cost (MEC) and Marginal User Cost (MUC)

Question 14

Rent in the Optimal Extraction of Non-Renewable Resources

Answer 14

The rent per unit of resource = Surplus value after all costs have been accounted for arising from scarcity and intertemporal consumption.
- If no rent is paid then MUC=0 (because no individual user is getting the benefits or lack of)
- Rent = price at equilbirium taking scarcity into account MINUS price at equilibrium only taking production into account.

Question 15

Property Rights in Optimal Extraction of Non-Renewables

Answer 15

MUC = 0 if open-access because no individual user is getting benefits or lack of
- So for open access = no rent = P = MEC(t)

Question 16

Recycled Resources

Answer 16

If we assume a perfect substitution between natural and recycled resources then there’s a 2-way link between markets and:
p(t) = MEC(t) + MUC(t) = MCC (t) + MUCS(t)

where MCC(t) = Marginal Recycling Cost
MUCS(t) = Marginal User Cost of Recycling Scrap (dependent on previously extracted resource and recycling rate)

Question 17

Net Benefit Function

Answer 17

Is the area between the demand and supply curve which will be a trapezoid so can find the function assuming:
- Base 1 = Difference between where functions hit the y-axis (at Q=0)
- Base 2 = Difference b/w two formulas at Q –> demand function - supply function
- Height = Q at that point
So Area = 0.5H(B1+B2)

Question 18

To Find PV(MNBfuture)

Answer 18

Divide the MNB equation by the discount rate. Then graph it opposite (on RHS axis) with MNBcurrent on LHS axis. The x-axis should be the length of the resource constraint. Where they hit is optimal allocation

Question 19

To Graph PV(MNBfuture) and MNBcurrent

Answer 19

Graph PV(MNBfuture) opposite (on RHS axis) with MNBcurrent on LHS axis. The x-axis should be the length of the resource constraint. Where they hit is optimal allocation

Question 20

Using policy, how would you impose the optimal allocation of resources between generations/two time period?

Answer 20

Most efficient way is adding a Piguovian tax in the current period to internalise the externality of using too much of the resource in the current period. To do this, make the tax = MNBcurrent (optimally) - MNBcurrent (at max production, probably =0). This should= the tax level
Can graph this by using the supply and demand curves and shifting the supply curve up to incorporate the tax amount.