Week 3 Exhaustible resources economics: energy/minerals Flashcards Preview

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Name key characteristics of exhaustible resources/resource economics.

  • Exhaustible resources economics is like a marathon and requires optimal allocation across time taking into account "today's impact on tomorrow".
  • Time component is essential, as exhaustible resources don't regrow, requiring the consideration of dynamic efficiency and resulting in a tradeoff between periods, as:
    • humans are impatient and prefer to receive payoffs sooner rather than later
    • return on investment varies (takes into consideration opportunity costs).


Dynamic vs static efficiency

  • Dynamic efficiency considers efficiency over a period of time (e.g. in the case of exhaustible resources).
  • Static efficiency considers efficiency at a given point in time (e.g. in the case of renewable resources).


What is discounting?

  • Discounting accounts for the different value assigned to the present and the future, by converting e.g. future dollars into current dollars.
  • Present has a higher value than the future, therefore benefits and costs incurred in the future will be worth less today.
  • Discount factor single period: 1/(1+r) where r is the interest rate or "exchange rate"
  • Discount factor multiple periods: 1/[(1+r)^t] where t is the number of periods (e.g. discounting form year 2 to the present (year 0) t = 2)


What does a demand curve represent? How can you calculated consumer surplus?

  • Represent quantity demanded as a function of price (x-axis: quantity, y-axis: price).
  • Height of the demand curve represents marginal willingness to pay = marginal benefit of consumption
  • Consumer surplus = marginal benefit - price (or area below demand curve and above price))


What does a supply curve represent? How do individual firm and market supply curves differ?

  • Represents quantity produced as a function of price (x-axis: quantity, y-axis: price).
  • Individual firm supply curve is upward-sloping as the firm becomes less productive with every additional unit (marginal cost of production increases)
  • Market supply curve, which allows for the entry and exit of firms is horizontal as additional units can be produced at the same marginal cost in the market


When is the market equilibrium reached in the case of standard goods? Does this also apply to exhaustible resources? Why/why not?

  • Standard goods:
    • when demand = supply
    • when price = marginal cost of production = marginal benefit of consumption
  • Exhaustible resources:
    • the same does not apply as:
    • it is impossible to produce more
    • as producers don't "produce" the good price = marginal cost of production no longer holds (can charge more than marginal cost of production and get scarcity rents)


How do you find the optimum quantity and marginal benefit in a two-period exhaustible resource model?

To find the optimum production in the two periiod model it is necessary to find the point at which the discounted marginal net benefit for both periods is equalized.

Mathematical solution - assuming both periods have the same demand curve:

  1. Find the marginal willingess to pay or marginal benefit (p(q). If given the demand curve as a q(p) solve for p(q)
    • e.g. q(p) = (1200/11) - (10/11)p would become p(q) = 120 - 1.1q
  2. Find the net marginal willingness to pay = Marginal benefit - marginal costs for both priods
    • e.g. p(q) = 120 - 1.1q - 10 =110 - 1.1q where MC = 10
  3. Discount marginal net benefits for period 2 by applyiing discount factor.
    • e.g. p(q2) = (110 - 1.1q)/1.1 = 100 - q where the discount rate is 10%
  4. Find optimum by equalizing discounted marginal net benefit
    • ​​e.g. 110 - 1.1q1 = 100 - q2
  5. Replace q2 in term of q1 or vice verse
    • ​e.g. q1 + q2 = 95 so q2 = 95 - q1, hence formula can be rewritten as 110 - 1.1q1 = 100 - (95 - q1)
  6. Solve for q1.
  7. Use q1 to solve for q2.
  8. Find discounted marginal net benefit by plugging q1 and q2 into the corresponding p(q) function.
  9. To find marginal net benefit for periond 2 multiply the marginal net benefit by (1+r).



Weak vs strong sustainability

  • Weak sustainability: ensures that future generations will be as well off as current or past generations.
    • based on utility
    • assumes trade-offs are allowed e.g. reduce oil stock for building up capital (e.g. knowledge stock, capital stock)
    • Examples:
      • Alska Permanent Fund - 25% of all mineral lease rentals, royalties, etc going to permanent fund (principal can only be used for income-producing investments
      • Norges Bank Investment Fund - for proceeds from oil extraction
      • Nauru Trust Fund - for proceeds from sales of phosphate
  • Strong sustainability: ensures that future generations will ahve the same capital stock as current or past generations
    • for exhaustible resources this would imply that no resource could be used!
    • more applicable to ecosystems (e.g. keeping ecosystems in place and not destroying the


In a two period model which period would receive more units (q1>q2)?

How does the interest rate used for discounting affect allocation?

  • q1 is higher as the marginal benefit of q2 without discounting would be higher in period two due to the applied interest rate of 10%, which creates an opportunity for arbitrage.
  • The larger the interest rate, the larger the difference in undiscounted marginal net benefits and thus the higher the difference between q1 and q2.


What happens to the optimal outcome if the stock increases?



  • Discounted marginal net benefit would decrease, as an increase in supply stretches the x-axis, pulling the two demand curves further apart and thereby lowering the point of intersection (=marginal net benefit).
  • As the marginal net benefit is lower, combined consumer surplus will increase.
  • As the marginal net benefit is lower, combined supplier surplus will decrease.
  • Combined surplus will be larger than in base case (as the stock available for sales/purchase increases), but producers will have smaller share.


What happens to the optimal outcome if there is no scarcity?

  • Producers won't receive scarcity rents so price = marginal cost, which eliminates producer surplus.
  • Consumption in period 1 and 2 is equal


What happens to the optimal outcome if the the interest/discount rate increases?

  • The quantitiy consumer in period 2 would decrease, while the quantity consumer in period 1 would increase, as period 2 is valued less in discount terms
  • Discounted net marginal benefit would decrease for both periods.
  • Price would decrease resulting in:
    •  a decrease in producer surplus.
    • an increase in consumer surplus in period 1, as more units are bought.
    • a larger decrease in consumer surplus in period 2, leading to an overall decrease in consumer surplus
  • Combined surplus would decrease.


What happens to the optimal outcome if a tax is levied on oil extraction?

  • Quantity consumed in period 1 and period 2 would remain the same.
  • Discounted net benefit woudl decrease
  • Price would decrease leading to:
    • a decrease in producer surplus significantly, who pay the majority of the tax.
    • a slight decrease in consumer surplus.
  • Combined surplus would decrease mostly due to producer surplus.
  • Government would gain tax payments.
  • Note: the smaller a country's share in overall oil use is, the more of the tax will be paid by the consumer as the country is too small to affect  the equilibrium price.


What happens to the optimal outcome if a cap is implemented?

  • Companies would be willing to pay for permits up until their maringal net benefit is zero in order to maximize profits. Thus producers are impacted more than consumers.
  • Discounted marginal net benefit would increase (without taking into account the permit price).
  • Due to the permit price producer surplus would be zero, as now permits rather than oil are scarce and the government receives the "scarcity rents"
  • Consumer surplus would decrease due to the higher price.
  • Overall surplus would decline.
  • It should be considred that the model is assuming constant marginal extraction cost. In a heterogeneous market, firms may have varying margial costs and hence firms with lower costs may still make a surplus.