1. Chapter 4 Dynamic Efficiency: Oil and Other Depletable Energy Resources: Part B
Peter M. Schwarz
Professor of Economics and Associate, Energy Production and Infrastructure Center (EPIC), UNC Charlotte

2. Outline Part B Introduction Dynamic Efficiency Competition Monopoly
Other Factors
Sustainability
Risk
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3. Monopoly (1)
Recall that monopoly may be the conservationist’s best friend.
But in a dynamic framework, competitive firms have a built-in incentive to conserve.
Perfect competition results in efficient conservation
Assuming no other market failures
Pollution
Using “too high” a discount rate
Monopolists over-conserve.
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4. Monopoly (2): Example 3
Gazprom is the sole supplier of natural gas to Finland. The company has remaining reserves of 100,000 cubic meters of natural gas. The company must sell its reserves today or one year from now.
Marginal extraction cost = 0.
Demand is P = Q, where Q is in thousands of cubic meters.
Discount rate is 10%.
How much should Gazprom sell in each period? Compare to the competitive outcome, and the DWL.
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5. Monopoly (3): Example 3 (cont.)
Profit maximization
MR = MC
Since MC = 0
MR0 = PV (MR1)
Equimarginal Principle
P = 180-1Q
MR = 180 –2Q
MR0 = 180 –2Q0 = PV (MR1) = (180 –2Q1)/1.1
Q0 + Q1 = 100 (thousand cu m).
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6. Monopoly (4): Example 3 (cont.)
MR0 = 180 –2Q0 = PV(MR1 ) = (180 –2(100 - Q0))/1.1.
Solving
Q0 = 51.9 thousand cu m (and P0 = $128.10).
In turn, Q1 = 100 – 51.9 thousand cu m = 48.1 tcm (and P1 = $131.90).
Note that Hotelling’s Rule no longer applies.
P - MC rises by less than the discount rate
between t = 0 and t = 1.
Inefficient. Monopoly over-conserves.
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7. Monopoly (5): Example 3 (cont.)
Case
Q0 (tcm)
Q1 (tcm) P0
($/tcm) P1
CS ($)
PS ($)
SW (S)
Monopoly
51.9
48.1
128.1
132
2,297.65
12,420.39
14,718.04
Compet’n.
56.2
43.8
123.8
136.2
2,451.24
12,381.34
14,832.58
Notes: Bolded figures highlight expected findings.
Table 1: A Comparison of Results for Monopoly and Competition for the Two-Period Dynamic Model.
Monopolist over-conserves.
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8. Other Factors (1): Change in Demand
Demand grows at g = r. Competitive Outcome Produce equal amount in each period. If g > r, leave more for the future If g < r, more will be produced today. P0 = (a – b Q0) = PV (P1) = ((a – b Q1) (1 + g))/ (1 + r). If g = r, right-hand terms cancel and (a – b Q0) = (a – b Q1) Q0 = Q1
Sustainable
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9. Other Factors (2): Increase in Total Reserves
Move towards static case Output in each period higher Price in each period lower.
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10. Other Factors (3): Change in Technology
Decreases MC of extraction.
MC = 2Q replaced by MC = Q.
Increases today’s production.
Leaves less for the future
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11. Other Factors (4): Backstop Technology
Renewable fuel available if price of conventional fuel gets high enough
Perfectly elastic supply
High fixed cost
Zero marginal cost
Example: Biofuel available at $40 per unit of oil-equivalent.
In initial competitive example:
P0 = $38.10, P1 = $41.90 (PV = $38.10).
Now, period 1 price is $40 (PV = 36.36).
So more production is shifted towards the present until
P0 = $36.36.
Q0 = (an increase from when there was no backstop technology available in period 1). That leaves Q1 = barrels of oil for the future. Since demand at next year’s price of $40 is 5.455, biofuel will equal 0.91 oil-equivalent units.
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12. Figure 4.4 Effect of Backstop Technology on Dynamic Equilibrium
Backstop quantity
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13. Other Factors (5): Change in Interest Rate
The higher the discount rate, the less we leave for the future.
Efficient outcome, as long as we use the socially efficient discount rate
Firms use cost of borrowing
Can make argument that social discount rate (s) = rate of growth in real GDP ≈ 3%.
If r > s, we will over-discount the future.
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14. Sustainability (1)
Discounting generally leaves less for the future than we consume today.
Revisit the question: Should we spend $10 million today to redesign car engines to emit less carbon, worth $50 million 50 years from now?
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15. Sustainability (2)
Future Value
Interest Rate (%)
Present Value
$50,000,000 0% 5%
$18,844,474
10%
$7,432,181
Yes, at interest rate of 0% or 5%. No, at interest rate of 10%
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16. Sustainability (3)
Sustainability advocates call for a 0% interest rate.
Then why lend or save money?
And would the future be better off if we invested the proceeds
In education (Texas)
In a social security pension system (like Norway)
In a bank, and let the future decide how to spend it?
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17. Sustainability (4)
And does it make sense to slow our rate of growth to help future generations?
Redistributes income from today’s citizens
Including today’s poor.
Future generations typically will be better off than the present.
And may actually leave the future with fewer resources.
Suppose we slow today’s growth from 3% to 2%
Rule of 72.
It will take 36 years, instead of 24, for income to double.
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18. Managing Energy Price Volatility(1)
Energy markets can be highly volatile.
Fluctuating prices
Oil, natural gas and wholesale electricity markets are among the most volatile markets.
Derivatives market
Derived from the underlying commodity, such as oil.
Derivatives allow you to lock in a price today for future delivery
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19. Managing Energy Price Volatility(II)
Southwest Airlines Example
Today’s jet fuel price is $2/gallon. Southwest Airlines wishes to protect itself against a rise in price six months from now.
How? It can buy a contract that will offer to deliver oil six months from now at $2 a gallon. The seller will charge a premium to cover the risk that gas may be higher in the future.
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20. Managing Energy Price Volatility(III)
Hedgers vs. Speculators
Southwest Airlines is hedging
Goal is to reduce price uncertainty
Not to earn a profit on the contract
The seller of the contract is speculating
Makes money if the price of oil in six months is lower
Still gets today’s price of $2
Of course, if oil price is higher in 6 months, speculator loses.
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21. Managing Energy Price Volatility(IV)
Speculators unpopular with the government
Accused of causing price spikes like in June 2008.
Economists believe speculators increase efficiency
And reduce price volatility
If speculators guess right, they buy when P is low and sell when P is high.
So they drive up low prices, but drive down high prices
Thus reducing P volatility.
More on oil derivatives in Chapter 5 on Oil.
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