1. Optimal Pricing of Renewable and Non-Renewable Energy
Agricultural, Food and Environmental Policy Analysis Summer School
Thomas G. Johnson
August 4-18, 2013

2. Optimality in Economics
Welfare economics is the branch of economic theory that identifies those condition that lead to the optimal use of limited resources (Just, Hueth and Schmitz, 2004)
Referred to as Pareto optimality
Efficiency conditions are referred to as Pareto efficiency

3. Correspondence between Pareto Optimality & Competitive Equilibria
A perfectly competitive market leads to a Pareto optimal set of prices and quantities
There are many possible Pareto optimums
Each Pareto optimal outcome has an associated resource endowment and initial prices.
A competitive equilibrium is a set of market clearing prices.

4. Perfect Competition Perfect competition assumes the following:
Perfect information
Large number of buyers and sellers in all markets (no participants in the market can influence prices)
Free access to markets (that is no regulations give incumbent buyers and sellers an advantage)
These conditions lead to known and consistent prices no matter who is buying or selling

5. Summarizing Pareto Efficiency
Consumers choose the bundle of goods that maximizes their utility given the prices of goods.
Producers purchase a mix of inputs that maximize profits given the prices of inputs.
Producers produce a mix of goods that maximizes their profits given the prices of goods
At a Pareto optimum, no one (producers or consumers) can be made better off without making at least one producer or consumer worse off

6. Optimal Production and Use of Energy over time
Optimal energy production and use will approximate optimality if markets are competitive, or if policy guides markets to comparable conditions
This requires that prices of inputs and energy itself reflect, real marginal costs and marginal value to consumers
Value to consumers is often referred to as willingness-to-pay

7. Intertemporal Welfare
When long periods of time are involved the future must be compared to the present in terms of intertemporal opportunity cost
This involves weighting of future and present benefits and costs
This is referred to as social discounting.

8. Net Present Value
Net present value of a stream of private revenues or benefits, and costs is
where r (the discount rate) is the market interest rate if the firm is borrowing money or the opportunity cost of money held by the firm.
NPV is the lump sum of money that would generate the same net benefits each year if it earned a rate of interest, r

9. Social Discounting
If B is the sum of consumers and producers’ willingness to pay (WTP) as indicated by their demand and derived demand and C is the sum of consumer and producers’ WTP for costs then NPV is the net present value
If NPV is positive, the situation is a Pareto improvement
A high discount rate means that consumption in the future has small opportunity costs in the present
A low discount rate makes the future much more important

10. Optimal Production and Use of Energy over time
Optimal consumption rates of renewable and non-renewable energy are quite different because of inter-temporal considerations
All calculations should consider the opportunity costs of consumption
The opportunity costs of consuming non-renewable energy consumption include the reductions in stocks

11. Non-renewable energy consumption over time
Non-renewable energy may be used in the present or saved to the future
The more energy used in the present the lower the value of the energy in the present and the lower the availability in the future.
Reduced availability of energy in the future will eventually raise energy prices

12. Non-renewable Energy
MXC0 is the marginal costs of extracting, processing and transporting the energy in the current period
Demand0 is the marginal benefit of consuming various levels of non-renewable energy in the present

13. Non-renewable Energy
If markets don’t consider the future, equilibrium will occur at p0 and q0

14. Non-renewable Energy
But quantities consumed now reduce potential consumption in the future
Extraction costs may be higher or lower in the future.
Thus current consumption has a marginal user cost that rises as current consumption is greater

15. Non-renewable Energy
If the marginal user cost is added to the present marginal extraction cost curve, , we get the optimal
supply curve for non-renewable energy, Supply0.
This also identifies the optimal price of non-renewable energy, and optimal current level of energy consumption

16. Renewable Energy
Renewable energy makes up a growing portion of the world’s energy supply
Like non-renewable energy the supply curve is determined by marginal costs of production, processing, marketing and transportation
In other respects the economic supply conditions are quite different from non-renewable energy
There are few scarcity-related user costs for renewable energy
Risks are quite different when producing renewable energy

17. Renewable Energy
Here is the marginal cost of production
Competition in leads to price and quantity
Similarly, competition in leads to a new equilibrium price and quantity. Demand generally rises while marginal cost may decrease or increase.
If marginal cost rises price rises to and quantity shifts to which may be greater or less than

18. Renewable Resources
If marginal cost falls, quantity produced increases to and price shifts to which may be greater or less than
Marginal cost will rise if:
Input costs, including land, rise
Policy conditions are less favorable
Marginal cost will fall if:
Technology reduces cost of production, processing or transport
Policy conditions are more favorable

19. Renewable but Destructible Resources
Current production can reduce future production of renewable resources
For example, degradation of soil for biomass production
Then each unit of current production has a user cost which is added to the marginal cost of production, , to get the optimal supply curve
Then the optimal current price of renewable resources is and the optimal quantity supplied is

20. Uncertainty in Renewable Energy Supply
Sources of uncertainty
Technological change affects the costs and feasibility of producing renewable energy
Changing tastes, preferences, economic and political situations in the future affect demand and prices for renewables
Weather and climate affects biomass production
Weather affects solar and wind power production
Uncertainty in non-renewable energy markets affect price of renewable energy
Policy changes affect profitability

21. Questions for discussion
Are markets adequately reflecting the scarcity value (use cost) of non-renewable resources?
How might changes in technology in the future affect the supply of and demand for renewable energy?
Are policy necessary to improve the pricing of non-renewable and renewable resources?
If so what might these be?

22. Citations
AmosWEB GLOSS*arama
EconEdLink
Just, R.J., D.L. Hueth and A. Schmitz The Economics of Public Policy: A Practical Guide to Policy and Project Evaluation, Edwin Elgar Press, Cheltenham UK. 
United States Geological Survey Arctic National Wildlife Refuge, 1002 Area, Petroleum Assessment, 1998, Including Economic Analysis. Fact Sheet 0028–01: Online Report.

23. Pareto Optimality and Natural Resource Consumption
Appendix
Pareto Optimality and Natural Resource Consumption

24. Perfect Competition
If all goods are priced equally (a single price to all sellers and buyers of each good), then all utility maximizing consumers have the same marginal rate of substitution for each pair of goods (see previous material on energy demand).

25. Perfect Competition
Producers maximize profit by minimizing cost where all products are produced such that Marginal rate of technical substitution (MRTS) of factors equals their price ratio (see previous lecture material)

26. Perfect Competition
Finally, since producers and consumers will face the same prices, producers will maximize profit by producing that mix of products where their marginal rate of transformation (MRT) for all pairs of products equals the marginal rate of substitution (MRS) for all consumers.

27. Time Preference
Quantity in present
If consumer were indifferent between the present and the future the trade off curve would be 1 to 1 (90o)
Quantity in future
Since consumers prefer the present, they require 1+r units in the future to compensate for foregoing each unit of present consumption

28. Time Preference
Quantity in present
The slope at this point defines the socially optimal discount rate.
Thus the discount rate is r
Quantity in future
A higher discount rate means more future consumption is equivalent to a given current consumption.

29. Non-renewable energy consumption over time
Consider a 2 period case with known demand curves for both periods, t1 and t2
The 2 relationships between demand (marginal value of energy) and supply (marginal cost of energy, q) can be arranged on a 4 quadrant diagram

30. Non-renewable Energy
The North East quadrant is a traditional supply and demand space that relates quantity of energy consumed to money.

31. Non-renewable Energy
The South West quadrant is also a supply and demand space but has been rotated 1800
This quadrant shows the predicted demand for energy in the future in undiscounted values

32. Non-renewable Energy
The South East quadrant is the supply constraint (similar to a budget constraint)
It shows combinations of energy consumption in the present and future

33. Non-renewable Energy
The North West quadrant shows the rate at which money in the future is discounted, that is the present value discount rate

34. Non-renewable Energy
Demand0 shows the marginal benefit of consuming various levels of non-renewable energy in the present
Demand1* is the benefits of using the non-renewable energy in the future
The asterisk indicates that these curves are in future values (have not been discounted)

35. Non-renewable Energy
MXC0 is the marginal costs of extracting, processing and transporting the energy in the current period
MXC1* is the expected marginal costs of extracting, processing and transporting the energy in the future
* The asterisk indicates that these curves are in future values (have not been discounted)

36. Non-renewable Energy
is the fixed amount of non-renewable energy available (proved reserve).
If is consumed in the present period, will be available for the future.
* The asterisk indicates that these curves are in future values (have not been discounted)

37. Non-renewable Energy
Now we discount future demand and supply in the North East quadrant
First trace each quantity demanded at its corresponding discounted price
Then trace the each quantity supplied at its discounted price

38. Non-renewable Energy This converts into and into
and are discounted future marginal benefits and costs of consuming non-renewable energy

39. Non-renewable Energy
Now focus on the North East quadrant that contains both present and future supply and demand
Marginal costs and benefits are displayed in present values and in comparable units.
This first diagram represents the case of an abundant nonrenewable resource.
is more than can be consumed in the two periods and is said to be non-depletable
An example may be nuclear energy

40. Non-renewable Energy Competition in leads to price and quantity
Similarly, competition in leads to price and quantity
Regardless of what the discount rate is, the optimal consumption in the period is the same.
Consumption is based on the preferences, technologies and costs in the respective period

41. Non-renewable Energy
If the energy source is limited in supply (depletable), rationing over time is necessary
Competition in leads to price and quantity
Competition in would lead to price and quantity

42. Non-renewable Energy
But if current consumption is then only is available in the future
Price would be much higher in the future, rising to
Future demand is not being considered in the current market but should be

43. Non-renewable Energy
If we subtract the current cost vertically from Demand0 we get the marginal net benefits from consuming in the present,
Subtracting the expected future extraction cost, from the future demand we get the marginal net benefits of consuming in the future

44. Non-renewable Energy
The two net benefit curves cross at which is the quantity that would be demanded in if the price was
This level of current consumption is optimal given the expected supply and demand in the future

45. Non-renewable Energy
This level of current consumption is optimal given the expected supply and demand in the future
The is referred to as the marginal user cost, , of consuming the resource in the present

46. Non-renewable Energy
If the marginal user cost is added to the present marginal extraction cost curve, , we get the optimal
supply curve for non-renewable energy, Supply0.
This also identifies the optimal price of non-renewable energy, and optimal current level of energy consumption