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

Outline Introduction Dynamic Efficiency Competition Monopoly Other Factors Sustainability Risk

of 16 Copyright Peter M. Schwarz Introduction (1) Will we run out of oil? Hubbert and other physical scientists say yes. Economists say no. Is our energy use sustainable? Ecologists and other physical scientists say no. Economists say yes. Both questions require a dynamic model Consider current vs. future use. of 16 Copyright Peter M. Schwarz

of 16 Copyright Peter M. Schwarz Introduction (2) Start with simplest setting Add complexity as needed As always, balance the ease of simplicity with greater predictive accuracy from a more complex model Marginal cost Zero Positive Increasing Backstop technologies Alternative technology available above some price Competition Monopoly of 16 Copyright Peter M. Schwarz

of 16 Copyright Peter M. Schwarz Dynamic Efficiency (1) Compare value today to value in future. Future dollars must be discounted Forgone opportunity to invest today. Present Value 𝑃𝑉= 𝐹𝑉 1+𝑟 𝑡 where r is (real, inflation-adjusted) discount rate, t is the number of years in the future when the earnings will be received. of 16 Copyright Peter M. Schwarz

Dynamic Efficiency (2): Example Suppose we could redesign car engines to emit less carbon at a cost of $10 million today to prevent $50 million in damage 50 years from now. Alternatively, we could invest the money and get an average return of 4% per year over the 50 year period. Is the redesign of car engines dynamically efficient? The present value of $50,000,000 to be received in 50 years, discounted at 4% is: PV = $50,000,000/(1.04)50 = $7,035,630.67, which is less than $10 million. So at 4%, or any higher interest rate, the answer is No. of 16 Copyright Peter M. Schwarz

Dynamic Efficiency (3): When to Use Renewable vs. non-renewable resources Renewables Depletable wood Non-depletable Solar, wind Non-renewables Oil Natural Gas Coal Uranium The more years of reserves remaining, the less difference it makes to use a dynamic model. Old-growth forests may take many years to replace, while oil reserves are increasing rapidly. of 16 Copyright Peter M. Schwarz

of 16 Copyright Peter M. Schwarz Competition (1): MC = 0 Simplified Model: Assume producer must sell oil today or one year from now. Competitive market. Maximize profit = maximize total revenue TRt = Pt Qt TR = TR0 + TR1 = P0 Q0 + P1 Q1 PV (TR)= P0 Q0 + (P1 Q1)/ (1 + r) Equimarginal Principle MR0 = PV (MR1) = (MR1)/(1+r) Under competition, P = MR P0 = PV (P1) = (P1)/(1+r) of 16 Copyright Peter M. Schwarz

Competition (2): Example Demand is P = 80 – 8Q Total remaining supply of oil is 10 barrels Interest rate is 10%. How much oil should the producer sell today, how much one year from now? We will present both an algebraic and a graphical solution. of 16 Copyright Peter M. Schwarz

Competition (2): Example (cont.) If static problem, P = MC. P = 0, since MC = 0. Q = 10. CS = 0.5* ($80)*10 = $400. PS = 0. SW = Total Surplus = CS + PS = $400. But that solution leaves no oil for the future. Suppose we produce 5 barrels in each period. P = $40. CS0 = 0.5* ($80-$40)*5 = $100 PS0 = $40*5 = $200 SW0 = $300b SW1 = $300/(1.1) = $272.73b SWT = $572.73b Does this solution maximize SW? of 16 Copyright Peter M. Schwarz

Competition (4): Example (cont.) Graphical Solution of 16 Copyright Peter M. Schwarz

Competition (5): Example (cont.) To maximize SW (Equimarginal Rule): P0 = P1 / (1+r) 80 – 8Q0 = (80 – 8Q1)/1.1 and Q0 + Q1 = 10 Substituting Q1 = 10 - Q0 and solving for Q0, Q0 = 5.238, Q1 = 4.762 P0 = 80 – 8Q0 = $38.10, P1 = 80 – 8(4.762) = $41.90 SW0 = CS0 + PS0 = $109.74 + $199.57 = $309.31 billion PV(SW1) = ($90.72 + $199.53)/1.1 ) = $290.24/1.1 = $263.86b Total SW = $573.17b > $572.73b when output was allocated equally in each period. Recall P0 = 80 – 8Q0 of 16 Copyright Peter M. Schwarz

of 16 Copyright Peter M. Schwarz Competition (4): MC = 20 Equimarginal Principle: P0 – MC0 = (P1 – MC1) / (1 + r) MNB = P - MC MNB0 = MNB1 / (1 + r) 80 – 8Q0 – 20 = (80 – 8Q1 – 20) / (1.1) Solving: Q0 = 5.12, Q1 = 4.88, P0 = $39.04, P1 = $40.96 PV(SW) = TNB0 + PV(TNB1) = CS0 + PS0 + PV(CS1 + PS1) TNB0 = 0.5(60-19.04)(5.12) + (39.04-20)5.12 = $202.34b TNB1 = 0.5(60-20.96)(4.88) + (40.96-20)4.88 = $197.54/1.1 = $179.58b TNB = $381.92b of 16 Copyright Peter M. Schwarz

Competition (5): Example (cont.) To obtain graphical solution: Replace P by Marginal Net Benefit (MNB) MNB = P – MC Efficient point is where MNB0 = PV (MNB1) of 16 Copyright Peter M. Schwarz

Competition (6): Increasing MC MC = 2Q 80 – 8Q0 – 2Q0 = (80 – 8Q1 – 2Q1) / (1 + r) Solution: Q0 = 5.14, Q1 = 4.86, P0 = 38.88, P1 = 41.12 MNB0 = 38.88 – 2*(5.14) = 28.74 MNB1 = 41.12 – 2*(4.86) = 31.40 PV(MNB1) = 31.40/1.1 = 28.55 MNB0 = PV(MNB1) = 28.60 (Differences are due to rounding) of 16 Copyright Peter M. Schwarz

Competition (7): Hotelling’s Rule Hotelling’s Rule: The dynamically efficient allocation occurs when the PV of MNB for the last unit consumed is equal across time periods. P0 – MC = PV (P1 – MC) Equivalently: (P0 – MC) (1+r) = (P1 – MC). Marginal User Cost (MUC) = PV (P-MC) is opportunity cost of selling today, sacrificing what you could earn in the future. Value of oil increases at the rate of interest, equal to what you would earn on alternative investment. Unlike static model, P > MC, because of MUC. MNB0 = 38.88 – 2*(5.14) = 28.74 MNB1 = 41.12 – 2*(4.86) = 31.40 28.74 = 31.40/1.1? Yes (except for rounding errors). of 16 Copyright Peter M. Schwarz