**Unformatted text preview: **EEP 101/ECON 125 Lecture 14: Natural Resources
Professor David Zilberman UC Berkeley Natural Resource Economics Natural Resource Economics addresses the allocation of resources over time. Natural Resource Economics distinguishes between nonrenewable resources and renewable resources. nonrenewable resources. Coal, gold, and oil are examples of Fish and water are examples of renewable resources, since they can be selfreplenishing. Natural Resource Economics Cont. Natural Resource Economics suggests policy intervention in situations where markets fail to maximize social welfare over time . where market forces cause depletion of nonrenewable natural resources too quickly or too slowly, or cause renewable resource use to not be sustainable over time (such as when species extinction occurs) Natural Resource Economics also investigates how natural resources are allocated under Key Elements of Dynamics: Interest Rate One of the basic assumptions of Dynamic Analysis is that individuals are impatient. They would like to consume the goods and services that they own today, rather than saving for the future or lending to another individual. Individuals will lend their goods and services to others only if they are compensated for delaying their own consumption. The Interest Rate The Interest Rate (often called the Discount Rate in resource contexts) is the fraction of the value of a borrowed resource paid by the borrower to the lender to induce the lender to delay her own consumption in order to make the loan. lender and the borrower. The interest rate is the result of negotiation between the The higher the desire of the lender to consume her resources In this sense, the interest rate is an equilibrium outcome, like the price level in a competitive market. today rather than to wait, and/or the higher the desire of the borrower to get the loan, the higher the resulting interest rate. Consumption Even an isolated individual must decide how much of his resources to consume today and how much to save for consumption in the future. In this situation, a single individual acts as both the lender and the borrower. The choices made by the individual reflect the individual's implicit interest rate of trading off consumption today for consumption tomorrow. Example Suppose Mary owns a resource. Mary would like to consume the resource today. John would like to borrow Mary's resource for one year. Mary agrees to loan John the resource for one year if John will pay Mary an amount to compensate her for the cost of delaying consumption for one year. The amount loaned is called the Principal. The payment from John to Mary in compensation for Mary's delayed consumption is called the Interest on the loan. Example Cont. Suppose Mary's resource is $100 in cash. Suppose the interest amount agreed to by Mary and John is $10. Then, at the end of the year of the loan, John repays Mary the principal plus the interest, or $110: Principal + Interest = $100 + $10 = $110 Example Cont. The (simple) interest rate of the loan, denoted r, can be found by solving the following equation for r: Principal + Interest = (1 + r) Principal For this example: So, we find: $110 = (1 + r) $100 r = 10/100 or 10% Hence, the interest rate on the loan was 10%. Example Cont. Generally, we can find the interest rate by noting that: B1 = B0 + r B1 = (1+r) B0 where B0 = Benefit today, and B1 = Benefit tomorrow The Interest Rate is an Equilibrium of Outcome C1 = consumption in period 1 C2 = consumption in period 2 Delay of consumption (saving) in period 1 reduces current utility but increases utility in period 2. The Interest Rate is an Equilibrium of Outcome Cont. The intertemporal production possibilities curve (IPP) denotes the between consumption today and consumption in the future. utility. technological possibilities for tradingoff present vs. future consumption. The curve S, is an indifference curve showing individual preferences Any point along a particular indifference curve leads to the same level of Utility maximization occurs at point A, where S is tangent to the IPP. The interest rate, r, that is implied by this equilibrium outcome, can be found by solving either of the following two equations for r: slope of S at point A = (1 + r) slope of IPP at point A = (1 + r) The Interest Rate is an Equilibrium of Outcome Cont. Therefore, if we can determine the slope of either S or IPP at tangency point A, then we can calculate the interest rate, r. This is often done by solving the following individual optimization problem where I is the total income available over the two periods:
Max.{ (C1, C 2 )} U
C1,C 2 . 1 . subject to: I = C1 + . . C2 . 1+ r. The Interest Rate is an Equilibrium of Outcome Cont. which can be written as:
1 L = U (C1, C 2) + l I - C1 + C2 1+ r FOCS: UC 1 = l l UC 2 = 1+ r UC 1 = 1+ r UC 2 The Indifference Curve The indifference curve is found by setting: UC 1dC 1 + UC 2 dC 2 = 0 dC 2 - UC 1 = = - (1 + r ) dC 1 UC 2 The indifference curve simply indicates that the equilibrium occurs where an individual cannot improve her intertemporal utility at the margin by changing the amount consumed today and tomorrow, within the constraints of her budget. The Components of Interest Rate Interest rates can be decomposed into several elements: Real interest rate, r Rate of inflation, IR Transaction costs, TC Risk factor, SR The interest rate that banks pay to the government (i.e., to the Federal Reserve) is the sum r + IR. This is the nominal interest rate. The interest rate that lowrisk firms pay to banks is the This interest rate is called the Prime Rate. sum r + IR + TCm + SRm, where TCm and SRm are minimum transactions costs and risk costs, respectively. The Components of Interest Rate Cont. Lenders (banks) analyze projects proposed by entrepreneurs before financing them. projects and to determine SR. They do this to assess the riskiness of the Creditrating services and other devices are used by lenders (and borrowers) to lower TC. Some Numerical Examples
(1) If the real interest rate is 3% and the inflation rate is 4%, then the nominal interest rate is 7%. (2) If the real interest rate is 3%, the inflation rate is 4% and TC and SR are each 1%, then the Prime Rate is 9%. Discounting Discounting is a mechanism used to compare streams of net benefits generated by alternative allocations of resources over time. There are two types of discounting, depending on how time is measured. If time is measured as a discrete variable (say, in days, months or years), discretetime discounting formulas are used, and the appropriate real interest rate is the "simple real interest rate". If time is measured as a continuous variable, then continuoustime formulas are used, and the appropriate real interest rate is the "instantaneous real interest rate". We will use discretetime discounting in this course. Hence, we will use discretetime discounting formulas, and the real interest rate we refer to is the simple real interest rate, r. Unless stated otherwise, assume that r represents the simple real Lender's Perspective From a lender's perspective, 10 dollars received at the beginning of the current time period is worth more than 10 dollars received at the beginning of the next time period. received today to someone else and earn interest during the current time period. That's because the lender could lend the 10 dollars In fact, 10 dollars received at the beginning of the current time period would be worth $10(1 + r) at the beginning of the next period, where r is the interest rate that the lender could earn on a loan. A Different Perspective & Discounting Cont. Viewed from a different perspective, if 10 dollars were received at the beginning of the next time period, it would be equivalent to receiving only $10/(1 + r) at the beginning of the current time period. discounted by multiplying it by 1/(1+r). The value of 10 dollars received in the next time period is Discounting is a central concept in natural resource economics. So, if $10 received at the beginning of the next period is only worth $10/(1 + r) at the beginning of the current period, how much is $10 received two periods from now worth? 2 Present Value In general, the value today of $B received t periods from now is $B/(1 + r)t. The value today of an amount received in the future is called the Present Value of the amount. well as to amounts received. r) . The concept of present value applies to amounts paid in the future as For example, the value today of $B paid t periods from now is $B/(1 + t Note that if the interest rate increases, the value today of an amount received in the future declines. Similarly, if the interest rate increases, then the value today of an amount paid in the future declines. You Win the Lottery! You are awarded aftertax income of $1M. However, this is not handed to you all at once, but at $100K/year for 10 years. If the interest rate is, r = 10%, net present value: NPV = 100K+(1/1.1)100K+(1/1.1)2100K + (1/1.1)3100K + ... + (1/1.1)9100K. = $675,900 The value of the last payment received is: NPV = (1/1.1)9100K = $42,410. would be indifferent between receiving the flow of $1M over 10 years and $675,900 today or between receiving a one time payment of $100K 10 years from now and $42,410 today. That is, if you are able to invest money at r = 10%, you The value of time :discounting
interest rate Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.05 0.1 Future Discou Future Discou earning nting earning nting 100 100 100 100 105 95.24 110 90.91 110.25 90.7 121 82.64 115.76 86.38 133.1 75.13 121.55 82.27 146.41 68.3 127.63 78.35 161.05 62.09 134.01 74.62 177.16 56.45 140.71 71.07 194.87 51.32 147.75 67.68 214.36 46.65 155.13 64.46 235.79 42.41 162.89 61.39 259.37 38.55 171.03 58.47 285.31 35.05 179.59 55.68 313.84 31.86 188.56 53.03 345.23 28.97 197.99 50.51 379.75 26.33 The Present Value of an Annuity An annuity is a type of financial property (in the same way that stocks and bonds are financial property) that specifies that some individual or firm will pay the owner of the annuity a specified amount of money at each time period in the future, forever! Although it may seem as if the holder of an annuity will receive an infinite amount of money, the Present Value of the stream of payments received over time is actually finite. rate r (this is the sum of an infinite geometric series). In fact, it is equal to the periodic payment divided by the interest Annuity Cont. Let's consider an example where you own an annuity that specifies that Megafirm will pay you $1000 per year forever. Question: What is the present value of the annuity? We know that NPV = $1000/r. Suppose r = 0.1 then the present value of your annuity is $1000/0.1 = $10,000. That is a lot of money, but far less than an infinite amount. Notice that if r decreases, then the present value of the annuity increases. Similarly, if r increases, then the present value of the annuity decreases. For example, you can show that a 50% decline in the interest rate will double the value of an annuity. Transition from flow to stock If a resource is generating $20.000/year for the forth seeable future future and the discount rate is 4% the price of the resource should be $500.000 If a resource generates $24K annually and is sold for $720K, the implied discount rate is 24/720=1/30=3.333% If the real price of the resource (oil) is The impact of price expectation expected to go up by 2% The real discount rate is 4% What is the value of an oil well which provides for the for seeable 5000 barrel annually, and each barrel earns 30$ (assume zero extraction costs)? 1. Is It (A) $3.750K (B) $7.500K ? 2.If the discount rate is 7% will you Pay $2 millions for the well? 3.What is your answer to 1. If inflation is 1%? Answers 1.B 5000*30/(.04.02)=150.000/.02
=$7.500.000 2. 150.000/(.07.02)=150.000/.05= 3000000>2000000 yes 3. If inflation is 1% real price growth is only 1% and 150.000/(.04.03)=150.000/.03= $5000000 One percentage interest reduce value by 1/3. The Social Discount Rate The social discount rate is the interest rate used to make decisions regarding public projects. It may be different from the prevailing interest rate in the private market. Some reasons are: Differences between private and public risk preferences --the public overall may be less risk averse than a particular individual due to pooling of individual risk. Externalities--In private choices we consider only benefits to the individuals; in public choices we consider benefits to everyone in society. private discount rate. In evaluating public projects, the lower social discount rate should be used when it is appropriate. It is argued that the social discount rate is lower than the Uncertainty and Interest Rates Lenders face the risk that borrowers may go bankrupt and not be able to repay the loan. To manage this risk, lenders may take several types of actions: Limit the size of loans. Demand collateral or cosigners. Charge highrisk borrowers higher interest rates. (Alternatively, different institutions are used to provide loans of varying degrees of risk.) RiskYield Tradeoffs Investments vary in their degree of risk. Generally, higher risk investments also tend to entail higher expected benefits (i.e., high yields). higher risk investments. If they did not, no one would invest money in the For this reason, lenders often charge higher interest rates on loans to highrisk borrowers, while large, low risk, firms can borrow at the prime rate. Net Present Value (NPV) is the sum of the present Criteria for Evaluating Alternative Allocations of Resources Over Time values of the net benefits accruing from an investment or project. Net benefit in time period t is Bt Ct, where Bt is the Total Benefit in time period t and Ct is the Total Cost in time period t. The discrete time formula for N time periods with constant r: ( - ) NPV = . =0 (1 + ) NFV and IRR Net Future Value (NFV) is the sum of compounded differences between project benefits and project costs. The discrete time formula for N time periods with constant r: =0 Internal Rate of Return (IRR) is the interest rate that is NFV = ( - ) (1 + ) - associated with zero net present value of a project. IRR is the x that solves the equation: 0= =0 (1 + ) ( - ) The Relationship Between IRR and NPV If r < IRR then the project has a positive NPV If r > IRR then the project has a negative NPV It is not worthwhile to invest in a project if you can get a better rate of return on an alternate investment. Familiarizing Ourselves with the Previous Concept Two period model: If we invest $I today, and receive $B next year in returns on this investment, the NPV of the investment is: $I + $B/(1 + r). Notice that the NPV declines as the interest rate r increases, and vice versa. considering an investment which costs you $100 now but which will pay you $150 next year. If r = 10%, then the NPV is: 100 + 150/1.1 = $36.36 If r = 20%, then the NPV is: 100 + 150/1.2 = $25 If r = 50%, then the NPV is: 100 + 150/1.5 = $0 Three period model: Suppose you are Familiarizing Ourselves with the Previous Concept Cont. Consider the "stream" of net benefits from an investment given in the following table: Time Period: 0 1 2 Bt Ct: 100 66 60.5 The NPV for this investment is: 66 60.5 NPV = -100 + 1 + 2 = 10 (1 + 0.1) (1+ 0.1 ) Time net benefits 0.02 0.03 0.04 0.05 0.00 1000.00 1000.00 1000.00 1000.00 1000.00 1.00 100.00 98.04 97.09 96.15 95.24 2.00 100.00 96.12 94.26 92.46 90.70 3.00 100.00 94.23 91.51 88.90 86.38 4.00 100.00 92.38 88.85 85.48 82.27 5.00 100.00 90.57 86.26 82.19 78.35 6.00 100.00 88.80 83.75 79.03 74.62 7.00 100.00 87.06 81.31 75.99 71.07 8.00 100.00 85.35 78.94 73.07 67.68 9.00 100.00 83.68 76.64 70.26 64.46 10.00 100.00 82.03 74.41 67.56 61.39 11.00 100.00 80.43 72.24 64.96 58.47 12.00 100.00 78.85 70.14 62.46 55.68 13.00 100.00 77.30 68.10 60.06 53.03 14.00 100.00 75.79 66.11 57.75 50.51 NPV 210.62 129.61 56.35 10.14
IRR=.049 BenefitCost Analysis Benefitcost analysis is a pragmatic method of economic decisionmaking. The procedure consists of the following two steps: that will occur in the current time period and in each future time period. compute internal rate of return of the project/investment. Use internal rate of return only in cases in which net benefits switches sign once, meaning that investment costs occur first and investment benefits return later. Step 1: Estimate the economic impacts (costs and benefits) Step 2: Use interest rate to compute net present value or BenefitCost Analysis Cont. A key assumption of benefitcost analysis is the notion of potential Some issues in benefitcost analysis to consider include: How discount rates affect outcomes of benefitcost analysis. When discount rates are low, more investments are likely to be justified. Accounting for public rate of discount vs. private rate of discount. Incorporating nonmarket environmental benefits in benefitcost analysis. Incorporating price changes because of market interaction in benefitcost analysis. Incorporating uncertainty considerations in benefitcost analysis. welfare improvement. That is, a project with a positive NPV has the potential to improve welfare, because utility rises with NPV. Time Case1 case2 case3 case4 case5 0.00 1000.00 1000.00 1000.00 1000.00 1000.00 1.00 100.00 100.00 100.00 120.00 100.00 2.00 120.00 120.00 120.00 140.00 120.00 3.00 140.00 140.00 140.00 160.00 140.00 4.00 150.00 150.00 150.00 170.00 150.00 5.00 160.00 160.00 160.00 180.00 160.00 6.00 180.00 180.00 180.00 200.00 180.00 7.00 160.00 160.00 160.00 180.00 160.00 8.00 140.00 140.00 140.00 140.00 140.00 9.00 160.00 160.00 160.00 160.00 160.00 10.00 140.00 140.00 140.00 140.00 140.00 11.00 40.00 40.00 40.00 40.00 40.00 12.00 80.00 80.00 80.00 80.00 80.00 13.00 120.00 120.00 120.00 120.00 120.00 14.00 160.00 160.00 160.00 160.00 0.00 interest 0.05 0.03 0.01 0.05 0.05 npv 106.725 44.732 18.5524 9.0029 25.914 ...

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