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Unformatted text preview: EEP 101/ECON 125 Lecture 14: Natural Resources
Professor David Zilberman UC Berkeley Announcements Problem Set 1 will be returned in sections Midterm: Tuesday, March 17 Midterm Review: Sunday, March 15 46pm Location: TBA Announcements Problem Set 2: Monopoly Question (1.b.iii) You can assume monopoly just supplies the group with the larger demand Problem Set 2: Essay Question (2.a) Clarification: answer part (a) from the government’s point of view. Natural Resources We distinguish between nonrenewable resources and renewable resources. Coal, gold, and oil are examples of nonrenewable resources. Fish and forests are examples of renewable resources, since they can be selfreplenishing. What about water? Old growth redwoods? Natural Resource Economics Natural Resource Economics addresses the allocation of resources over time: How much oil do we pump now? later? Are we fishing sustainably? Natural Resource Economics Cont. Market forces may cause depletion of natural resources too quickly or too slowly Natural Resource Economics also investigates how natural resources are allocated under alternative economic institutions. Key Elements of Dynamics: Key Interest Rate Interest 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. $ Today vs. $ Future $ Today vs. $ Future For an individual, say: $ 1000 today ~ $ 1000 (1+δ) future δ – personal discount rate The Interest Rate The interest rate is the result of negotiations between the lenders and the borrowers. The higher the desire of the lenders to consume resources today rather than to wait, and/or the higher the desire of the borrowers to get the loans, the higher the resulting interest rate. In this sense, the interest rate is an equilibrium outcome, like the price level in a competitive market. Example The amount loaned is called the Principal. The payment from me to you in compensation for your delayed consumption is called the Interest on the loan. Example Cont. The (simple) interest rate of the loan, denoted r, can be expressed: Principal + Interest = (1 + r) Principal Or B1 = B0 + r B0 = (1+r) B0 The Interest Rate is an Equilibrium of Outcome C1 = consumption in period 1 C2 = consumption in period 2 The Interest Rate is an Equilibrium of The Outcome Cont. Outcome Delay of consumption (saving) in period 1 reduces current utility but increases utility in period 2. The intertemporal production possibilities curve (IPP) denotes the technological possibilities for tradingoff present vs. future consumption. The curve S, is an indifference curve showing individual preferences between consumption today and consumption in the future. Any point along a particular indifference curve leads to the same level of utility. 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 atpoint A = (1 + r) The Interest Rate is an Equilibrium of The Outcome Cont. Outcome 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: 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. The Interest Rate is an Equilibrium of The Outcome Cont. Outcome max { U (C1, C 2)} 1 subject to C1 + C2 ≤ I 1+ r The Interest Rate is an Equilibrium of The Outcome Cont. Outcome which can be written as: 1 L = U (C1, C 2) + λ I − C1 − C 2 1+ r FOCS : UC 1 = λ UC 1 = 1+ r λ⇒ UC 2 UC 2 = 1+ r 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 sum r + IR + TCm + SRm, where TCm and SRm are minimum transactions costs and risk costs, respectively. This interest rate is called the Prime Rate. The Components of Interest Rate The Cont. Cont. Lenders (banks) analyze projects proposed by entrepreneurs before financing them. They do this to assess the riskiness of the projects and to determine SR. 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. Depending on how time is measured – discretely (say, in days months or years) or continuously – we might use different formulas for measuring netpresent value. We will use discretetime discounting in this course. Unless stated otherwise, assume that r represents the simple real interest rate. 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. That's because the lender could lend the 10 dollars received today to someone else and earn interest during the current time period. 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 & Different Discounting Cont. Discounting 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. The value of 10 dollars received in the next time period is discounted by multiplying it by 1/(1+r). 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. The concept of present value applies to amounts paid in the future as well as to amounts received. Note that if the interest rate increases, the value today of an amount received in the future declines. Similarly, if the interest rate decreases, then the value today of an amount paid in the future increases. 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. That is, if you are able to invest money at r = 10%, you 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. The Present Value of an The Annuity 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. In fact, it is equal to the periodic payment divided by the interest rate r (this is the sum of an infinite geometric series). 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? Answer: NPV = $1000/r Suppose r = 0.1 then the present value of your annuity is $1000/0.1 = $10,000. 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% 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. It is argued that the social discount rate is lower than the private discount rate. In evaluating public projects, the lower social discount rate should be used when it is appropriate. 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). If they did not, no one would invest money in the higher risk investments. 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. Criteria for Evaluating Alternative Criteria Allocations of Resources Over Time Time Net Present Value (NPV) is the sum of the present 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: (Bt − C t ) NPV = ∑ t. t = 0 (1 + r) N 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: Internal Rate of Return (IRR) is the interest rate that is t =0 associated with zero net present value of a project. IRR is the x that solves the equation: NFV = (Bt − Ct ) ⋅ (1 + r )N − t ∑ N (Bt − Ct ) 0= ∑ t t = 0 (1 + x) N The Relationship Between IRR and The NPV 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 Familiarizing Previous Concept Previous 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. Three period model: Suppose you are 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 Familiarizing Ourselves with the Familiarizing Previous Concept Cont. Previous
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) BenefitCost Analysis Benefitcost analysis is a pragmatic method of economic decisionmaking. The procedure consists of the following two steps: Step 1: Estimate the economic impacts (costs and benefits) that will occur in the current time period and in each future time period. Step 2: Use interest rate to compute net present value or 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. ...
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 Spring '09
 ZELBERMAN
 Environmental Economics, Monopoly

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