# Determinants of Social Discount Rate, general case

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Determinants of Social Discount Rate, general case The resulting equation r = ρ + θ g is known as the Ramsey equation after Frank Ramsey (928) The equation states tt that t in an optimal intertemporal t allocation: the productivity of capital (interest rate) = the return on investment is the sum of The rate of pure time preference (describing impatience) And the product of the consumption elasticity of marginal utility θ (describing how fast marginal consumption decreases in consumption) the growth rate g (describing how fast consumption increases) Spring 09 UC Berkeley Traeger 4 Discounting 20

2 The Economics of Climate Change C 75 Christian Traeger Part 4: Discounting continued Lecture 7 Background still Cameron Hepburn s (2006), Discounting climate change damages: Working note for the Stern review. Spring 09 UC Berkeley Traeger 3 Instruments 2

3 Review Problem: How to compare costs and benefits that occur at different points in time? Economic solution concept involves: Discounting: Describes the valuation in present day terms of future outcomes (damages, costs, benefits, utility values) Cost Benefit analysis: Assess costs and benefits in monetary units Epress all benefits and costs in present value terms Net present value NPV: Support a project if present value benefits eceed present value costs NPV B C T t t t 0 t ( r) ) Spring 09 UC Berkeley Traeger 4 Discounting 22

4 Answer to Homework Eample II Cost Benefit analysis: Consider the two modified projects and a discount rate of 5%. Benefits (in \$) Year Project A Project B Assume you only have \$30 that you can invest in the first period. Which project would you invest in? NPV 05) 05) 05) A = \$30+\$20/(,05) +\$0/(,05) 2 +\$0/(,05) 3 = \$6.76 NPV B = \$30+\$0/(,05) +\$20/(,05) 2 +\$20/(,05) 3 = \$4.94 Project B because NPV B >NPV A Spring 09 UC Berkeley Traeger 4 Discounting 23

5 Review: How to find the discount rate? Recall importance of discounting for long time horizons: At a 0% discount rate \$ Mio in 50 years have present value of % discount rate \$ Mio in 50 years have present value of \$ High discount rate implies A dollar today is much more valuable than a dollar tomorrow Hard to justify climate policy where costs occur today but benefits (abated damages) accrue later How do we find the correct discount rate? Market Intertest Rate > BUT: might not eist for long time horizons or not represent correct information (market failures, responsibilities for future generations) Identify components of the Social Discount Rate Spring 09 UC Berkeley Traeger 4 Discounting 24

6 Review: The Social Discount Rate We have derived how the optimal real interest rate should be composed if markets were perfect and represented all information: Then: MRS = MRT (Marginal rate of substitution = Marginal rate of transformation) Where: Good = consumption today Good 2 = consumption tomorrow Result is the Ramsey equation: r = ρ + θ g We derived the equation for a two period setting, but holds in general, also in continuous time: r(t) = ρ + θ((t)) g(t) Remark: θ((t)) is determined by the utility function. If utility is a power function (i.e. α ) then θ = α independent of (t). Spring 09 UC Berkeley Traeger 4 Discounting 25

7 Review: Determinants of Social Discount Rate Ramsey equation: r(t) = ρ + θ g(t) Optimal productivity of capital (r) equals The rate of pure time preference (ρ) (describing impatience) And the product of the consumption elasticity of marginal utility θ (describing how fast marginal utility decreases in consumption) Relative change of marginal utility du '( X ) under a relative change of consumption. U ''( X ) X U '( X ) or U '( X ) dx By how many percent does marginal X utility change if consumption increases by one percent the growth rate g (describing how fast consumption increases) Spring 09 UC Berkeley Traeger 4 Discounting 26

8 So what s the rate? Normative vs Descriptive Two approaches Descriptive: Observe r(t) and g(t). Either in market or in eperiments. Different combinations of ρ and θ are generally compatible with these observations. Dt Determining ii θ by observation is harder but would identify corresponding ρ. Prescriptive: Start with deciding on ρ and θ. Then growth rate g(t) determines the corresponding real interest rate r(t). () Arguments for picking iki ρ and θ generally rely on ethical reasoning. Spring 09 UC Berkeley Traeger 4 Discounting 27

9 So what s the rate? Pure Time Preference ρ: Some opinions that it should be zero: Ramsey (928) describes placing different weights upon the utility of different generations, as ethically indefensible. ibl Harrod (948) stated that discounting utility represented a polite epression for rapacity and the conquest of reason by passion. Stern Review (2007) to be encountered in integrated assessment part > These are mostly ethical arguments and thus prescriptive i Remark: Ramsey equation including (undetermined!) parameter ρ can be derived from aioms, i.e. assumptions on behavior rather than starting with our utility model Changing the aioms to include risk attitude in a more comprehensive way can eliminate ρ, that is, make it zero starting from assumptions on rational and consistent behavior rather than for ethical reasons (paper on my homepage) Spring 09 UC Berkeley Traeger 4 Discounting 28

10 So what s the rate? Descriptive Descriptive take on ρ: By reverse engineering from observations economists often take values between 2% and 3%. Similarly il l θ is engineered to be between and 4. Remark: The high (& even higher) values of θ are obtained from risk studies where θ also represents risk aversion rather than just reduction in marginal utility from growth over time. The growth rate g is observed and predicted to be approimately in the range % to 3% The real interest rate employed as observed rate ranges approimately from 2% to 7% A convenient eample of somewhat reasonable values (Weitzman 2007) ρ=2%, θ=2, g=2%, r=6% Other eamples Stern review (2007), Nordhaus (2007) on problem set. Spring 09 UC Berkeley Traeger 4 Discounting 29

11 So what s the rate? Prescriptive ρ: possibly zero for ethical reasons as proposed on earlier slide θ: Normative/ethical information conveyed: Equalizing consumption across generations If θ =0, then more or less consumption in the future does not change willingness to invest (r independent of growth rate g) If θ is large, then with positive growth > not willing to invest in future (future generations have more anyhow) If θ is large, then with negative growth > very willing to invest in future (future generations are poorer than today s) Proposed range for θ ranges from to 4 Remark: Willing to invest in future = low real interest rate in optimal allocation. Spring 09 UC Berkeley Traeger 4 Discounting 30

12 Distributive Justice Ecursion: Rawls theory of justice applied to intertemporal distribution Would set ρ to zero and increase θ to More generally, an egalitarian perspective with respect to time yields ρ small and thus r small distribution across generations (stripping off the time dimension) yields θ large and thus r large if positive growth Spring 09 UC Berkeley Traeger 4 Discounting 3

13 Sustainability is another normative value theory that relates to the discount rate Definitions: Sustainable development is development that t meets the needs of the present without compromising the ability of future generations to meet their own needs (WCED 987). Common denominator of sustainability theories is the acknowledgment of the long run mutual dependence d of environmental quality and resource availability on the one hand, and economic development on the other hand. Van den Bergh & Hofkes (998, ) One distinguishes: weak sustainability: preservation of a non decreasing overall welfare. To this end, a substitution between environmental and manmade capital is permitted. strong sustainability: requires a non declining value or physical amount of natural capital and its service flows. Substitution possibilities between man made goods and natural resources and service flows are either limited or ethically indefensible. Spring 09 UC Berkeley Traeger 4 Discounting 32

14 Sustainability A Formalization The Economics of Climate Change C 75 To formalize this idea, we need to model environmental goods E AND produced goods P AND the fact that both goods are not perfect substitutes Assume that substitutability between environmental goods and produced goods is of Cobb Douglas form. Assume that the decrease of marginal utility in overall consumption is g y p is parameterized by a power function (parameter θ, see problem 3.3) ) ( ) ( P E P E U U W ) ( ) ( ) ( ) ( ), ( ), ( P E P E U U W Spring 09 UC Berkeley Traeger 4 Discounting 33

15 Sustainability & Discounting In general growth rates of environmental goods g E lie below the growth rates of produced goods g P : g E < g P Now we can derive two discount rates: A discount rate for environmental goods r E and A discount rate for produced goods r P A similar but slightly more complicated derivation as earlier yields: r E = ρ + θ (.5 5 g E +.55 g P ) (.5 5 g P.55 g E ) r P = ρ + θ (.5 g E +.5 g P ) + (.5 g P.5 g E ) For coinciding growth rates g E = g P = g we have same formulas as earlier For g E < g P however, we find that environmental goods have to be discounted at a lower than average rate and produced goods have to be discounted at a higher than average rate. Spring 09 UC Berkeley Traeger 4 Discounting 34

16 Sustainability & Discounting r E = ρ + θ (.5 g E +.5 g P ) (.5 g P.5 g E ) r P = ρ + θ (.5 g E +.5 g P ) + (.5 g P.5 g E ) For g E < g P however: environmental goods have to be discounted at a lower than average rate produced d goods have to be discounted d at a higher h than average rate In general it can be shown that The more oesubstitutable u both classes of goods, the smaller the reduction of r E and the smaller the increase in r P The less substitutable both classes of goods, the larger the reduction of r E and the larger the increase in r P Remark: The reasoning in terms of lower discount rates for environmental goods is equivalent to arguing in an aggregate one commodity model that due to increasing relative scarcity the monetary value of environmental goods increases in the future. Spring 09 UC Berkeley Traeger 4 Discounting 35

17 Hyperbolic Discounting I It has been suggested from a normative perspective: to discount the close future at higher/observed rates to discount the far future at relatively lower rates Analogy: I care more for myself than for someone close (e.g. my close relatives). I care more for someone close than for someone I hardly know (e.g. more for my close relatives than for my far relatives). But I really don t make a big difference between hardly knowing and not knowing (or I really don t care whether it s my cousin of degree 00 or 0). T Formally (Version ): W ( ) where ρ a t+< ρ a t t U 0 a t t ( t ) Here ρ a t is the average discount rate between t and the present Spring 09 UC Berkeley Traeger 4 Discounting 36

18 Hyperbolic Discounting II Alternatively (Version 2): Can epress the welfare evaluation in terms of per period discount rates. Here ρ t is the rate that discounts period t welfare into period t values (also called instantaneous discount rate). The corresponding welfare function writes as W U ( T U ( ) t0 t t ( ) 0 ) U ( ) ( ) ( )( )... ( )...( U ( U ( ) ) T T ) again with ρ t+ < ρ t Spring 09 UC Berkeley Traeger 4 Discounting 37

19 Hyperbolic Discounting III Both forms are equivalent for modeling hyperbolic discounting The second form looks more complicated, but turns out to be preferable in many occasions. A similar discounting problem of form 2 appears in problem 3.2, however, in terms of real interest discounting consumption rather than pure time preference discounting utility. In that problem you will learn that hyperbolic (=falling) discount rates can make a project worth investing in the present not worth inversing anymore in the future. This dependence of the worthiness of a project on the period in which it is evaluated is referred to as time inconsistency. Time inconsistencies can lead to a continuous reversion of a (thought to be optimal) project and lead to dynamic inefficiencies. Spring 09 UC Berkeley Traeger 4 Discounting 38

20 Heterogeneity So far we have not looked at distribution and heterogeneity! Distribution: > see problem 3.3 and Integrated Assessment section Eample of heterogeneity: What happens if individuals have different rates of pure time preference? Aggregating individual utility functions yields: The further into the future, the more important become the smaller time preferences in the aggregate welfare function (yielding hyperbolic discounting) In the long run limit only the lowest discount rate counts Spring 09 UC Berkeley Traeger 4 Discounting 39

21 So what s the rate? Asking the eperts: Wi Weitzman (200) surveyed 260 economists asking: Taking all relevant considerations into account, what real interest rate do you think should be used to discount over time the (epected) benefits and (epected) costs of projects being proposed to mitigate the possible effects of global climate change? Spring 09 UC Berkeley Traeger 4 Discounting 40

22 So what s the rate? Asking the eperts: The result: Spring 09 UC Berkeley Traeger 4 Discounting 4

23 Final Remarks Note that discount rates changes, if growth rate changes. In the etreme: discount rates could be negative if negative growth. The correct discount rate has not yet been agreed upon The parameters ρ and θ can be associated with individual trade offs over time as well as with intergenerational trade offs. Building a model that depicts both as different parameters is likely to help in the dispute between the normative and the descriptive interpretations i of ρ and θ Related thought: Assume we give less weight to generations born at a later date. Those generations overlap with generations born earlier. Thus, we effectively discriminate between welfare of different generations alive at the same time. Ethically correct? Spring 09 UC Berkeley Traeger 4 Discounting 42

### Appropriate discount rates for long term public projects

Appropriate discount rates for long term public projects Kåre P. Hagen, Professor Norwegian School of Economics Norway The 5th Concept Symposium on Project Governance Valuing the Future - Public Investments

### Using Discount Rate for Water Sector Planning in Bangladesh under Climatic Changes

Using Discount Rate for Water Sector Planning in Bangladesh under Climatic Changes Dr. Mohammad Ismail Khan Associate professor, Department of Agricultural Economics Bangabndhu Sheikh Mujibur Rahman Agricultural

### Time declining social discount rate Alex Dubgaard

Time declining social discount rate Alex Dubgaard Pearce, David, Ben Groom, Cameron Hepburn & Phoebe Koundouri (2003): Valuing the Future. Recent advances in social discounting, World Economics. Vol. 4,

### Public Goods & Externalities

Market Failure Public Goods & Externalities Spring 09 UC Berkeley Traeger 2 Efficiency 26 Climate change as a market failure Environmental economics is for a large part about market failures: goods (or

### Expected net present value, expected net future value, and the Ramsey rule

Expected net present value, expected net future value, and the Ramsey rule Christian Gollier Toulouse School of Economics (LERNA and IDEI) June 21, 2010 Abstract Weitzman (1998) showed that when future

### Chapter 21: The Discounted Utility Model

Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporal

### What's the Rate? Disentangling the Weitzman and the Gollier Effect

University of California, Berkeley Department of Agricultural & Resource Economics CUDARE Working Papers Year 2012 Paper 1121 What's the Rate? Disentangling the Weitzman and the Gollier Effect Christian

### The UK Treasury rate as set out in the Green Book is for a STPR, based on g at 2%, n at 1.0 and p at 1.5%, give an overall discount rate of 3.

Notes on the Discount rate The choice of discount rate for project economic analysis has been the subject of considerable debate in both theoretical and operational terms. In theory the discount rate for

### Example: two period consumption

Example: two period consumption 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

### C(t) (1 + y) 4. t=1. For the 4 year bond considered above, assume that the price today is 900\$. The yield to maturity will then be the y that solves

Economics 7344, Spring 2013 Bent E. Sørensen INTEREST RATE THEORY We will cover fixed income securities. The major categories of long-term fixed income securities are federal government bonds, corporate

### THE CHOICE OF DISCOUNT RATE FOR CLIMATE CHANGE POLICY EVALUATION

Climate Change Economics, Vol. 3, No. 4 (2012) 1250024 (18 pages) World Scientific Publishing Company DOI: 10.1142/S2010007812500248 THE CHOICE OF DISCOUNT RATE FOR CLIMATE CHANGE POLICY EVALUATION LAWRENCE

### Macroeconomics Lecture 1: The Solow Growth Model

Macroeconomics Lecture 1: The Solow Growth Model Richard G. Pierse 1 Introduction One of the most important long-run issues in macroeconomics is understanding growth. Why do economies grow and what determines

### Marginal Functions in Economics

Marginal Functions in Economics One of the applications of derivatives in a real world situation is in the area of marginal analysis. Marginal analysis uses the derivative (or rate of change) to determine

### 2.4. Factoring Quadratic Expressions. Goal. Explore 2.4. Launch 2.4

2.4 Factoring Quadratic Epressions Goal Use the area model and Distributive Property to rewrite an epression that is in epanded form into an equivalent epression in factored form The area of a rectangle

### Climate policies deserve a negative discount rate

Climate policies deserve a negative discount rate Marc Fleurbaey Princeton University mfleurba@princeton.edu Stéphane Zuber CNRS CERSES and Paris Descartes stephane.zuber@parisdescartes.fr Introduction

### 1 The Black-Scholes Formula

1 The Black-Scholes Formula In 1973 Fischer Black and Myron Scholes published a formula - the Black-Scholes formula - for computing the theoretical price of a European call option on a stock. Their paper,

### Taxes and Subsidies PRINCIPLES OF ECONOMICS (ECON 210) BEN VAN KAMMEN, PHD

Taxes and Subsidies PRINCIPLES OF ECONOMICS (ECON 210) BEN VAN KAMMEN, PHD Introduction We have already established that taxes are one of the reasons that supply decreases. Subsidies, which could be called

### DISCUSSION PAPER. The Choice of Discount Rate for Climate Change Policy Evaluation. Lawrence H. Goulder and Roberton C.

DISCUSSION PAPER September 2012 RFF DP 12-43 The Choice of Discount Rate for Climate Change Policy Evaluation Lawrence H. Goulder and Roberton C. Williams III 1616 P St. NW Washington, DC 20036 202-328-5000

### Thomas Piketty Academic year 2014-2015

Public Economics: Tax & Transfer Policies (Master PPD & APE, Paris School of Economics) Thomas Piketty Academic year 2014-2015 Lecture 3: Externalities & corrective taxation: illustration with global warming

### Mathematics 31 Pre-calculus and Limits

Mathematics 31 Pre-calculus and Limits Overview After completing this section, students will be epected to have acquired reliability and fluency in the algebraic skills of factoring, operations with radicals

### BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets Ch. 3: Decision Rules Harry Campbell & Richard Brown School of Economics The University of Queensland Applied Investment Appraisal

### Prep. Course Macroeconomics

Prep. Course Macroeconomics Intertemporal consumption and saving decision; Ramsey model Tom-Reiel Heggedal tom-reiel.heggedal@bi.no BI 2014 Heggedal (BI) Savings & Ramsey 2014 1 / 30 Overview this lecture

Which Would You Choose: Funding Retirement or Paying Off Consumer Debt? By James M. Grayson, Ph.D.; Peter M. Basciano, Ph.D.; and Christopher L. Cain, J.D., Ph.D., CFA EXECUTIVE SUMMARY Paying off consumer

### The Real Business Cycle model

The Real Business Cycle model Spring 2013 1 Historical introduction Modern business cycle theory really got started with Great Depression Keynes: The General Theory of Employment, Interest and Money Keynesian

### Lecture Notes 5: General Equilibrium. mrkts

Lecture Notes 5: General Equilibrium We are now ready to analyze the equilibrium in all markets, that is why this type of analysis is called general equilibrium analysis. Recall our graphical overview

### The Reinvestment Assumption Dallas Brozik, Marshall University

The Reinvestment Assumption Dallas Brozik, Marshall University Every field of study has its little odd bits, and one of the odd bits in finance is the reinvestment assumption. It is an artifact of the

### Why do merchants accept payment cards?

Why do merchants accept payment cards? Julian Wright National University of Singapore Abstract This note explains why merchants accept expensive payment cards when merchants are Cournot competitors. The

### Simplification of Rational Expressions and Functions

7.1 Simplification of Rational Epressions and Functions 7.1 OBJECTIVES 1. Simplif a rational epression 2. Identif a rational function 3. Simplif a rational function 4. Graph a rational function Our work

### How to Value SEO By Kevin Bailey, President of Slingshot SEO

WHITEPAPER How to Value SEO By Kevin Bailey, President of Slingshot SEO What s Inside 1. Eecutive Summary 2. Valuing SEO as a Comp Analysis 3. Annual Value of First Page Google Ranking 4. Annual Value

### Public Goods : (b) Efficient Provision of Public Goods. Efficiency and Private Goods

Public Goods : (b) Efficient Provision of Public Goods Efficiency and Private Goods Suppose that there are only two goods consumed in an economy, and that they are both pure private goods. Suppose as well

### Optimal Paternalism: Sin Taxes and Health Subsidies

Optimal Paternalism: Sin Taxes and Health Subsidies Thomas Aronsson and Linda Thunström Department of Economics, Umeå University SE - 901 87 Umeå, Sweden April 2005 Abstract The starting point for this

### Pricing in a Competitive Market with a Common Network Resource

Pricing in a Competitive Market with a Common Network Resource Daniel McFadden Department of Economics, University of California, Berkeley April 8, 2002 I. This note is concerned with the economics of

### DISCUSSION PAPER. How Should Benefits and Costs Be Discounted in an Intergenerational Context? M a u r e e n L. Cropper. October 2012 RFF DP 12-42

DISCUSSION PAPER October 2012 RFF DP 12-42 How Should Benefits and Costs Be Discounted in an Intergenerational Context? M a u r e e n L. 1616 P St. NW Washington, DC 20036 202-328-5000 www.rff.org How

### Cost-Benefit Analysis. 131 Undergraduate Public Economics Emmanuel Saez UC Berkeley

Cost-Benefit Analysis 131 Undergraduate Public Economics Emmanuel Saez UC Berkeley 1 OUTLINE Chapter 8 8.1 Measuring the Costs of Public Projects 8.2 Measuring the Benefits of Public Projects 8.3 Putting

### Declining Discount Rates: Economic Justifications and Implications for Long-Run Policy

DECLINING DISCOUNT RATES 1 Declining Discount Rates: Economic Justifications and Implications for Long-Run Policy Christian Gollier, Phoebe Koundouri, Theologos Pantelidis IDEI, Université Toulouse I;

### Integration of Rational Expressions by Partial Fractions

Integration of Rational Epressions by Partial Fractions INTRODUTION: We start with a few definitions rational epression is formed when a polynomial is divided by another polynomial In a proper rational

### Polynomial Degree and Finite Differences

CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial

MATH 11 Quadratic Functions and Parabolas A quadratic function has the form Dr. Neal, Fall 2008 f () = a 2 + b + c where a 0. The graph of the function is a parabola that opens upward if a > 0, and opens

### Investment Decision Analysis

Lecture: IV 1 Investment Decision Analysis The investment decision process: Generate cash flow forecasts for the projects, Determine the appropriate opportunity cost of capital, Use the cash flows and

### Indifference Curves and the Marginal Rate of Substitution

Introduction Introduction to Microeconomics Indifference Curves and the Marginal Rate of Substitution In microeconomics we study the decisions and allocative outcomes of firms, consumers, households and

### MODULE 2. Capital Budgeting

MODULE 2 Capital Budgeting Capital Budgeting is a project selection exercise performed by the business enterprise. Capital budgeting uses the concept of present value to select the projects. Capital budgeting

### 9 Decision criteria BCR NPV FYRR NPVI IBCR

4 9 Decision criteria The decision criteria provide an indication of the economic performance of the proposal. This section provides the formula used to calculate the decision criteria employed in CBA6.

Econ 497 Barry W. Ickes Spring 2007 Midterm Exam:Answer Sheet 1. (25%) Consider a portfolio, c, comprised of a risk-free and risky asset, with returns given by r f and E(r p ), respectively. Let y be the

Hurley, Chapter 7 (see also review in chapter 3) Chris Auld Economics 318 February 20, 2014 Why is health care different? Is health care different from other commodities? Yes, but not because it s really

### Unit #14 - Integral Applications in Physics and Economics Section 8.6

Unit #14 - Integral Applications in Physics and Economics Section 8.6 Some material from Calculus, Single and MultiVariable by Hughes-Hallett, Gleason, McCallum et. al. Copyright 25 by John Wiley & Sons,

### . In this case the leakage effect of tax increases is mitigated because some of the reduction in disposable income would have otherwise been saved.

Chapter 4 Review Questions. Explain how an increase in government spending and an equal increase in lump sum taxes can generate an increase in equilibrium output. Under what conditions will a balanced

### LESSON EIII.E EXPONENTS AND LOGARITHMS

LESSON EIII.E EXPONENTS AND LOGARITHMS LESSON EIII.E EXPONENTS AND LOGARITHMS OVERVIEW Here s what ou ll learn in this lesson: Eponential Functions a. Graphing eponential functions b. Applications of eponential

### THE IMPACT OF LEVIES ON AIR TRANSPORT SUSTAINABILITY

DEVELOPMENT OF AIR TRANSPORT SETTING THE COURSE, MONTREAL 7-8 MAY, 2014 THE IMPACT OF LEVIES ON AIR TRANSPORT SUSTAINABILITY Dr. Andreas Kopp World Bank, TWI 1 OUTLINE 1. The fiscal argument for levies

### Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole

Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole Luís M. B. Cabral New York University and CEPR November 2005 1 Introduction Beginning with their seminal 2002 paper,

### Topic 3: Time Value of Money And Net Present Value

Topic 3: Time Value of Money And Net Present Value Laurent Calvet calvet@hec.fr John Lewis john.lewis04@imperial.ac.uk From Material by Pierre Mella-Barral MBA - Financial Markets - Topic 3 1 2. Present

### Mathematics 96 (3581) CA (Class Addendum) 3: Inverse Properties Mt. San Jacinto College Menifee Valley Campus Spring 2013

Mathematics 96 (358) CA (Class Addendum) 3: Inverse Properties Mt. San Jacinto College Menifee Valley Campus Spring 203 Name This class handout is worth a maimum of five (5) points. It is due no later

### AP Microeconomics Chapter 12 Outline

I. Learning Objectives In this chapter students will learn: A. The significance of resource pricing. B. How the marginal revenue productivity of a resource relates to a firm s demand for that resource.

### CHAPTER 5. Interest Rates. Chapter Synopsis

CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)

### 1 The Black-Scholes model: extensions and hedging

1 The Black-Scholes model: extensions and hedging 1.1 Dividends Since we are now in a continuous time framework the dividend paid out at time t (or t ) is given by dd t = D t D t, where as before D denotes

### Chapter 5.1 Systems of linear inequalities in two variables.

Chapter 5. Systems of linear inequalities in two variables. In this section, we will learn how to graph linear inequalities in two variables and then apply this procedure to practical application problems.

### A Quick Algebra Review

1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals

### 2. Efficiency and Perfect Competition

General Equilibrium Theory 1 Overview 1. General Equilibrium Analysis I Partial Equilibrium Bias 2. Efficiency and Perfect Competition 3. General Equilibrium Analysis II The Efficiency if Competition The

### CHAPTER 8 STOCK VALUATION

CHAPTER 8 STOCK VALUATION Answers to Concepts Review and Critical Thinking Questions 5. The common stock probably has a higher price because the dividend can grow, whereas it is fixed on the preferred.

### CHAPTER 4: FINANCIAL ANALYSIS OVERVIEW

In the financial analysis examples in this book, you are generally given the all of the data you need to analyze the problem. In a real-life situation, you would need to frame the question, determine the

### Valuing the Future: the social discount rate in cost-benefit analysis

Valuing the Future: the social discount rate in cost-benefit analysis Visiting Researcher Paper April 2010 Mark Harrison The views expressed in this paper are those of the individual involved and do not

### Net present value is the difference between a project s value and its costs.

1 2 Net present value is the difference between a project s value and its costs. We need to calculate the Present Value of future cash flows (discounted by the opportunity cost of capital) and subtract

### 1 Uncertainty and Preferences

In this chapter, we present the theory of consumer preferences on risky outcomes. The theory is then applied to study the demand for insurance. Consider the following story. John wants to mail a package

### Reforming the Tax System Lecture II: The Taxation of Savings. December 2015 Richard Blundell University College London

Econ 3007 Economic Policy Analysis Reforming the Tax System Lecture II: The Taxation of Savings December 205 Richard Blundell niversity ollege London Teaching Resources at: http://www.ucl.ac.uk/~uctp39a/lect.html

### Problem Set #3 Answer Key

Problem Set #3 Answer Key Economics 305: Macroeconomic Theory Spring 2007 1 Chapter 4, Problem #2 a) To specify an indifference curve, we hold utility constant at ū. Next, rearrange in the form: C = ū

### DISCUSSION PAPER. How Should Benefits and Costs Be Discounted in an Intergenerational Context? The Views of an Expert Panel

DISCUSSION PAPER December 2012 RFF DP 12-53 How Should Benefits and Costs Be Discounted in an Intergenerational Context? The Views of an Expert Panel K e n n e t h J. Ar r ow, Maureen L. Cropper, Christia

### Polynomial and Synthetic Division. Long Division of Polynomials. Example 1. 6x 2 7x 2 x 2) 19x 2 16x 4 6x3 12x 2 7x 2 16x 7x 2 14x. 2x 4.

_.qd /7/5 9: AM Page 5 Section.. Polynomial and Synthetic Division 5 Polynomial and Synthetic Division What you should learn Use long division to divide polynomials by other polynomials. Use synthetic

### Objectives. By the time the student is finished with this section of the workbook, he/she should be able

QUADRATIC FUNCTIONS Completing the Square..95 The Quadratic Formula....99 The Discriminant... 0 Equations in Quadratic Form.. 04 The Standard Form of a Parabola...06 Working with the Standard Form of a

### Energy and Economics

Energy and Economics Willem van Groenendaal Tilburg University Tilburg School of Economics and Management (TiSEM) w.j.h.vgroenendaal@tilburguniversity.nl 1 Can energy use be limited by change in economic

### chapter >> Consumer and Producer Surplus Section 3: Consumer Surplus, Producer Surplus, and the Gains from Trade

chapter 6 >> Consumer and Producer Surplus Section 3: Consumer Surplus, Producer Surplus, and the Gains from Trade One of the nine core principles of economics we introduced in Chapter 1 is that markets

### Expected net present value, expected net future value, and the Ramsey rule

Expected net present value, expected net future value, and the Ramsey rule Christian Gollier Toulouse School of Economics (LERNA and IDEI) June 13, 2009 Abstract Weitzman (1998) showed that when future

### UGBA 103 (Parlour, Spring 2015), Section 1. Raymond C. W. Leung

UGBA 103 (Parlour, Spring 2015), Section 1 Present Value, Compounding and Discounting Raymond C. W. Leung University of California, Berkeley Haas School of Business, Department of Finance Email: r_leung@haas.berkeley.edu

### FNCE 301, Financial Management H Guy Williams, 2006

Review In the first class we looked at the value today of future payments (introduction), how to value projects and investments. Present Value = Future Payment * 1 Discount Factor. The discount factor

### Dividend valuation models Prepared by Pamela Peterson Drake, Ph.D., CFA

Dividend valuation models Prepared by Pamela Peterson Drake, Ph.D., CFA Contents 1. Overview... 1 2. The basic model... 1 3. Non-constant growth in dividends... 5 A. Two-stage dividend growth... 5 B. Three-stage

### Current Accounts in Open Economies Obstfeld and Rogoff, Chapter 2

Current Accounts in Open Economies Obstfeld and Rogoff, Chapter 2 1 Consumption with many periods 1.1 Finite horizon of T Optimization problem maximize U t = u (c t ) + β (c t+1 ) + β 2 u (c t+2 ) +...

### Forward Contracts and Forward Rates

Forward Contracts and Forward Rates Outline and Readings Outline Forward Contracts Forward Prices Forward Rates Information in Forward Rates Reading Veronesi, Chapters 5 and 7 Tuckman, Chapters 2 and 16

### Inflation. Chapter 8. 8.1 Money Supply and Demand

Chapter 8 Inflation This chapter examines the causes and consequences of inflation. Sections 8.1 and 8.2 relate inflation to money supply and demand. Although the presentation differs somewhat from that

### Net Present Value and Capital Budgeting. What to Discount

Net Present Value and Capital Budgeting (Text reference: Chapter 7) Topics what to discount the CCA system total project cash flow vs. tax shield approach detailed CCA calculations and examples project

### Notes for Lecture 2 (February 7)

CONTINUOUS COMPOUNDING Invest \$1 for one year at interest rate r. Annual compounding: you get \$(1+r). Semi-annual compounding: you get \$(1 + (r/2)) 2. Continuous compounding: you get \$e r. Invest \$1 for

### Why Use Net Present Value? The Payback Period Method The Discounted Payback Period Method The Average Accounting Return Method The Internal Rate of

1 Why Use Net Present Value? The Payback Period Method The Discounted Payback Period Method The Average Accounting Return Method The Internal Rate of Return Problems with the IRR Approach The Profitability

### Time Value of Money. Background

Time Value of Money (Text reference: Chapter 4) Topics Background One period case - single cash flow Multi-period case - single cash flow Multi-period case - compounding periods Multi-period case - multiple

### Valuing Stock Options: The Black-Scholes-Merton Model. Chapter 13

Valuing Stock Options: The Black-Scholes-Merton Model Chapter 13 Fundamentals of Futures and Options Markets, 8th Ed, Ch 13, Copyright John C. Hull 2013 1 The Black-Scholes-Merton Random Walk Assumption

### Summing up ECON4310 Lecture. Asbjørn Rødseth. University of Oslo 27/

Summing up 4310 ECON4310 Lecture Asbjørn Rødseth University of Oslo 27/11 2013 Asbjørn Rødseth (University of Oslo) Summing up 4310 27/11 2013 1 / 20 Agenda Solow, Ramsey and Diamond Real Business Cycle

### Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...

Lecture: II 1 Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...! The intuitive basis for present value what determines the effect of timing on the value

### 380.760: Corporate Finance. Financial Decision Making

380.760: Corporate Finance Lecture 2: Time Value of Money and Net Present Value Gordon Bodnar, 2009 Professor Gordon Bodnar 2009 Financial Decision Making Finance decision making is about evaluating costs

### Computational Finance Options

1 Options 1 1 Options Computational Finance Options An option gives the holder of the option the right, but not the obligation to do something. Conversely, if you sell an option, you may be obliged to

### Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator

University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights

### MBA Finance Part-Time Present Value

MBA Finance Part-Time Present Value Professor Hugues Pirotte Spéder Solvay Business School Université Libre de Bruxelles Fall 2002 1 1 Present Value Objectives for this session : 1. Introduce present value

### Topic 7 General equilibrium and welfare economics

Topic 7 General equilibrium and welfare economics. The production possibilities frontier is generated using a production Edgeworth box diagram with the input goods on the axes. The following diagram illustrates

### Module 2 Lecture 5 Topics

Module 2 Lecture 5 Topics 2.13 Recap of Relevant Concepts 2.13.1 Social Welfare 2.13.2 Demand Curves 2.14 Elasticity of Demand 2.14.1 Perfectly Inelastic 2.14.2 Perfectly Elastic 2.15 Production & Cost

### Time Value of Money (TVM)

BUSI Financial Management Time Value of Money 1 Time Value of Money (TVM) Present value and future value how much is \$1 now worth in the future? how much is \$1 in the future worth now? Business planning

### Figure 1, A Monopolistically Competitive Firm

The Digital Economist Lecture 9 Pricing Power and Price Discrimination Many firms have the ability to charge prices for their products consistent with their best interests even thought they may not be

### Chapter 3: Commodity Forwards and Futures

Chapter 3: Commodity Forwards and Futures In the previous chapter we study financial forward and futures contracts and we concluded that are all alike. Each commodity forward, however, has some unique

### (First 6 problems from Caves, Frankel and Jones, 1990)

Professor Robert Staiger Economics 39F Problem Set 1 (First 6 problems from Caves, Frankel and Jones, 1990) 1. With reference to the home country s trade triangle illustrated in Figure 2.3, suppose that

### Determination of Forward and Futures Prices. Chapter 5

Determination of Forward and Futures Prices Chapter 5 Fundamentals of Futures and Options Markets, 8th Ed, Ch 5, Copyright John C. Hull 2013 1 Consumption vs Investment Assets Investment assets are assets

### A SOCIAL DISCOUNT RATE FOR THE UNITED KINGDOM. David Pearce and David Ulph. CSERGE Working Paper GEC 95-01

A SOCIAL DISCOUNT RATE FOR THE UNITED KINGDOM by David Pearce and David Ulph CSERGE Working Paper GEC 95-01 A SOCIAL DISCOUNT RATE FOR THE UNITED KINGDOM by David Pearce and David Ulph Centre for Social

### PUBLIC HEALTH OPTOMETRY ECONOMICS. Kevin D. Frick, PhD

Chapter Overview PUBLIC HEALTH OPTOMETRY ECONOMICS Kevin D. Frick, PhD This chapter on public health optometry economics describes the positive and normative uses of economic science. The terms positive

### How Should Benefits and Costs Be Discounted in an Intergenerational Context?

How Should Benefits and Costs Be Discounted in an Intergenerational Context? Kenneth J. Arrow, Maureen L. Cropper, Christian Gollier, Ben Groom, Geoffrey M. Heal, Richard G. Newell, William D. Nordhaus,