Experiencing the whole electricity market chain

Size: px
Start display at page:

Download "Experiencing the whole electricity market chain"

Transcription

1 Experiencing the whole electricity market chain Pierre Pinson Technical University of Denmark. DTU Electrical Engineering - Centre for Electric Power and Energy mail: ppin@dtu.dk - webpage: 19 March Renewables in Electricity Markets 1

2 Learning objectives Through this lecture and additional study material, it is aimed for the students to be able to: 1 Have a complete understanding of the market timeline 2 Have a complete understanding of the various actors roles 3 Understand differences between one-price and two-price balancing mechanisms 4 Caculate revenues and payments of market players combining the various market floors Renewables in Electricity Markets 2

3 As part of the overall context... Now we look at it altogether! Renewables in Electricity Markets 3

4 Outline 1 Setting the scene 2 Case 1: Renewable energy impact in day-ahead electricity markets 3 Case 2: From day-ahead to balancing market (one-price) 4 Case 3: From day-ahead to balancing market (two-price) 5 Discussion: Impact one-price and two-price balancing settlement on strategic behaviour Renewables in Electricity Markets 4

5 1 Setting the scene Renewables in Electricity Markets 5

6 We will need... To direct and control the game: Mr. Market Mr. System Operator Mrs. Nature Renewables in Electricity Markets 6

7 We will also need... A number of market players: Mr. Greedy Miss Sunshine Mr. Clever and one more? Renewables in Electricity Markets 7

8 1 Setting the scene Renewables in Electricity Markets 8

9 2 Case 1: Impact of renewable energy on day-ahead electricity markets Renewables in Electricity Markets 9

10 3 Case 2: From day-ahead to balancing market (one-price) Renewables in Electricity Markets 10

11 4 Case 3: From day-ahead to balancing market (two-price) Renewables in Electricity Markets 11

12 5 Discussion: Strategic behaviour with one-price and two-price balancing mechanisms Renewables in Electricity Markets 12

13 Thanks for your attention! - Contact: ppin@dtu.dk - web: pierrepinson.com Renewables in Electricity Markets 13

14 6 Appendix: Reminder on balancing markets Renewables in Electricity Markets 14

15 Is the system (really) in imbalance? There may be 3 possible situations, for the system as a whole: Positive imbalance: Supply > Demand need for downward regulation Negative imbalance: Supply < Demand need for upward regulation No imbalance: Supply Demand no need for regulation Similarly, supply and demand participants may also have positive and negative imabalance: Positive imbalance: Actual generation > Scheduled generation (if supply) or... Negative imbalance: Actual generation < Scheduled generation (if supply) or... No imbalance: Actual generation Scheduled generation (if supply) or Renewables in Electricity Markets 15

16 Nomenclature From the (previously cleared) day-ahead market: Balance of generation and consumption at quantity: P S Day ahead price: λ S Generators schedules: ŷj G, j = 1,..., N G Demands schedules: ŷi D, i = 1,..., N D Then reaching the balancing market: Imbalance to be handled: P Assume N B balancing generators, able to move both up ( ) and down ( )... Their offers: Upward regulation: P j, at price λ j, j = 1,..., N B Downward regulation: P j, at price λ j, j = 1,..., N B One necessarily has: λ j λ j > λ S, j = 1,..., N B < λ S,, j = 1,..., N B Renewables in Electricity Markets 16

17 Example list of balancing offers This is a follow up on our basic example in the course on day-ahead markets! System price: 37.5 e - Accepted offers: see lecture (link) Deadline for offers: 9 th of February, 10:15 - Delivery period: 9 th of February, 11:00-12:00 Balancing offers include: Company id P j (MWh) λ j (e/mwh) P j (MWh) λ j (e/mwh) BlueHydro B 1 (/G 3) LastMinute B FlexiFast B DirtyPower B 4 (/G 8) already scheduled after day-ahead market clearing Here, only generators offer balancing - Demand could actually also contribute Renewables in Electricity Markets 17

18 Graphically as a supply curve... This is the same type of supply curves than for day-ahead auctions, except that: offers are for adjustment from the day-ahead quantity P S (both upward and downward) demand is here seen as inelastic (so, no demand curve - or seen as a vertical straight line) price [Euros/MWh] λ S P S quantity [MWh] Renewables in Electricity Markets 18

19 Intuitively, two possible situations P > 0 P < 0 price [Euros/MWh] λ B λ S P S P S + P price [Euros/MWh] λ S λ B P S + P P S quantity [MWh] quantity [MWh] Renewables in Electricity Markets 19

20 Writing the balancing auction as an LP Similarly to the day-market clearing, the auction can be solved through a Linear Program (LP): min {y },{y } j j subject to j j λ j y j y j 0 y i 0 y j y j λ j y j = P : λ B P i, j = 1,..., N B P j, j = 1,..., N B The balancing price λ B can then be obtained by solving the dual LP It corresponds to the lagrange multiplier for the updated balance equation Using this balancing price directly for the settlement yields one-price imbalance settlement being referred to as a one-price balancing market Renewables in Electricity Markets 20

21 The one-price imbalance settlement Basic properties: P > 0 P 0 P < 0 λ B > λ S λ B = λ S λ B < λ S Consequences on settlement for those dispatched through the day-ahead market: P > 0: Generator i producing less than scheduled must buy ŷi G yi G at price λ B Demand j consuming more than scheduled must buy ŷj D yj D at price λ B Generator i producing more than scheduled must sell yi G ŷi G at price λ B Demand j consuming less than scheduled must sell yj D ŷj D at price λ B P < 0:... basically, the same type of reasoning Meanwhile, balancing generators simply sell or buy at price λ B Renewables in Electricity Markets 21

22 Example case 1: Outage of G 5 Even though scheduled, the unit G 5 of KøbenhavnCHP will be down during that hour, and the operator could not get a match in the intra-day market... All others are producing and consuming as planned. For the balancing auction, one has: P = 60 MWh (since demand is higher than generation by 60 MWh for that hour) λ B = 45 e/mwh Scheduled balancing generators: B 1 and B 2 (only 30 MWh upward) The settlement leads to: G 5 paying = 2700 e B 1 (/G 3 ) and B 2 each receiving = 1350 e Considering both day-ahead and balancing stages: G 5 receives = 2250 e, and has to pay = 2700 e... That is a loss of 450 e(!) B 1 (/G 3 ) receives = 7500 e (day-ahead) and = 1350 e at the balancing stage Renewables in Electricity Markets 22

23 Example case 2: Wind forecast errors For both wind farms G 1 and G 2 (operated by RT R and WeTrustInWind), the actual generation is not equal to that foreseen when clearing the day-ahead market, i.e. for G 1 : ŷ1 G = 50 MWh but actual generation is y 1 G = 30 MWh for G 2 : ŷ2 G = 120 MWh but actual generation is y 2 G = 155 MWh All others are producing and consuming as planned. For the balancing auction, one has: P = 15 MWh (since generation is higher that demand by 15 MWh for that hour) λ B = 35 e/mwh Scheduled balancing generators: B 1 (only 15 MWh downward) The settlement leads to: G 1 paying = 700 e G 2 receiving = 1225 e B 1 paying = 525 e Considering both day-ahead and balancing stages: G 1 receives = 1875 e, then pays = 700 e - Gives 1175 e G 2 receives = 4500 e, then receives again = 1225 e - Gives 5775 e B 1 (/G 3 ) receives = 7500 e, then pays = 525 e - Gives 7175 e Renewables in Electricity Markets 23

24 Comments on the one-price balancing markets The total payment/revenue of day-ahead market participants for deviations from schedule equals the revenue/payment of the balancing generators Regarding deviations: if one s own deviation contributes to setting the system off-balance (e.g., generator overproduce while there is too much power overall), this leads to a loss but... if one s own deviation is of the helping the system go back to balance (e.g., generator overproduce while there is a lack of power overall), this leads to extra profit(!) What could be the consequences? And, how could we fix that? Renewables in Electricity Markets 24

25 The two-price imbalance settlement Basic properties: (well, the same for market clearing) P > 0 P 0 P < 0 λ B > λ S λ B = λ S λ B < λ S Settlement is rethought: those putting the system off-balance are to be penalized those supporting the system (unintentionally) will not get extra rewards P > 0: Generator i producing less than scheduled must buy ŷi G yi G at price λ B Demand j consuming more than scheduled must buy ŷj D yj D at price λ B Generator i producing more than scheduled must sell yi G ŷi G at price λ S Demand j consuming less than scheduled must sell yj D ŷj D at price λ S P < 0:... basically, the opposite type of reasoning Meanwhile, balancing generators simply sell or buy at price λ B Renewables in Electricity Markets 25

26 Example case 1: Outage of G 5 Even though scheduled, the unit G 5 of KøbenhavnCHP will be down during that hour, and the operator could not get a match in the intra-day market... All others are producing and consuming as planned. For the balancing auction, one has: P = 60 MWh (since demand is higher than generation by 60 MWh for that hour) λ B = 45 e/mwh Scheduled balancing generators: B 1 and B 2 (only 30 MWh upward) The settlement leads to: G 5 paying = 2700 e B 1 (/G 3 ) and B 2 each receiving = 1350 e Considering both day-ahead and balancing stages: G 5 receives = 2250 e, and has to pay = 2700 e... That is a loss of 450 e(!) B 1 (/G 3 ) receives = 7500 e (day-ahead) and = 1350 e at the balancing stage Renewables in Electricity Markets 26

27 Example case 2: Wind forecast errors For both wind farms G 1 and G 2 (operated by RT R and WeTrustInWind), the actual generation is not equal to that foreseen when clearing the day-ahead market, i.e. for G 1 : ŷ G 1 = 50 MWh but actual generation is y G 1 for G 2 : ŷ G 1 = 120 MWh but actual generation is y G 1 All others are producing and consuming as planned. For the balancing auction, one has: = 30 MWh = 155 MWh P = 15 MWh (since generation is higher than demand by 15 MWh for that hour) λ B = 35 e/mwh (while day-ahead price is λ S = 37.5 e/mwh) Scheduled balancing generators: B 1 (only 15 MWh downward) The settlement leads to: G 1 paying = 750 e (instead of 700 e in the one-price case) G 2 receiving = 1225 e B 1 (/G 3 ) paying = 525 e Considering both day-ahead and balancing stages: G 1 receives = 1875 e, then pays = 750 e - Gives 1050 e G 2 receives = 4500 e, then receives again = 1225 e - Gives 5775 e B 1 (/G 3 ) receives = 7500 e, then pays = 525 e - Gives 7175 e Renewables in Electricity Markets 27

28 Final remarks We gave here the big picture, and there may be additional aspects that could deserve consideration (for another time...), e.g. There can be both up- and down-regulation situations at the same time... The actual time step of operations is much smaller (for instance, 5 minutes) than the market time unit (say, 1 hour) Demand-side could also be pro-active and participate in the balancing market Network effects and inter-zone coordination can substantially impact the balancing mechanisms etc. Let s have a look at the current situation in Scandinavia: Nord Pool s balancing page Renewables in Electricity Markets 28

29 Further readings For those who want to go into the more mathematical aspects of balancing markets: J.M. Morales et al. (2014). Integrating Renewables in Electricity Markets, Chapter 4: Balancing markets (pdf) For those interested in current challenges and discussion at the European level: F. Borggrefe and K. Neuhoff (2011). Balancing and intraday market design: Options for wind integration (pdf) Renewables in Electricity Markets 29

Optimal sale bid for a wind producer in Spanish electricity market.

Optimal sale bid for a wind producer in Spanish electricity market. COMPUTATIONAL MANAGEMENT SCIENCE 2012 Optimal sale bid for a wind producer in Spanish electricity market. Simona Sacripante F.-Javier Heredia Cristina Corchero RD 436/2004 RD 661/2007 New regulation Regulated

More information

Report on Proposed principles for Common Balance Management

Report on Proposed principles for Common Balance Management Report on Proposed principles for Common Balance Management 2007-11-16 1 Contents 1. INTRODUCTION AND BACKGROUND...3 2. COMMON COST ALLOCATION...3 3. FEE STRUCTURE... 4 4. NEW MODEL FOR ENCOMPASSING TWO

More information

Math: Deriving supply and demand curves

Math: Deriving supply and demand curves Chapter 0 Math: Deriving supply and demand curves At a basic level, individual supply and demand curves come from individual optimization: if at price p an individual or firm is willing to buy or sell

More information

Economic Dispatch. Quantitative Energy Economics. Anthony Papavasiliou 1 / 21

Economic Dispatch. Quantitative Energy Economics. Anthony Papavasiliou 1 / 21 1 / 21 Economic Dispatch Quantitative Energy Economics Anthony Papavasiliou Economic Dispatch 2 / 21 1 Optimization Model of Economic Dispatch 2 Equilibrium Model of Economic Dispatch Outline 3 / 21 1

More information

Notes on a Basic Business Problem MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W

Notes on a Basic Business Problem MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W Notes on a Basic Business Problem MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W This simple problem will introduce you to the basic ideas of revenue, cost, profit, and demand.

More information

Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati

Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati Module No. # 03 Illustrations of Nash Equilibrium Lecture No. # 02

More information

Math 1070 Sample Exam 2

Math 1070 Sample Exam 2 University of Connecticut Department of Mathematics Math 1070 Sample Exam 2 Exam 2 will cover sections 6.1, 6.2, 6.3, 6.4, F.1, F.2, F.3, F.4, 1.1, and 1.2. This sample exam is intended to be used as one

More information

We want to solve for the optimal bundle (a combination of goods) that a rational consumer will purchase.

We want to solve for the optimal bundle (a combination of goods) that a rational consumer will purchase. Chapter 3 page1 Chapter 3 page2 The budget constraint and the Feasible set What causes changes in the Budget constraint? Consumer Preferences The utility function Lagrange Multipliers Indifference Curves

More information

15 MINUTES IMBALANCE SETTLEMENT PERIOD MARKET IMPACTS OF LATE IMPLEMENTATION Final report. June 15, 2018

15 MINUTES IMBALANCE SETTLEMENT PERIOD MARKET IMPACTS OF LATE IMPLEMENTATION Final report. June 15, 2018 15 MINUTES IMBALANCE SETTLEMENT PERIOD MARKET IMPACTS OF LATE IMPLEMENTATION Final report June 15, 2018 DISCLAIMER AND RIGHTS This report has been prepared by Pöyry Management Consulting Oy ( Pöyry ) for

More information

Foundational Preliminaries: Answers to Within-Chapter-Exercises

Foundational Preliminaries: Answers to Within-Chapter-Exercises C H A P T E R 0 Foundational Preliminaries: Answers to Within-Chapter-Exercises 0A Answers for Section A: Graphical Preliminaries Exercise 0A.1 Consider the set [0,1) which includes the point 0, all the

More information

Exercise 1. Jan Abrell Centre for Energy Policy and Economics (CEPE) D-MTEC, ETH Zurich. Exercise

Exercise 1. Jan Abrell Centre for Energy Policy and Economics (CEPE) D-MTEC, ETH Zurich. Exercise Exercise 1 Jan Abrell Centre for Energy Policy and Economics (CEPE) D-MTEC, ETH Zurich Exercise 1 06.03.2018 1 Outline Reminder: Constraint Maximization Minimization Example: Electricity Dispatch Exercise

More information

Stochastic Optimal Regulation Service Strategy for a Wind Farm Participating in the Electricity Market Zhang, Baohua; Hu, Weihao; Chen, Zhe

Stochastic Optimal Regulation Service Strategy for a Wind Farm Participating in the Electricity Market Zhang, Baohua; Hu, Weihao; Chen, Zhe Aalborg Universitet Stochastic Optimal Regulation Service Strategy for a Wind Farm Participating in the Electricity Market Zhang, Baohua; Hu, Weihao; Chen, Zhe Published in: Proceedings of IEEE PES Innovative

More information

Problem 1 / 25 Problem 2 / 25 Problem 3 / 25 Problem 4 / 25

Problem 1 / 25 Problem 2 / 25 Problem 3 / 25 Problem 4 / 25 Department of Economics Boston College Economics 202 (Section 05) Macroeconomic Theory Midterm Exam Suggested Solutions Professor Sanjay Chugh Fall 203 NAME: The Exam has a total of four (4) problems and

More information

Anders Plejdrup Houmøller 10 May Wholesale market models and the role of exchanges and traders. Prepared by Anders Plejdrup Houmøller

Anders Plejdrup Houmøller 10 May Wholesale market models and the role of exchanges and traders. Prepared by Anders Plejdrup Houmøller Wholesale market models and the role of exchanges and traders Prepared by Anders Plejdrup Houmøller www. erranet.org Agenda The trading system. The spot market. Transparency. Surveillance of the market.

More information

The market setup in the Baltics explanation with examples

The market setup in the Baltics explanation with examples The market setup in the Baltics explanation with examples Table of Contents The market setup in the Nordic-... 3 Baltic exchange area... 3 Daily routines at Nord Pool... 4 Price calculation principles...

More information

These notes essentially correspond to chapter 13 of the text.

These notes essentially correspond to chapter 13 of the text. These notes essentially correspond to chapter 13 of the text. 1 Oligopoly The key feature of the oligopoly (and to some extent, the monopolistically competitive market) market structure is that one rm

More information

Game Theory Tutorial 3 Answers

Game Theory Tutorial 3 Answers Game Theory Tutorial 3 Answers Exercise 1 (Duality Theory) Find the dual problem of the following L.P. problem: max x 0 = 3x 1 + 2x 2 s.t. 5x 1 + 2x 2 10 4x 1 + 6x 2 24 x 1 + x 2 1 (1) x 1 + 3x 2 = 9 x

More information

ISO Tariff Original Sheet No. 637 ISO TARIFF APPENDIX L. Rate Schedules

ISO Tariff Original Sheet No. 637 ISO TARIFF APPENDIX L. Rate Schedules Original Sheet No. 637 ISO TARIFF APPENDIX L Rate Schedules Original Sheet No. 638 Schedule 1 Grid Management Charge The Grid Management Charge (ISO Tariff Section 8.0) is a formula rate designed to recover

More information

Econ 101A Final exam May 14, 2013.

Econ 101A Final exam May 14, 2013. Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final

More information

Department of Market Monitoring White Paper. Potential Impacts of Lower Bid Price Floor and Contracts on Dispatch Flexibility from PIRP Resources

Department of Market Monitoring White Paper. Potential Impacts of Lower Bid Price Floor and Contracts on Dispatch Flexibility from PIRP Resources Department of Market Monitoring White Paper Potential Impacts of Lower Bid Price Floor and Contracts on Dispatch Flexibility from PIRP Resources Revised: November 21, 2011 Table of Contents 1 Executive

More information

I. Taxes and Economic Welfare

I. Taxes and Economic Welfare University of California, Merced ECON 1-Introduction to Economics Chapter 8 Lecture Notes Professor Jason Lee I. Taxes and Economic Welfare How do taxes affect the welfare of a society? We saw in Chapter

More information

Proposed Reserve Market Enhancements

Proposed Reserve Market Enhancements Proposed Reserve Market Enhancements Energy Price Formation Senior Task Force December 14, 2018 Comprehensive Reserve Pricing Reform The PJM Board has determined that a comprehensive package inclusive

More information

Day-ahead Market Regulations. Nord Pool AS

Day-ahead Market Regulations. Nord Pool AS Day-ahead Market Regulations Nord Pool AS DAY-AHEAD MARKET REGULATIONS 1. INTRODUCTION 1.1 These Day-ahead Market Regulations contain detailed provisions on Orders and the calculation of Prices in the

More information

Problem Set # Public Economics

Problem Set # Public Economics Problem Set #5 14.41 Public Economics DUE: Dec 3, 2010 1 Tax Distortions This question establishes some basic mathematical ways for thinking about taxation and its relationship to the marginal rate of

More information

Part 1: Short answer, 60 points possible Part 2: Analytical problems, 40 points possible

Part 1: Short answer, 60 points possible Part 2: Analytical problems, 40 points possible Midterm #1 ECON 322, Prof. DeBacker September 25, 2018 INSTRUCTIONS: Please read each question below carefully and respond to the questions in the space provided (use the back of pages if necessary). You

More information

SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT. BF360 Operations Research

SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT. BF360 Operations Research SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT BF360 Operations Research Unit 3 Moses Mwale e-mail: moses.mwale@ictar.ac.zm BF360 Operations Research Contents Unit 3: Sensitivity and Duality 3 3.1 Sensitivity

More information

1 Maximizing profits when marginal costs are increasing

1 Maximizing profits when marginal costs are increasing BEE12 Basic Mathematical Economics Week 1, Lecture Tuesday 9.12.3 Profit maximization / Elasticity Dieter Balkenborg Department of Economics University of Exeter 1 Maximizing profits when marginal costs

More information

Linear Modeling Business 5 Supply and Demand

Linear Modeling Business 5 Supply and Demand Linear Modeling Business 5 Supply and Demand Supply and demand is a fundamental concept in business. Demand looks at the Quantity (Q) of a product that will be sold with respect to the Price (P) the product

More information

ELECTRICITY BALANCING IN EUROPE

ELECTRICITY BALANCING IN EUROPE EUROPEAN ELECTRICITY BALANCING GUIDELINE NOVEMBER 2018 AN OVERVIEW OF THE EUROPEAN BALANCING MARKET AND ELECTRICITY BALANCING GUIDELINE European Network of Transmission System Operators for Electricity

More information

Lecture Notes #3 Page 1 of 15

Lecture Notes #3 Page 1 of 15 Lecture Notes #3 Page 1 of 15 PbAf 499 Lecture Notes #3: Graphing Graphing is cool and leads to great insights. Graphing Points in a Plane A point in the (x,y) plane is graphed simply by moving horizontally

More information

California Independent System Operator Corporation Fifth Replacement Electronic Tariff

California Independent System Operator Corporation Fifth Replacement Electronic Tariff Table of Contents 28. Inter-SC Trades... 2 28.1 Inter-SC Trades Of Energy... 2 28.1.1 Purpose... 2 28.1.2 Availability Of Inter-SC Trades Of Energy... 2 28.1.3 Submission Of Inter-SC Trades Of Energy...

More information

Optimal trading strategies for wind power producers in futures and short-term electricity markets

Optimal trading strategies for wind power producers in futures and short-term electricity markets WIND ENERGY Wind Energ. 2017; 00:1 14 RESEARCH ARTICLE Optimal trading strategies for wind power producers in futures and short-term electricity markets Athanasios Papakonstantinou 1, Georgia Champeri,

More information

Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati

Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati Module No. # 03 Illustrations of Nash Equilibrium Lecture No. # 03

More information

1. You are given two pairs of coordinates that have a linear relationship. The two pairs of coordinates are (x, y) = (30, 70) and (20, 50).

1. You are given two pairs of coordinates that have a linear relationship. The two pairs of coordinates are (x, y) = (30, 70) and (20, 50). Economics 102 Fall 2017 Answers to Homework #1 Due 9/26/2017 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework

More information

ACTIVATION PURPOSES BSG. 7 March 2017

ACTIVATION PURPOSES BSG. 7 March 2017 ACTIVATION PURPOSES BSG 7 March 2017 Disclaimer All answers provided are based on current applied principles and methods. Other options may exist. Many questions relate to deliverables of the EBGL and

More information

not to be republished NCERT Chapter 2 Consumer Behaviour 2.1 THE CONSUMER S BUDGET

not to be republished NCERT Chapter 2 Consumer Behaviour 2.1 THE CONSUMER S BUDGET Chapter 2 Theory y of Consumer Behaviour In this chapter, we will study the behaviour of an individual consumer in a market for final goods. The consumer has to decide on how much of each of the different

More information

Course notes for EE394V Restructured Electricity Markets: Locational Marginal Pricing

Course notes for EE394V Restructured Electricity Markets: Locational Marginal Pricing Course notes for EE394V Restructured Electricity Markets: Locational Marginal Pricing Ross Baldick Copyright c 2017 Ross Baldick www.ece.utexas.edu/ baldick/classes/394v/ee394v.html Title Page 1 of 205

More information

Chapter 10 Aggregate Demand I CHAPTER 10 0

Chapter 10 Aggregate Demand I CHAPTER 10 0 Chapter 10 Aggregate Demand I CHAPTER 10 0 1 CHAPTER 10 1 2 Learning Objectives Chapter 9 introduced the model of aggregate demand and aggregate supply. Long run (Classical Theory) prices flexible output

More information

Name: Midterm #1 EconS 425 (February 20 th, 2015)

Name: Midterm #1 EconS 425 (February 20 th, 2015) Name: Midterm # EconS 425 (February 20 th, 205) Question # [25 Points] Player 2 L R Player L (9,9) (0,8) R (8,0) (7,7) a) By inspection, what are the pure strategy Nash equilibria? b) Find the additional

More information

LINES AND SLOPES. Required concepts for the courses : Micro economic analysis, Managerial economy.

LINES AND SLOPES. Required concepts for the courses : Micro economic analysis, Managerial economy. LINES AND SLOPES Summary 1. Elements of a line equation... 1 2. How to obtain a straight line equation... 2 3. Microeconomic applications... 3 3.1. Demand curve... 3 3.2. Elasticity problems... 7 4. Exercises...

More information

Chapter 21. The Monetary Policy and Aggregate Demand Curves

Chapter 21. The Monetary Policy and Aggregate Demand Curves Chapter 21 The Monetary Policy and Aggregate Demand Curves The Federal Reserve and Monetary Policy The Fed of the United States conducts monetary policy by setting the federal funds rate the interest rate

More information

A Macroeconomic Theory of the Open Economy. Lecture 9

A Macroeconomic Theory of the Open Economy. Lecture 9 1 A Macroeconomic Theory of the Open Economy Lecture 9 2 What we learn in this Chapter? In Chapter 29 we defined the basic concepts of an open economy, such as the Balance of Payments, NX = NFI and the

More information

C2-102 COMMON NORDIC BALANCE MANAGEMENT. K.LINDSTRÖM FINGRID (Finland)

C2-102 COMMON NORDIC BALANCE MANAGEMENT. K.LINDSTRÖM FINGRID (Finland) 21, rue d'artois, F-75008 Paris http://www.cigre.org C2-102 Session 2004 CIGRÉ COMMON NORDIC BALANCE MANAGEMENT O.GJERDE* STATNETT (Norway) F.WIBROE ELTRA (Denmark) J-E. FISCHER ELKRAFT (Denmark) K.LINDSTRÖM

More information

Scarcity Pricing Market Design Considerations

Scarcity Pricing Market Design Considerations 1 / 49 Scarcity Pricing Market Design Considerations Anthony Papavasiliou, Yves Smeers Center for Operations Research and Econometrics Université catholique de Louvain CORE Energy Day April 16, 2018 Outline

More information

Problem set 5. Asset pricing. Markus Roth. Chair for Macroeconomics Johannes Gutenberg Universität Mainz. Juli 5, 2010

Problem set 5. Asset pricing. Markus Roth. Chair for Macroeconomics Johannes Gutenberg Universität Mainz. Juli 5, 2010 Problem set 5 Asset pricing Markus Roth Chair for Macroeconomics Johannes Gutenberg Universität Mainz Juli 5, 200 Markus Roth (Macroeconomics 2) Problem set 5 Juli 5, 200 / 40 Contents Problem 5 of problem

More information

Lecture # 14 Profit Maximization

Lecture # 14 Profit Maximization Lecture # 14 Profit Maximization I. Profit Maximization: A General Rule Having defined production and found the cheapest way to produce a given level of output, the last step in the firm's problem is to

More information

HEnEx s Spot Markets Trading Rulebook: Intra-Day Market Operations

HEnEx s Spot Markets Trading Rulebook: Intra-Day Market Operations Friday July 20th ΟΤΕAcademy, Athens HEnEx s Spot Markets Trading Rulebook: Intra-Day Market Operations Dr. Nikolaos P. Ziogos Introduction CACM XBID Participation in ID Market LIDAs GRIDAs XBID Results

More information

The Best Cell Phone Plan

The Best Cell Phone Plan Overview Activity ID: 8605 Math Concepts Materials Students will compare two cell phone plans and determine linear functions TI-30XS which plan is better for a specific situation. They will utilize graphing

More information

Linear Programming: Simplex Method

Linear Programming: Simplex Method Mathematical Modeling (STAT 420/620) Spring 2015 Lecture 10 February 19, 2015 Linear Programming: Simplex Method Lecture Plan 1. Linear Programming and Simplex Method a. Family Farm Problem b. Simplex

More information

Aggregate Supply and Aggregate Demand

Aggregate Supply and Aggregate Demand Aggregate Supply and Aggregate Demand ECO 301: Money and Banking 1 1.1 Goals Goals Specific Goals Be able to explain GDP fluctuations when the price level is also flexible. Explain how real GDP and the

More information

Final Examination December 14, Economics 5010 AF3.0 : Applied Microeconomics. time=2.5 hours

Final Examination December 14, Economics 5010 AF3.0 : Applied Microeconomics. time=2.5 hours YORK UNIVERSITY Faculty of Graduate Studies Final Examination December 14, 2010 Economics 5010 AF3.0 : Applied Microeconomics S. Bucovetsky time=2.5 hours Do any 6 of the following 10 questions. All count

More information

Intraday Cross Border The Netherlands-Belgium

Intraday Cross Border The Netherlands-Belgium Intraday Cross Border The Netherlands-Belgium Content 1. Overall design 1. 2. 3. 4. 5. Process description Capacity calculation Elbas trading platform Tradable products Timeline & Nominations 2. Contractual

More information

ANCILLARY SERVICES TO BE DELIVERED IN DENMARK TENDER CONDITIONS

ANCILLARY SERVICES TO BE DELIVERED IN DENMARK TENDER CONDITIONS Ancillary services to be delivered in Denmark. Tender conditions 1/49 Energinet.dk Tonne Kjærsvej 65 DK-7000 Fredericia +45 70 10 22 44 info@energinet.dk VAT no. 28 98 06 71 Date: 30. august 2017 Author:

More information

Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 5

Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 5 Economics 2 Spring 2017 Professor Christina Romer Professor David Romer SUGGESTED ANSWERS TO PROBLEM SET 5 1. The tool we use to analyze the determination of the normal real interest rate and normal investment

More information

ECON Micro Foundations

ECON Micro Foundations ECON 302 - Micro Foundations Michael Bar September 13, 2016 Contents 1 Consumer s Choice 2 1.1 Preferences.................................... 2 1.2 Budget Constraint................................ 3

More information

ECON 6022B Problem Set 1 Suggested Solutions Fall 2011

ECON 6022B Problem Set 1 Suggested Solutions Fall 2011 ECON 6022B Problem Set Suggested Solutions Fall 20 September 5, 20 Shocking the Solow Model Consider the basic Solow model in Lecture 2. Suppose the economy stays at its steady state in Period 0 and there

More information

1 Supply and Demand. 1.1 Demand. Price. Quantity. These notes essentially correspond to chapter 2 of the text.

1 Supply and Demand. 1.1 Demand. Price. Quantity. These notes essentially correspond to chapter 2 of the text. These notes essentially correspond to chapter 2 of the text. 1 Supply and emand The rst model we will discuss is supply and demand. It is the most fundamental model used in economics, and is generally

More information

STARRY GOLD ACADEMY , , Page 1

STARRY GOLD ACADEMY , ,  Page 1 ICAN KNOWLEDGE LEVEL QUANTITATIVE TECHNIQUE IN BUSINESS MOCK EXAMINATION QUESTIONS FOR NOVEMBER 2016 DIET. INSTRUCTION: ATTEMPT ALL QUESTIONS IN THIS SECTION OBJECTIVE QUESTIONS Given the following sample

More information

INTERMEDIATE MICROECONOMICS LECTURE 9 THE COSTS OF PRODUCTION

INTERMEDIATE MICROECONOMICS LECTURE 9 THE COSTS OF PRODUCTION 9-1 INTERMEDIATE MICROECONOMICS LECTURE 9 THE COSTS OF PRODUCTION The opportunity cost of an asset (or, more generally, of a choice) is the highest valued opportunity that must be passed up to allow current

More information

Department of Economics ECO 204 Microeconomic Theory for Commerce (Ajaz) Test 2 Solutions

Department of Economics ECO 204 Microeconomic Theory for Commerce (Ajaz) Test 2 Solutions Department of Economics ECO 204 Microeconomic Theory for Commerce 2016-2017 (Ajaz) Test 2 Solutions YOU MAY USE A EITHER A PEN OR A PENCIL TO ANSWER QUESTIONS PLEASE ENTER THE FOLLOWING INFORMATION LAST

More information

Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 5

Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 5 Economics 2 Spring 2016 Professor Christina Romer Professor David Romer SUGGESTED ANSWERS TO PROBLEM SET 5 1. The left-hand diagram below shows the situation when there is a negotiated real wage,, that

More information

Mathematics of Financial Derivatives

Mathematics of Financial Derivatives Mathematics of Financial Derivatives Lecture 9 Solesne Bourguin bourguin@math.bu.edu Boston University Department of Mathematics and Statistics Table of contents 1. Zero-coupon rates and bond pricing 2.

More information

Market Design. Econ University of Notre Dame

Market Design. Econ University of Notre Dame Market Design Econ 400.40 University of Notre Dame What is market design? Increasingly, economists are asked not just to study or explain or interpret markets, but to design them. This requires different

More information

Journal of Cooperatives

Journal of Cooperatives Journal of Cooperatives Volume 28 214 Pages 36 49 The Neoclassical Theory of Cooperatives: Mathematical Supplement Jeffrey S. Royer Contact: Jeffrey S. Royer, Professor, Department of Agricultural Economics,

More information

ECS2602. Tutorial letter 201/1/2018. Macroeconomics. Department of Economics First semester ECS2602/201/1/2018

ECS2602. Tutorial letter 201/1/2018. Macroeconomics. Department of Economics First semester ECS2602/201/1/2018 ECS2602/201/1/2018 Tutorial letter 201/1/2018 Macroeconomics ECS2602 Department of Economics First semester Answers to Assignment 01 Answers to Assignment 02 Answers to Self-assessment Assignment 04 BARCODE

More information

2 Maximizing pro ts when marginal costs are increasing

2 Maximizing pro ts when marginal costs are increasing BEE14 { Basic Mathematics for Economists BEE15 { Introduction to Mathematical Economics Week 1, Lecture 1, Notes: Optimization II 3/12/21 Dieter Balkenborg Department of Economics University of Exeter

More information

Chapter 11: Cost Minimisation and the Demand for Factors

Chapter 11: Cost Minimisation and the Demand for Factors Chapter 11: Cost Minimisation and the Demand for Factors 11.1: Introduction We assume a very simple objective for firms namely, that they want to maximise profits 1. We will explore the implications of

More information

ECO 352 International Trade Spring Term 2010 Week 3 Precepts February 15 Introduction, and The Exchange Model Questions

ECO 352 International Trade Spring Term 2010 Week 3 Precepts February 15 Introduction, and The Exchange Model Questions ECO 35 International Trade Spring Term 00 Week 3 Precepts February 5 Introduction, and The Exchange Model Questions Question : Here we construct a more general version of the comparison of differences

More information

Lecture IV Portfolio management: Efficient portfolios. Introduction to Finance Mathematics Fall Financial mathematics

Lecture IV Portfolio management: Efficient portfolios. Introduction to Finance Mathematics Fall Financial mathematics Lecture IV Portfolio management: Efficient portfolios. Introduction to Finance Mathematics Fall 2014 Reduce the risk, one asset Let us warm up by doing an exercise. We consider an investment with σ 1 =

More information

Solutions to Extra Business Problems

Solutions to Extra Business Problems Solutions to Extra Business Problems 5/28/11 1. (a).taking the derivative of C(q), we find that MC(q) = 12q + 14. Thus MC(5) = 74 - the marginal cost at a production level of 5 is 74 thousand dollars/unit.

More information

Uttar Pradesh Electricity Regulatory Commission

Uttar Pradesh Electricity Regulatory Commission Uttar Pradesh Electricity Regulatory Commission In exercise of the powers conferred under Section 181 of the Electricity Act, 2003 and all powers enabling it in this behalf, the Uttar Pradesh Electricity

More information

This is Appendix B: Extensions of the Aggregate Expenditures Model, appendix 2 from the book Economics Principles (index.html) (v. 2.0).

This is Appendix B: Extensions of the Aggregate Expenditures Model, appendix 2 from the book Economics Principles (index.html) (v. 2.0). This is Appendix B: Extensions of the Aggregate Expenditures Model, appendix 2 from the book Economics Principles (index.html) (v. 2.0). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/

More information

1 Income statement and cash flows

1 Income statement and cash flows The Chinese University of Hong Kong Department of Systems Engineering & Engineering Management SEG 2510 Course Notes 12 for review and discussion (2009/2010) 1 Income statement and cash flows We went through

More information

The Core of Macroeconomic Theory

The Core of Macroeconomic Theory PART III The Core of Macroeconomic Theory 1 of 33 The level of GDP, the overall price level, and the level of employment three chief concerns of macroeconomists are influenced by events in three broadly

More information

Eastern Mediterranean University Faculty of Business and Economics Department of Economics Fall Semester. ECON 101 Mid term Exam

Eastern Mediterranean University Faculty of Business and Economics Department of Economics Fall Semester. ECON 101 Mid term Exam Eastern Mediterranean University Faculty of Business and Economics Department of Economics 2014 15 Fall Semester ECON 101 Mid term Exam Suggested Solutions 28 November 2014 Duration: 90 minutes Name Surname:

More information

Economics 102 Discussion Handout Week 5 Spring 2018

Economics 102 Discussion Handout Week 5 Spring 2018 Economics 102 Discussion Handout Week 5 Spring 2018 GDP: Definition and Calculations Gross Domestic Product (GDP) is the market value of all goods and services produced within a country over a given time

More information

Solutions to Homework 3

Solutions to Homework 3 Solutions to Homework 3 AEC 504 - Summer 2007 Fundamentals of Economics c 2007 Alexander Barinov 1 Price Discrimination Consider a firm with MC = AC = 2, which serves two markets with demand functions

More information

Martingale Pricing Theory in Discrete-Time and Discrete-Space Models

Martingale Pricing Theory in Discrete-Time and Discrete-Space Models IEOR E4707: Foundations of Financial Engineering c 206 by Martin Haugh Martingale Pricing Theory in Discrete-Time and Discrete-Space Models These notes develop the theory of martingale pricing in a discrete-time,

More information

EC 202. Lecture notes 14 Oligopoly I. George Symeonidis

EC 202. Lecture notes 14 Oligopoly I. George Symeonidis EC 202 Lecture notes 14 Oligopoly I George Symeonidis Oligopoly When only a small number of firms compete in the same market, each firm has some market power. Moreover, their interactions cannot be ignored.

More information

Notes for Econ FALL 2010 Midterm 1 Exam

Notes for Econ FALL 2010 Midterm 1 Exam Notes for Econ 302-001 FALL 2010 Midterm 1 Exam The Fall 2010 Econ 302-001 course used Hall and Papell, Macroeconomics (Norton) as a textbook. The notation differs from Blanchard, Macroeconomics 5/2 (Pearson).

More information

Lecture 1: A Robinson Crusoe Economy

Lecture 1: A Robinson Crusoe Economy Lecture 1: A Robinson Crusoe Economy Di Gong SBF UIBE & European Banking Center c Macro teaching group: Zhenjie Qian & Di Gong March 3, 2016 Di Gong (UIBE & EBC) Intermediate Macro March 3, 2016 1 / 27

More information

University of Toronto Department of Economics ECO 204 Summer 2013 Ajaz Hussain TEST 1 SOLUTIONS GOOD LUCK!

University of Toronto Department of Economics ECO 204 Summer 2013 Ajaz Hussain TEST 1 SOLUTIONS GOOD LUCK! University of Toronto Department of Economics ECO 204 Summer 2013 Ajaz Hussain TEST 1 SOLUTIONS TIME: 1 HOUR AND 50 MINUTES DO NOT HAVE A CELL PHONE ON YOUR DESK OR ON YOUR PERSON. ONLY AID ALLOWED: A

More information

ADAPTING THE TARGET MODEL TO VALUE FLEXIBILITY

ADAPTING THE TARGET MODEL TO VALUE FLEXIBILITY ADAPTING THE TARGET MODEL TO VALUE FLEXIBILITY Stephen Woodhouse 3 November 2015 AGENDA ADAPTING THE TARGET MODEL TO VALUE FLEXIBILITY To be covered in this session: What is flexibility? Reality and misconceptions

More information

Introduction to Microeconomics AP/ECON C Test #2 (c)

Introduction to Microeconomics AP/ECON C Test #2 (c) YORK UNIVERSITY FACULTY OF LIBERAL ARTS AND PROFESSIONAL STUDIES Introduction to Microeconomics AP/ECON 1000.03C Test #2 (c) Course Director: Ida Ferrara November 13 th, 2009 Name Student Number Instructions:

More information

Economics 101 Fall 2010 Homework #3 Due 10/26/10

Economics 101 Fall 2010 Homework #3 Due 10/26/10 Economics 101 Fall 2010 Homework #3 Due 10/26/10 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework (legibly).

More information

Eco504 Fall 2010 C. Sims CAPITAL TAXES

Eco504 Fall 2010 C. Sims CAPITAL TAXES Eco504 Fall 2010 C. Sims CAPITAL TAXES 1. REVIEW: SMALL TAXES SMALL DEADWEIGHT LOSS Static analysis suggests that deadweight loss from taxation at rate τ is 0(τ 2 ) that is, that for small tax rates the

More information

Suggested Solutions to Assignment 3

Suggested Solutions to Assignment 3 ECON 1010C Principles of Macroeconomics Instructor: Sharif F. Khan Department of Economics Atkinson College York University Summer 2005 Suggested Solutions to Assignment 3 Part A Multiple-Choice Questions

More information

Economics 11: Second Midterm

Economics 11: Second Midterm Economics 11: Second Midterm Instructions: The test is closed book/notes. Calculators are allowed. Please write your answers on this sheet. There are 100 points. Name: UCLA ID: TA: Question Score Questions

More information

Exponential Modeling. Growth and Decay

Exponential Modeling. Growth and Decay Exponential Modeling Growth and Decay Identify each as growth or Decay What you should Know y Exponential functions 0

More information

ALGEBRAIC REPRESENTATION

ALGEBRAIC REPRESENTATION Elasticity - 1 ALGEBRAIC REPRESENTATION Demand curve: QD = a b P Supply curve: QS = c + d P At equilibrium, QD = QS Solving for the values of P and Q will give the following answers: Equilibrium price:

More information

Global Financial Management

Global Financial Management Global Financial Management Bond Valuation Copyright 24. All Worldwide Rights Reserved. See Credits for permissions. Latest Revision: August 23, 24. Bonds Bonds are securities that establish a creditor

More information

Electricity Markets and Principle Market Design Models

Electricity Markets and Principle Market Design Models Electricity Markets and Principle Market Design Models (prepared for the European Copper Institute) Dr. Konstantin Petrov KEMA Consulting GmbH Kurt-Schumacher-Straße 8 53113, Bonn Tel: + 49 228 4469000

More information

Table of Contents List of Figures...3 List of Tables...3 Definitions and Abbreviations...4 Introduction...7

Table of Contents List of Figures...3 List of Tables...3 Definitions and Abbreviations...4 Introduction...7 Explanatory document to all TSOs proposal for a methodology for the TSO-TSO settlement rules for the intended exchange of energy in accordance with Article 50(1) of Commission Regulation (EU) 2017/2195

More information

FINALTERM EXAMINATION Fall 2009 MGT411- Money & Banking (Session - 3) Time: 120 min Marks: 87

FINALTERM EXAMINATION Fall 2009 MGT411- Money & Banking (Session - 3) Time: 120 min Marks: 87 FINALTERM EXAMINATION Fall 2009 MGT411- Money & Banking (Session - 3) Time: 120 min Marks: 87 Question No: 1 ( Marks: 1 ) - Please choose one If more students didn't pay back their student loans then which

More information

XBID Information Package Published February 2018 Updated December 2018

XBID Information Package Published February 2018 Updated December 2018 XBID Information Package Published February 2018 Updated December 2018 1. Purpose of this document This document centralises, consolidates and comprehensively describes the necessary information which

More information

Homework 2 ECN205 Spring 2011 Wake Forest University Instructor: McFall

Homework 2 ECN205 Spring 2011 Wake Forest University Instructor: McFall Homework 2 ECN205 Spring 2011 Wake Forest University Instructor: McFall Instructions: Answer the following problems and questions carefully. Just like with the first homework, I ll call names randomly

More information

EconS 301 Intermediate Microeconomics Review Session #4

EconS 301 Intermediate Microeconomics Review Session #4 EconS 301 Intermediate Microeconomics Review Session #4 1. Suppose a person's utility for leisure (L) and consumption () can be expressed as U L and this person has no non-labor income. a) Assuming a wage

More information

(Blackline) VOLUME NO. III Page No. 878 SCHEDULING PROTOCOL

(Blackline) VOLUME NO. III Page No. 878 SCHEDULING PROTOCOL VOLUME NO. III Page No. 878 SCHEDULING PROTOCOL VOLUME NO. III Page No. 879 SCHEDULING PROTOCOL Table of Contents SP 1 SP 1.1 OBJECTIVES, DEFINITIONS AND SCOPE Objectives SP 1.2 Definitions SP 1.2.1 Master

More information

A BOND MARKET IS-LM SYNTHESIS OF INTEREST RATE DETERMINATION

A BOND MARKET IS-LM SYNTHESIS OF INTEREST RATE DETERMINATION A BOND MARKET IS-LM SYNTHESIS OF INTEREST RATE DETERMINATION By Greg Eubanks e-mail: dismalscience32@hotmail.com ABSTRACT: This article fills the gaps left by leading introductory macroeconomic textbooks

More information

Statistical Arbitrage in Balancing Markets

Statistical Arbitrage in Balancing Markets Statistical Arbitrage in Balancing Markets and the Impact of Time Delay Stefan Kermer, Derek Bunn 1 Agenda Introduction Austrian Imbalance Settlement Design Market Players Perspectives Predicting the Conditional

More information