String Theory

MBA911 Quantitative Economics

Dr. Florian Gerth Faculty of Business [email protected]

Dr. Florian Gerth Academic Background:

• BSc International Management • University of Applied Sciences Karlsruhe, Germany • Tecnologico de Monterrey, Mexico

• Diploma in Economics • University of Kent, UK

• MSc Economics and Econometrics • University of Kent, UK

• PhD Economics • University of Kent, UK

• MA International Relations and Affairs • UOW, Australia

Dr. Florian Gerth - MBA911 - Quantitative Economics

Dr. Florian Gerth

Professional Background:

• Schaeffler Group, Germany • SEAT SA, Spain • University of Kent, UK • Central Bank of Ireland, Ireland • Researchers Sans Frontiers, UAE • Gulf and Global Development &

Security Forum, UAE • UOWD, UAE

Primary Research Field: Quantitative Macroeconomics (Business Cycle Fluctuations, Firm Dynamics, Productivity Analysis, Resource Misallocation)

Specialist in macroeconomics, firm dynamics and financial crises. My research asks on the one hand, how, during financial crises, firm behaviour affects the macroeconomy, particularly aggregate productivity, and on the other, how financial crises propagate within the economic system.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Administration Consultation Hours:

• Wednesday:

• Thursday:

• By appointment only

8.30 to 10.30am

12.30 to 2.30pm

Dr. Florian Gerth - MBA911 - Quantitative Economics

Course Material

Required Text (Economics section):

• Title: Economics for Today (6th Asia Pacific edition),

Author: Allan Layton, et al. Publisher: Cengage Learning Australia

• Please read the assigned chapters before coming to the class.

Dr. Florian Gerth - MBA911 - Quantitative Economics

 Also E-Book available in the library!!!

Course Material

Required Text (Quantitative section):

• Title: Quantitative Analysis for Management (13th edition),

Author: Render, et al. Publisher: Pearson Education Ltd., UK.

• Please read the assigned chapters before coming to the class.

Dr. Florian Gerth - MBA911 - Quantitative Economics

 Also E-Book available in the library!!!

Assessments Assessment Tasks:

Weighting Due Date

• Reflective Blogs (4x) 20% next slide

• Economics in the 30% 18th of November Media presentation

• Research Report 50% 2nd of December

Dr. Florian Gerth - MBA911 - Quantitative Economics

1. Reflective blogs The reflective blogs are intended to capture the development of your critical analysis skills as an economist. You will be given four topics to think about and reflect upon, capturing your increasing knowledge of the application of economics concepts to daily business and social issues

1. 8th of October (due today!  what do I think is economics?!) 2. 28th of October 3. 13th of November 4. 2nd of December

• Each 5% of final mark

Dr. Florian Gerth - MBA911 - Quantitative Economics

2. Economics in the media presentation • This assessment provides you with the opportunity to analyse the economic

foundations and validity of propositions put forth in contemporary media stories.

• You need to form groups (2-3 people) during the second block and are to select a media story for their presentation for approval on Friday, the 4th of November

• After unpacking the economic elements of the story, you are to provide a critique of the reporting, and suggest alternative recommendations taking into account multiple stakeholder and policy viewpoints

Dr. Florian Gerth - MBA911 - Quantitative Economics

2. Economics in the media presentation

• Your presentation should be pre-recorded and not exceed 10 minutes.

• Each member needs to speak!

• Due date is the 18th of November

• 30% of final mark

Dr. Florian Gerth - MBA911 - Quantitative Economics

3. Research report • You are to select a topic of global and contemporary significance for empirical

analysis

• For approval by Sunday, the 20th of November

• Using appropriate data, you will apply critical thinking and quantitative skills to aid with the analyses of the topic

• Individual assignment

Dr. Florian Gerth - MBA911 - Quantitative Economics

3. Research report

• 3,000 words

• Due date is the 2nd of December Turnitin

• 50% of final mark

Dr. Florian Gerth - MBA911 - Quantitative Economics

Ground Rules – Class discipline • Be on time and do not leave class early

• Switch off your mobile before coming to the class

• Talk/ask in a respectful manner

• Respect others’ time and commitment

• No cross talking during lectures

• Read chapter before attending class

• Do tutorial work

• Come to office hours (if questions)

• Listen actively and attentively

Dr. Florian Gerth - MBA911 - Quantitative Economics

Ground Rules – Class discipline • Ask for clarification if you are confused

• Consider anything that is said in class strictly confidential

• Respect other peoples’ opinion

• There is no such thing as a “stupid” question, so ask

• Contribute and think!

• Do not sleep

• Course material is very powerful! Do not waste your (and my) time!!!

Dr. Florian Gerth - MBA911 - Quantitative Economics

Learning Outcomes

Dr. Florian Gerth - MBA911 - Quantitative Economics

1. Critically analyse the economic elements of contemporary global business issues and events.

2. Select and apply appropriate quantitative tools for the analyses of international economic data.

3. Propose evidence-based solutions to economic problems that encompass multiple stakeholder perspectives.

4. Collaborate responsibly to achieve individual and collective outcomes. 5. Effectively communicate complex concepts and information, through a

range of media.

What this course is about? ECONOMICS

• This subject deals with the micro- and macroeconomic analysis of economies. • Microeconomics

• How do individual consumers and businesses interact with each other in a market economy. • Behaviour of individuals, firms, and industries.

• Macroeconomics • Aggregate behaviour of different sectors of the economy to determine how changes in

behaviour in each of these sectors influence the overall level of economic activity. • Mainly interested in the questions:

• Unemployment • Economic Growth • Inflation

Dr. Florian Gerth - MBA911 - Quantitative Economics

What this course is about?

QUANTITATIVE ANALYSIS

• Tools that help us measure economic concepts • Data behaviour and frequency

• Forecasting • Understanding the relationship and interaction/dynamics between variables

Dr. Florian Gerth - MBA911 - Quantitative Economics

Structure of MBA911

1. Short videos (15-20 minutes) 2. Face-to-Face lecture (60-90 minutes) 3. MCQs (30 minutes) 4. Tutorial questions (45 + 30 minutes) 5. Economics discussion (30 + 15 minutes)

Dr. Florian Gerth - MBA911 - Quantitative Economics

1. Short videos (15-20 minutes)

• Short videos which you watch on your own

• To be found on within the slides (direct links)

• Before the lecture starts

• To give you an overview of what is being discussed

Dr. Florian Gerth - MBA911 - Quantitative Economics

2. Face-to-Face lecture (60-90 minutes)

• In-depth lecture based on the chapters in the book

• Lecture slides and notes on board will be the medium of exchange of information

• To facilitate grounded understanding in Quantitative Economics

Dr. Florian Gerth - MBA911 - Quantitative Economics

3. MCQs (30 minutes)

• Quizzes are found on Moodle

• To test your understanding of the material being discussed during the lecture

• Not marked!

• You can always go back and attempt the quiz again Dr. Florian Gerth - MBA911 - Quantitative Economics

4. Tutorial questions (45 + 30 minutes)

• Hands-on approach to the material being discussed during the lecture

• You need to write your answer for each questions in the 45- minute slot

• Discussion in class (30 minutes) to check your answers and to brain-storm on ideas

Dr. Florian Gerth - MBA911 - Quantitative Economics

5. Economics discussion (30 + 15 minutes)

• Discuss your perception of the article and give your qualified opinion (30 minutes)

• Discussion in class after you submitted your answer (15 minutes) • Possible topics:

• Zimbabwe pushed to brink of famine • Poland attacks EU aid as “smoke and mirrors” • Coronavirus Economic Impact Could Decimate the Middle East • Turkey's economic plight could impact MENA • Oil prices fall to lowest level in 17 years as demand slumps • etc.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Session 1 – Part A • What is economics? • Production possibilities and opportunity costs • Market demand and supply • Markets in action

• Market equilibrium • Surplus vs. shortage • Price ceiling vs. price floor

• Elasticities (= measure of responsiveness)

Dr. Florian Gerth - MBA911 - Quantitative Economics

What to do now…

1. Watch videos (16 minutes) 1. What is economics? (5 minutes) 2. Microeconomics vs. Macroeconomics (3 minutes) 3. Production Possibility Frontier (5 minutes) 4. Opportunity cost (3 minutes)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Chapter 1 Thinking like an economist

Dr. Florian Gerth - MBA911 - Quantitative Economics

The problem of scarcity

• The condition in which human wants are forever greater than the available supply of time, goods, services and resources.

• Examples: • Individuals: Bigger flat-screen TV, more restaurant meals, more

leisure time • Governments: Education, highways, defense

Dr. Florian Gerth - MBA911 - Quantitative Economics

The problem of scarcity • Cornerstone and essential fundament of the discipline of

economics

• Coping with scarcity is the essence of the human condition: • Wants > Supply • Because of scarcity it is impossible to satisfy every desire • Scarcity is manifested in the prices one must pay for goods and

services

Dr. Florian Gerth - MBA911 - Quantitative Economics

Scarce resources and production • Because of the economic problem of scarcity, no society has

enough resources to produce all the goods and services necessary to satisfy all human wants.

• Resources are the basic categories of inputs used to produce goods and services  a.k.a factors of production

• Economists divide resources into three categories: land, labour and capital

Dr. Florian Gerth - MBA911 - Quantitative Economics

Three categories of resources

Dr. Florian Gerth - MBA911 - Quantitative Economics

Resources: land • Any resource provided by nature

• Includes anything natural above or below the ground; e.g. forests, minerals, oil, wildlife, rivers, lakes, oceans

• May be renewable or non-renewable

Dr. Florian Gerth - MBA911 - Quantitative Economics

Resources: labour • The mental and physical human capacity of workers to produce

goods and services

• Examples: Services of farmers, factory workers, lawyers, professional football players and economists

• Entrepreneurship is the creative ability of individuals to seek profits by combining resources to produce new or existing products

Dr. Florian Gerth - MBA911 - Quantitative Economics

Resources: labour

• Both, the number of people available for work and the skills or quality of workers (labour productivity) measure the labour resource

• Differs in countries due to education, experience, health and motivation of workers

Dr. Florian Gerth - MBA911 - Quantitative Economics

Resources: Capital • The physical plant, machinery and equipment used to produce

other goods

• Human-made goods that do not directly satisfy human wants

• In economics, money is not capital; it simply gives a measure of the value of assets, including capital goods  ≠ financial capital

Dr. Florian Gerth - MBA911 - Quantitative Economics

Economics

…the study of how society chooses to allocate its scarce resources to the production of goods and services in order to satisfy unlimited wants

Dr. Florian Gerth - MBA911 - Quantitative Economics

Economics: the study of scarcity and choice

• The problem of scarcity forces people to make choices. It is the basis for the definition of economics

• Society makes two kinds of choices: –individual (microeconomics) –economy-wide (macroeconomics)

Dr. Florian Gerth - MBA911 - Quantitative Economics

TWO BRANCHES OF ECONOMICS

• Studies decision-making by a single individual, household, firm or industry

Microeconomics

• Studies the performance of, and decision-making in, the economy as a whole.

Macroeconomics

Dr. Florian Gerth - MBA911 - Quantitative Economics

Microeconomics

• The branch of economics that studies decision-making by a single individual, household, firm or industry

• Focus is on the behavior of small economic units, such as the economic decision of particular groups of consumers or businesses

Dr. Florian Gerth - MBA911 - Quantitative Economics

Macroeconomics

• The branch of economics that studies decision-making for the economy as a whole

• Applies an overview perspective to an economy by examining economy-wide variables such as inflation, unemployment, money supply and the flows of export, imports and international financial capital

• …decision making considers “big picture” policies

Dr. Florian Gerth - MBA911 - Quantitative Economics

The methodology of economics

• Economists use the same scientific method used in other disciplines (e.g. criminology, biology, physics)

• The scientific method is a step-by-step procedure for solving problems

Dr. Florian Gerth - MBA911 - Quantitative Economics

The steps in the model-building process

Dr. Florian Gerth - MBA911 - Quantitative Economics

Example: petrol consumption

• Petrol consumption by motorists has fallen. Why?

Identifying the problem:

• Identify the variables (e.g. petrol prices, car prices). • Express these verbally, graphically or mathematically.

Developing a model:

• Gather data that tell us how well the model estimates or predicts relationships.

Testing the model:

Dr. Florian Gerth - MBA911 - Quantitative Economics

The methodology of economics • Model

• Simplified description of reality used to understand and predict the relationship between variables

• Foundation of underlying theory • Looks at the factors -variables- that explain the event • Construct an abstraction from real-world complexities and make events

understandable

Dr. Florian Gerth - MBA911 - Quantitative Economics

Hazards of the economic way of thinking Ceteris paribus assumption

• “While certain variables change, all other things remain unchanged”

• This assumption holds everything constant and therefore allows to concentrate on the study of the relationship between two key variables: X and Y

• A model cannot be tested legitimately unless the ceteris paribus assumption is satisfied

Dr. Florian Gerth - MBA911 - Quantitative Economics

Hazards of the economic way of thinking Association/Correlation versus Causation

• We cannot always assume that, when one event follows another, the first caused the second

• For example, suppose that in the last month, Indonesian exports to Australia increased and the hole in the ozone layer grew.

• Is there any economic relation between the two events? Is this association or causation?

Dr. Florian Gerth - MBA911 - Quantitative Economics

Why do economists disagree? • As in other professions, disagreements occur in economics

• A major reason for these disagreements is the assumptions made about human nature

• Mainstream economics assumes that individuals are motivated almost exclusively by pleasure/pain principle. That is, in deciding how to react to a given set of circumstances, individuals weigh up the costs and benefits of a particular action (the pain and the pleasure) in a straightforward way and then decide what to do  rational behavior

• Gave rise to behavioural economics Dr. Florian Gerth - MBA911 - Quantitative Economics

Behavioural economics • Behavioural economics is a branch of economics in which more

comprehensive assumptions about human behaviour are employed.

• It is determined by: • the pleasure/pain principle • ethical and moral beliefs • social norms • class relationships

Dr. Florian Gerth - MBA911 - Quantitative Economics

Why do economists disagree?

Due to…

1. Positive economics: matters of fact

• Mainstream economics vs. behavioural economics

2. Normative economics: matters of opinion

Dr. Florian Gerth - MBA911 - Quantitative Economics

Positive economics • Positive economics is an analysis limited to statements that are

verifiable

• The key consideration for a positive statement is whether the statement is testable, not whether it is true or false

• Examples: • ‘Airbags save lives’ • ‘Smoking is harmful to your health’

Dr. Florian Gerth - MBA911 - Quantitative Economics

Normative economics • Normative economics is an analysis based on value judgements

• It cannot be proven by facts to be true or false

• Examples: • ‘Every teenager who wants a job should have one’. • ‘Keeping inflation under control is more important than teenage

unemployment’.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Chapter 2 Production possibilities and opportunity cost

Dr. Florian Gerth - MBA911 - Quantitative Economics

The three fundamental economic questions

The fundamental economic questions around production are:

What?

Scarcity imposes restrictions on ability to

produce.

How?

What production technique should be used?

For whom?

Who receives the goods and services that are produced?

Dr. Florian Gerth - MBA911 - Quantitative Economics

What? • The problem of scarcity imposes a restriction on the ability to

produce everything we want during a given period, so that the choice to produce “more” of a good requires producing “less” of another good

• Democratic societies determine what to produce on the basis of individual preferences expressed by consumers in the marketplace

Dr. Florian Gerth - MBA911 - Quantitative Economics

How? • How to mix technology and scarce resources in order to

produce them  whether a production technique will be more or less capital intensive

• Education and training are important

Dr. Florian Gerth - MBA911 - Quantitative Economics

For whom? • Of all the people who desire to consume the goods and

services produced, who actually receives them?

• This will depended largely on the way in which incomes are distributed among different members of the community

Dr. Florian Gerth - MBA911 - Quantitative Economics

Opportunity cost • Because of scarcity, people must make choices and each

choice incurs a cost (sacrifice). Once one option is chosen, another option is given up

• The relevant cost of taking a decision is the opportunity cost of a choice  the next best alternative sacrificed for a chosen alternative

Dr. Florian Gerth - MBA911 - Quantitative Economics

Opportunity cost: Examples

• What would you be doing if you were not currently studying?

• How many new roads have to be forgone if the government spends tax revenues on hospitals?

Dr. Florian Gerth - MBA911 - Quantitative Economics

Marginal analysis • Marginal analysis examines the effects of additions to or

subtractions from a current situation

• It is a very valuable tool in economics because it considers the effects of change resulting from decision-making

• Individuals, firms and governments all face marginal analysis

Dr. Florian Gerth - MBA911 - Quantitative Economics

Marginal analysis: examples • Would you devote one extra hour in preparation for an

economics exam or nap for an hour? (What is the scarce resource?)

• Should the economy allocate more of its resources in producing capital goods or consumer goods?

Dr. Florian Gerth - MBA911 - Quantitative Economics

Marginal analysis applied

‘To fertilise or not to fertilise … that is the question.’

A farmer will only add fertiliser to an area of land if the value of the extra yield exceeds the cost of the fertiliser.

Marginal analysis helps decide between options.

Dr. Florian Gerth - MBA911 - Quantitative Economics

The production possibilities frontier (PPF)

• The economic problem of scarcity means that society’s capacity to produce combinations of goods is constrained by its limited resources  represented by a model called the PPF

• The PPF shows the maximum combinations of two outputs that an economy can produce, given its available resources and technology.

Dr. Florian Gerth - MBA911 - Quantitative Economics

The production possibilities frontier (PPF) Three basic assumptions underlie the PPF model:

1. Fixed resources Quantity and quality of all resource inputs remain unchanged

2. Fully employed resources Economy operates with all its factors of production fully employed and producing the greatest output possible without waste

3. Unchanged technology Existing technology (body of knowledge applied to how goods and services are produced) is fixed

Dr. Florian Gerth - MBA911 - Quantitative Economics

Hypothetical economy that has the capacity to manufacture any combination of consumer goods and consumer services per year along its PPF

Dr. Florian Gerth - MBA911 - Quantitative Economics

The production possibilities frontier (PPF) • All points along the frontier are “maximum” output levels with the given resources

and technology, e.g. efficient points. A movement between any two efficient points on the frontier means that more of one output is produced only by producing less of the other output

• Z: Any point outside the PPF is unattainable because it is beyond the economy’s present production capabilities. Society would prefer this combination, but the economy cannot reach this point with its existing resources and technology

• U: inefficient output level for any economy operating without all of its resources fully employed  economy is under-producing because it could satisfy more of society’s wants if it were producing at some point along the PPF

Dr. Florian Gerth - MBA911 - Quantitative Economics

The law of increasing opportunity costs • Principle that opportunity cost increases as production of one

output expands at the expense of another

• This occurs because factors of production are generally not equally suited to producing one good compared to another good

• That is, opportunity costs rise as resources are shifted away from their best use

Dr. Florian Gerth - MBA911 - Quantitative Economics

• Holding the stock of resource and technology constant (ceteris paribus), the law of increasing opportunity costs causes the PPF to display a convex shape  the factors of production (labour and capital) are not equally suited to producing one good, compared to another good

Dr. Florian Gerth - MBA911 - Quantitative Economics

Shifting the PPF • The PPF can be used to represent changes in the level of

technology and available resources

• Economic growth (the ability of an economy to produce greater levels of output) is represented by an outward shift of the production possibilities curve

• Economic growth happens either through an increase in the resource base or through technological advances

Dr. Florian Gerth - MBA911 - Quantitative Economics

Dr. Florian Gerth - MBA911 - Quantitative Economics

Shifting the PPF 1. Changes in resources

One way to accelerate economic growth is to gain additional resources; e.g., natural resources, increase immigration, factories

2. Technological change Another way to achieve economic growth is through R&D of new technologies  Inventions vs. Innovations

Dr. Florian Gerth - MBA911 - Quantitative Economics

Present investment and future PPF • Deciding the output combination of capital and consumer goods now

can determine future production capacity

• Countries that forgo current consumption today in favour of investment (producing capital equipment) tend to expand their growth rate; that is, the PPF shifts outwards

• Countries with high levels of positive net investment include Singapore, China and South Korea

Dr. Florian Gerth - MBA911 - Quantitative Economics

Low-investment country and future PPF • Assume Splurgeland spends just enough capital output to replace

the capital being worn out each year

• Splurgeland’s PPF remains the same. Why?

• To shift its PPF to the right by 2020, Splurgeland would need to sacrifice consumer goods for capital formation, which means that the current standard of living has to fall

Dr. Florian Gerth - MBA911 - Quantitative Economics

Future possibilities frontier

Dr. Florian Gerth - MBA911 - Quantitative Economics

High-investment country and future PPF • Assume Thriftyland spends more than enough capital output to

replace the capital being worn out each year

• Thriftyland is thus adding to its capital stock and creating extra production

• Thriftyland’s PPF will shift to the right by 2020, and the country will have a higher standard of living than Splurgeland

• Producing capital goods = investment: • The process of producing capital, such as factories, machines and

inventories Dr. Florian Gerth - MBA911 - Quantitative Economics

What to do now… 1. Tutorial on Linear Equations (20 minutes) 2. MCQs (30 minutes) 3. Tutorial questions (45 minutes) 4. Come back and we discuss the tutorial questions (30 minutes) 5. Assignment #1 (45 minutes) – Reflective blog #1 6. Watch videos (30 minutes)

1. Supply and demand (10 minutes) 2. Supply and demand in action (6 minutes) 3. Price ceilings and floors (4 minutes) 4. The minimum wage in action (10 minutes)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Chapter 3 Market demand and supply

Dr. Florian Gerth - MBA911 - Quantitative Economics

The answers to the questions about “what?”, “how?” and “to whom?” can be found in the working of markets:

 in a market economy, goods and services are bought and sold when individuals and organisations come together as buyers and sellers  ultimately, the market determines the price and quantity exchanged  Demand: choice-making behaviour of consumers  Supply: decision of producers

Dr. Florian Gerth - MBA911 - Quantitative Economics

The law of demand • The law of demand represents an inverse relationship between the

price of a good or service and the quantity that buyers are willing to purchase in a defined time period, ceteris paribus

• A demand schedule (table) shows the specific quantity of a good or service that people are willing and able to buy at different prices

• The demand curve shows this relationship

Dr. Florian Gerth - MBA911 - Quantitative Economics

AN INDIVIDUAL’S DEMAND CURVE AND SCHEDULE

• Demand curve allows to find the quantity demanded by a buyer at any possible selling price by moving along the curve

Dr. Florian Gerth - MBA911 - Quantitative Economics

Individual demand curves and market demand

Dr. Florian Gerth - MBA911 - Quantitative Economics

Changes in quantity demanded vs. changes in demand • Price is not the only variable that determines how much of a good or

service consumers will buy  remember ceteris paribus?! • A variety of factors can influence the position of the demand curve  non-price determinants:

1. Number of buyers 2. Tastes and preferences 3. Income 4. Expectations 5. Prices of related goods

Dr. Florian Gerth - MBA911 - Quantitative Economics

Changes in quantity demanded vs. changes in demand Important distinction

• Change in quantity demanded • Movement between points along a stationary demand curve, ceteris paribus

• Change in demand • An increase or decrease in the demand at each possible price. An increase in

demand is a rightward shift in the entire demand curve. A decrease in demand is a leftward shift in the entire demand curve. Ceteris paribus no longer applies  at all possible prices, consumers wish to purchase a larger quantity than before the shift occurred

Dr. Florian Gerth - MBA911 - Quantitative Economics

Movement along demand curve and shift in demand

Dr. Florian Gerth - MBA911 - Quantitative Economics

Non-price determinants 1. Number of buyers

• At all possible prices, there is extra quantity demanded by the new customer, and the market demand curve for X shifts rightward (an increase in demand)

• Population growth therefore tends to increase the number of buyers, which shifts the market demand curve for a good or service rightward, and vice versa

• Can be domestic or foreign buyers 2. Tastes and preferences

• Fads, fashions, advertising and new products can influence consumer preferences to buy a particular good or service

3. Income a) Normal good: any good for which there is a direct positive relationship between

changes in income and its demand  Corr(income,demand) > 0 b) Inferior good: any good for which there is an inverse relationship between changes in

income and its demand  Corr(income,demand) < 0 Dr. Florian Gerth - MBA911 - Quantitative Economics

Non-price determinants 4. Expectations of buyers

a) Expected price increase  increase in demand b) Expected price drop  decrease in demand

5. Prices of related goods a) Substitute good: a good that competes with another good for consumer purchases. As

a result, there is a direct relationship between a price change for one good and the demand for its “competitor” good

b) Complementary good: a good that is jointly consumed with another good. As a result, there is an inverse relationship between a price change for one good and the demand for its “complementary” good

Dr. Florian Gerth - MBA911 - Quantitative Economics

The law of supply • The law of supply represents a direct relationship between the price

of a good and the quantity that sellers are willing to offer for sale in a defined time period, ceteris paribus

• A supply schedule (table) shows the quantity of a good or service that firms are willing and able to offer for sale at different prices

• The supply curve shows this relationship

• The higher price works as an incentive in supplying/producing more Dr. Florian Gerth - MBA911 - Quantitative Economics

AN INDIVIDUAL’ S SUPPLY CURVE AND SCHEDULE • Each point on the

curve represents a quantity supplied at a particular price  corr(supply,price)>0

Dr. Florian Gerth - MBA911 - Quantitative Economics

Individual SUPPLY curves and market SUPPLY

Dr. Florian Gerth - MBA911 - Quantitative Economics

Changes in quantity supplied vs. changes in supply • Price is not the only variable that determines how much of a good or

service producers will supply  remember ceteris paribus?! • A variety of factors can influence the position of the supply curve 

non-price determinants: 1. Number of sellers 2. Technology 3. Input prices 4. Taxes and subsidies 5. Expectations of producers 6. Prices of other goods

Dr. Florian Gerth - MBA911 - Quantitative Economics

Changes in quantity supplied vs. changes in supply Important distinction

• Change in quantity supplied • Movement between points along a stationary supply curve, ceteris paribus

• Change in supply • An increase or decrease in the supply at each possible price. An increase in

supply is a rightward shift in the entire supply curve. A decrease in supply is a leftward shift in the entire supply curve. Ceteris paribus no longer applies  at all possible prices, producers wish to supply a larger quantity than before the shift occurred

Dr. Florian Gerth - MBA911 - Quantitative Economics

Movement along a SUPPLY curve and shift in SUPPLY

Dr. Florian Gerth - MBA911 - Quantitative Economics

Non-price determinants 1. Number of sellers

• Drought destroys wheat • Outbreak of disease ruins apple crop • etc.

Damaging effect means that fewer goods can be supplied at each possible price  supply decreases (shifts to the left)

2. Technology • New and more efficient technology  manufacture more products at any possible selling

price

Dr. Florian Gerth - MBA911 - Quantitative Economics

Non-price determinants 3. Input prices

• Natural resources • Labour • Capital • Entrepreneurship Required to produce products  prices of these resources affect supply

 Increase (decrease) in production cost caused by the increase (decrease) in the price of inputs will have an opposite effect and decrease (increase) supply

4. Taxes and subsidies • Certain taxes have the same effect on supply as an increase in the price of a resource 

causes additional production cost and the supply shifts Dr. Florian Gerth - MBA911 - Quantitative Economics

Non-price determinants

5. Expectations of producers • Expect price to rise  less supply today  leftward shift • Expect price to drop  more supply today  rightward shift

6. Prices of other good the firm could produce • A rise in the price of one product relative to the price of other products signals to

suppliers that switching production to the product with the higher relative price yields higher profit  increase in supply: this happens because the opportunity cost for Y, measured in foregone X profits, increases

Dr. Florian Gerth - MBA911 - Quantitative Economics

Market supply and demand analysis

• A market is any arrangement in which the interaction of buyers and sellers determines the price and quantity of goods and services exchanged

• The market is the key institution in capitalist economies

• Important question for market supply and demand analysis is: “which selling price and quantity will prevail in the market?”

Dr. Florian Gerth - MBA911 - Quantitative Economics

Market demand and supply

Dr. Florian Gerth - MBA911 - Quantitative Economics

Surplus and shortage

• A surplus is a market condition existing at any price at which the quantity supplied is greater than the quantity demanded

• Downward pressure on price until S=D

• A shortage is a market condition existing at any price at which the quantity supplied is less than the quantity demanded

• Upward pressure on price until S=D

Dr. Florian Gerth - MBA911 - Quantitative Economics

Equilibrium and efficiency • Equilibrium efficiency is a market condition that occurs at any

price at which the quantity demanded and the quantity supplied are equal

• At equilibrium, the market is operating efficiently

• Efficiency occurs when society maximises the benefits it gains from the use of scarce resources

Dr. Florian Gerth - MBA911 - Quantitative Economics

Equilibrium price and quantity

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price System

• The price system is a mechanism that uses the forces of supply and demand to create an equilibrium through rising and falling prices

• Price plays a rationing role

• Invisible hand

Dr. Florian Gerth - MBA911 - Quantitative Economics

Chapter 4 Markets in action

Dr. Florian Gerth - MBA911 - Quantitative Economics

Changes in demand

• If one of the non-price determinants of demand changes, the equilibrium price and quantity will change:

• An increase in a non-price determinant of demand will raise the price and quantity supply  temporary shortage

• A decrease in a non-price determinant of demand will lower the price and quantity supply  temporary surplus

Dr. Florian Gerth - MBA911 - Quantitative Economics

Changes in demand

Dr. Florian Gerth - MBA911 - Quantitative Economics

Changes in supply

• If one of the non-price determinants of supply changes, the equilibrium price and quantity will change:

• An increase in a non-price determinant of supply will lower the price and increase the quantity supply  temporary surplus

• A decrease in a non-price determinant of supply will raise the price and lower the quantity supply  temporary shortage

Dr. Florian Gerth - MBA911 - Quantitative Economics

Changes in supply

Dr. Florian Gerth - MBA911 - Quantitative Economics

Can the laws of supply and demand be repealed?

• For various reasons, governments implement price controls to influence market forces

• There are two types of price controls: 1. Price ceilings 2. Price floors

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price ceilings • A price ceiling is a legally established maximum price that a

seller can charge

• The rationale is to provide an ‘essential service’ that would be unaffordable to many people at the equilibrium price

• It always results in an excess of quantity demanded over quantity supplied at the ceiling price  shortage

Dr. Florian Gerth - MBA911 - Quantitative Economics

Example: Rent Control

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Price ceilings • Creates persistent market shortage because the rental price cannot

rise • Impact on Consumer:

• Consumers must spend more time on waiting lists and searching for housing, as a substitute for paying higher prices  opportunity costs

• Illegal market, black market, can arise because of the excess quantity demanded

• Impact on Sellers: • Landlords do not maintain apartments; leading to a decrease in well-

maintained apartments in the long run • Landlords may use discriminatory practices to replace the price system

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price Floors • A price floor is a legally established minimum price that a seller

can be paid

• Governments impose these to lower the consumption of a good or to ensure that some employees are not disadvantaged

• It always results in an excess of quantity supplied over quantity demanded at the floor price  surplus

Dr. Florian Gerth - MBA911 - Quantitative Economics

Example: Minimum wage

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Minimum wage • A central wage-fixing authority sets a minimum wage which is a

price floor above the equilibrium wage rate

• The intent of this action is to make lower-paid workers better off

• Number of workers willing to offer their labour increases upward along the supply curve

• Number of workers that firms are willing to hire decreases downward along the demand curve

Dr. Florian Gerth - MBA911 - Quantitative Economics

Minimum wage • Outcome is a labour surplus of unskilled workers who are now

unemployed

• Employers are encouraged to substitute machines and skilled labour for the unskilled labour previously employed at the equilibrium wage

• Minimum wage is counterproductive because employers lay off the lowest-skilled workers who are the type of workers minimum wage legislation intends to help

Dr. Florian Gerth - MBA911 - Quantitative Economics

Market failure • Market failure is a situation in which the price system fails to

operate efficiently, creating a problem for society

• Three examples of market failure: • Government intervention (price ceiling, price floor) • Externalities • Public goods • Lack of competition

Dr. Florian Gerth - MBA911 - Quantitative Economics

Externalities

• An externality is a cost or benefit imposed on third parties (i.e. people other than the buyers and sellers of the good)

• Economic side effects/ neighborhood effects/ spillover effects

• Externalities can be: • negative (harmful spillovers) • positive (beneficial spillovers)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Externalities Negative externality • Social costs > individual costs • E.g., loud music, pollution, etc.

Positive externality • Social gain > individual gain • E.g., pretty garden, R&D, etc.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Negative externalities

• Negative externalities are those that are detrimental to third parties. For example:

• noise pollution caused by aircraft • smoke from a factory

• Approaches to solving these ‘failures’ include: • taxes and charges • regulation • compensation

Dr. Florian Gerth - MBA911 - Quantitative Economics

Negative externalities

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Positive externalities • Positive externalities are those that are beneficial to third

parties. For example: • a beautiful garden for neighbours to enjoy • immunisation

• Approaches to preventing these ‘failures’ include: • subsidies • regulation • compensation

Dr. Florian Gerth - MBA911 - Quantitative Economics

Positive externalities

Dr. Florian Gerth - MBA911 - Quantitative Economics

Public goods

• A public good or service is one that the government, rather than the market, must provide if it is to be made available in sufficient quantity

• Once produced, it has two special properties: 1. Users collectively consume benefits 2. It is non-exclusive. There is no way to prevent non-purchasers

(free riders) from reaping benefits

Dr. Florian Gerth - MBA911 - Quantitative Economics

Lack of competition • Firms without competitors tend to restrict supply through

collusion, which raises prices to maximise the firms’ profits

• This leads to non-optimal allocation

• Examples include: • the Visy and Amcor price-fixing case • the 11 international airlines that were involved in an air-cargo cartel

Dr. Florian Gerth - MBA911 - Quantitative Economics

Lack of competition

Dr. Florian Gerth - MBA911 - Quantitative Economics

What to do now… 1. MCQs (30 minutes) 2. Tutorial questions (45 minutes) 3. Come back and we discuss the tutorial questions (30 minutes) 4. Economics discussion (30 minutes) – Corona in the Middle East 5. Come back and we discuss the economic discussion (15 minutes) 6. Watch videos (29 minutes)

1. Elasticities I (6 minutes) 2. Elasticities II (8 minutes) 3. Probabilities (8 minutes) 4. Probability distributions (7 minutes)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Chapter 5 Elasticity of demand and supply

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price elasticity of demand • Price elasticity of demand is the ratio of the percentage change in

the quantity demanded of a product to a percentage change in its price:

• Elasticity coefficients are negative because price and quantity demanded are inversely related

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price elasticity of demand • Measure of (Consumer) Responsiveness

• What percentage does the quantity demanded increase when the price falls by x percent?

• Vital for pricing and targeting markets for goods and services

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price elasticity of demand

• When price rises by 1%, quantity demand falls by 2.5%.

What is the Ed if a cinema complex raises ticket prices from $25 to $30, and the number of seats sold falls from 20 000 to 10 000 (ceteris paribus)?

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price elasticity of demand

• When price falls by 1%, quantity demand rises by 5.9%.

What is the Ed if a cinema complex lowers ticket prices from $30 to $25, and the number of seats sold rises from 10 000 to 20 000 (ceteris paribus)?

Dr. Florian Gerth - MBA911 - Quantitative Economics

Disparity in elasticity coefficients • When we move along a demand curve between two points, we

get different answers for the elasticity (in our example, 2.5 if price is raised and 5.9 if price is cut)

• The elasticity coefficient changes because it involves changes between two possible base points

• Solution: Midpoint formula for price elasticity of demand  refers to elasticity over an arc of the demand curve

Dr. Florian Gerth - MBA911 - Quantitative Economics

The midpoint formula • To address this problem, we use the midpoint formula:

Dr. Florian Gerth - MBA911 - Quantitative Economics

The midpoint formula

• Because the midpoint method uses averages, it does not matter if Q1 or P1 is the first number in each term:

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price elasticity of demand • Elastic demand: change in price < change in quantity

• Inelastic demand: change in price > change in quantity

• Unitary elastic: change in price = change in quantity

Dr. Florian Gerth - MBA911 - Quantitative Economics

Total revenue test • Depending on the value of the elasticity coefficient, changes in

price can affect total revenue • For a decrease in price:

• TR increasesElastic (Ed > 1)

• TR decreasesInelastic (Ed < 1)

• No change to TRUnitary elastic (Ed = 1)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Impact of a decrease in price on total revenue

Notes on board Dr. Florian Gerth - MBA911 - Quantitative Economics

Perfectly elastic and inelastic demand

Dr. Florian Gerth - MBA911 - Quantitative Economics

Variations along a straight-line demand curve

Dr. Florian Gerth - MBA911 - Quantitative Economics

Determinants of price elasticity of demand • Factors that influence the price elasticity of a good or service

include: 1. the availability of substitutes 2. share of budget spent on the product 3. adjustment to a price change over time

Dr. Florian Gerth - MBA911 - Quantitative Economics

Availability of substitutes • Demand is more price-elastic for goods that have close substitutes,

because consumers can switch to alternative products

• Price elasticity depends on how broadly (or narrowly) we define the good or service:

• Example: The Ed for Hyundai cars is greater than that for cars in general. Hyundai competes with cars sold by Kia, Toyota, Mitsubishi and other car makers.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Share of budget spent on the product • Consumers are more sensitive to a price change, and the demand

curve is more elastic, when the good or service takes a large proportion of their income

• This is because consumers think more carefully about alternatives when prices change

Dr. Florian Gerth - MBA911 - Quantitative Economics

Adjustment to a price change over time

• As time passes, buyers can respond fully to a change in the price of a product by finding more substitutes

• The longer consumers have to adjust, the more sensitive they are to a price change, and the more elastic the demand curve

Dr. Florian Gerth - MBA911 - Quantitative Economics

Other measures of demand elasticity

• Income elasticity of demand

• Cross-elasticity of demand

Dr. Florian Gerth - MBA911 - Quantitative Economics

Income elasticity of demand • Income elasticity of demand is the ratio of the percentage

change in the quantity demanded of a good or service to a given percentage change in the price of a related good or service:

Dr. Florian Gerth - MBA911 - Quantitative Economics

Income elasticity coefficients

• normal good • consumers purchase more when their

income rises If Ey is positive:

• inferior good • consumers purchase less when their

income rises. If Ey is negative:

Dr. Florian Gerth - MBA911 - Quantitative Economics

Income elasticity of demand • Suppose consumers’ incomes increase from $1000 to $1250 per month, which

then results in an increase in the quantity of cinema tickets demanded from 10 000 to 15 000:

• The Ey calculated is positive, suggesting that a cinema ticket is a normal good • Ticket sales are responsive to a change in income

Dr. Florian Gerth - MBA911 - Quantitative Economics

Cross-elasticity of demand • Cross-elasticity of demand is the ratio of the percentage

change in the quantity demanded of a good or service to a given percentage change in the price of a related good or service:

Dr. Florian Gerth - MBA911 - Quantitative Economics

Cross-elasticity coefficients

• substitutesIf Ec is positive:

• complements.If Ec is negative:

Dr. Florian Gerth - MBA911 - Quantitative Economics

Cross-elasticity coefficients • If the price of Coke rose by 10%, causing consumers to buy 5% more Pepsi, the

Ec would be +0.5. oPepsi is a substitute for Coke.Substitutes

• If the price of nail polish rose by 50%, causing consumers to buy 10% less nail polish remover, the Ec would be –0.2. oNail polish and nail-polish remover are complementary goods.Complements

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price elasticity of supply • The ratio of the percentage change in the quantity supplied of

a product to the percentage change in its price.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price elasticity of supply

• Es > 1 • Perfectly elastic when Es = infinityElastic:

• Es = 1Unit elastic:

• Es < 1 • Perfectly inelastic when Es = 0Inelastic:

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price elasticity of supply

Dr. Florian Gerth - MBA911 - Quantitative Economics

Price elasticity and the impact of taxation

• Taxes imposed on price inelastic goods are an important source of revenue for governments:

–Examples: Petrol, tobacco products, alcohol

• The study of the incidence of tax shows us who bears the burden • Tax incidence: the share of a tax ultimately paid by consumers or by

sellers • Depends on the price elasticity of demand and supply

Dr. Florian Gerth - MBA911 - Quantitative Economics

The incidence of a tax on petrol

Dr. Florian Gerth - MBA911 - Quantitative Economics

Session 1 – Part B • Basic rules of probability • Marginal vs. conditional probability • Expected value (mean) • Standard deviation • Skeweness • Kurtosis • Probability distributions

Dr. Florian Gerth - MBA911 - Quantitative Economics

Chapter 2 Probability concepts and probability distributions

Dr. Florian Gerth - MBA911 - Quantitative Economics

Introduction

• Life is uncertain; we are not sure what the future will bring

• Probability is a numerical statement about the likelihood that an event will occur

Dr. Florian Gerth - MBA911 - Quantitative Economics

Two Basic Rules of Probability 1. The probability, P, of any event or state of nature occurring is greater than or

equal to 0 and less than or equal to 1. That is, 0 ≤ P(event) ≤ 1

A probability of 0 indicates that an event is never expected to occur. A probability of 1 means that an event is always expected to occur.

2. The sum of the simple probabilities for all possible outcomes of an activity must equal 1.

Regardless of how probabilities are determined, they must adhere to these two rules.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Types of Probability

1. Objective Approach

2. Subjective Approach

Dr. Florian Gerth - MBA911 - Quantitative Economics

Types of Probability – Objective Approach a) Relative frequency approach - probability assigned to an event is the relative

frequency of that occurrence.

Number of occurrences of the eventevent = Total number of trials or outc

( ) omes

P

Dr. Florian Gerth - MBA911 - Quantitative Economics

Example - Relative frequency approach • Historical demand for white paint at = 0, 1, 2, 3, or 4 gallons per day

• Observed frequencies over the past 200 days

QUANTITY DEMANDED (GALLONS) NUMBER OF DAYS PROBABILITY

0 40 0.20(= 40÷200)

1 80 0.40(= 80÷200)

2 50 0.25(= 50÷200)

3 20 0.10(= 20÷200)

4 10 0.05(= 10÷200)

Blank Total 200 Total 1.00(= 200÷200)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Example - Relative frequency approach • Historical demand for white paint at = 0, 1, 2, 3, or 4 gallons per day

• Observed frequencies over the past 200 days

QUANTITY DEMANDED (GALLONS) NUMBER OF DAYS PROBABILITY

0 40 0.20(= 40÷200)

1 80 0.40(= 80÷200)

2 50 0.25(= 50÷200)

3 20 0.10(= 20÷200)

4 10 0.05(= 10÷200)

Blank Total 200 Total 1.00(= 200÷200)

• Individual probabilities are all between 0 and 1 • 0 ≤ P (event) ≤ 1

• Total of all event probabilities equals 1

• ∑ P (event) = 1.00

Dr. Florian Gerth - MBA911 - Quantitative Economics

b) Classical or logical method – without performing a series of trials, we can often logically determine what the probabilities of various events should be.

( )

( )

← ←

← ←

1head = 2 13spade = 52

01= .25= 4

= 25%

Number of ways of getting a head P

Number of possible outcomes head or tail Number of chances of drawing a spade

P Number of possible outcomes

( )

Types of Probability – Objective Approach

Dr. Florian Gerth - MBA911 - Quantitative Economics

Types of Probability – Subjective Approach

• Subjective Approach • Based on the experience and judgment of the person making the estimate

• Opinion polls • Judgment of experts • Delphi method

Dr. Florian Gerth - MBA911 - Quantitative Economics

Mutually Exclusive Events

• Events are said to be mutually exclusive if only one of the events can occur on any one trial

• Tossing a coin will result in either a head or a tail • Rolling a die will result in only one of six possible outcomes

Dr. Florian Gerth - MBA911 - Quantitative Economics

Venn Diagrams FIGURE 2.1 Venn Diagram for Events That Are Mutually Exclusive

FIGURE 2.2 Venn Diagram for Events That Are Not Mutually Exclusive

Events do NOT overlap Events do overlap

A = event that a head is tossed B = event that a tail is tossed

52 card set A = event that a 7 is drawn B = event that a heart is drawn

Intersection is whatever is common to both.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Collectively Exhaustive Events • Events are said to be collectively exhaustive if the list of outcomes includes

every possible outcome • Both heads and tails as possible outcomes of coin flips • All six possible outcomes of the roll of a die

OUTCOME OF ROLL PROBABILITY

1 1/6

2 1/6

3 1/6

4 1/6

5 1/6

6 1/6

Blank Total 1

Dr. Florian Gerth - MBA911 - Quantitative Economics

Drawing a Card

• Draw one card from a deck of 52 playing cards A = event that a 7 is drawn

B = event that a heart is drawn

P (a 7 is drawn) = P(A)= 4/52 = 1/13 P (a heart is drawn) = P(B) = 13/52 = 1/4

– These two events are not mutually exclusive since a 7 of hearts can be drawn

– These two events are not collectively exhaustive since there are other cards in the deck besides 7s and hearts

Dr. Florian Gerth - MBA911 - Quantitative Economics

Differences DRAWS MUTUALLY

EXCLUSIVE COLLECTIVELY

EXHAUSTIVE 1. Draws a spade and a club Yes No

2. Draw a face card and a number card Yes Yes

3. Draw an ace and a 3 Yes No

4. Draw a club and a non-club Yes Yes

5. Draw a 5 and a diamond No No

6. Draw a red card and a diamond No No

Dr. Florian Gerth - MBA911 - Quantitative Economics

Unions and Intersections of Events • Intersection – the set of all outcomes that are common to both events

Intersection of event A and event B = A and B = A ∩ B = AB

– Probability notation P(Intersection of event A and event B) = P(A and B)

= P(A ∩ B) = P(AB)

– Sometimes called joint probability – Implies that both events are occurring at the same time or jointly.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Unions and Intersections of Events

• Union – the set of all outcomes that are contained in either of two events

Union of event A and event B = A or B

– Probability notation

P(Union of event A and event B)= P(A or B) = P(A ∪ B)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Unions and Intersections of Events

• In the previous example • Intersection of event A and event B

(A and B) = the 7 of hearts is drawn P(A and B) = P(7 of hearts is drawn) = 1/52

• Union of event A and event B

(A or B) = either a 7 or a heart is drawn P(A or B) = P(any 7 or any heart is drawn) = 16/52

Dr. Florian Gerth - MBA911 - Quantitative Economics

What have we seen so far… • Objective Approach to Probabilities  the one we focus on! • Subjective Approach to probabilities

• Mutually Exclusive Events • Collectively Exhaustive Events

• Unions • Intersections  Joint Probabilities

• Now  Probability rules

Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Rules • General rule for union of two events,

additive rule

P(A or B) = P(A) + P(B) − P(A and B)

• Union of two events, a 7 or a heart

P(A or B) = P(A) + P(B) − P(A and B) = 4/52 + 13/52 − 1/52

= 16/52

Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Rules

• Conditional probability – probability that an event occurs given another event has already happened

( )( | ) ( )

( ) ( |

=

= ) ) (

P ABP A B P B

P AB P A B P B

• Probability of a 7 given a heart has been drawn

1( ) 52 1( | ) = = = 1313( ) 52

P ABP A B P B

Probability of event A given that even B has occurred.

Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Rules

• Which sets are independent?

1. (a) Your education (b) Your income level

2. (a) Draw a jack of hearts from a full 52-card deck (b) Draw a jack of clubs from a full 52-card deck

3. (a) Chicago Cubs win the National League pennant (b) Chicago Cubs win the World Series

4. (a) Snow in Santiago, Chile (b) Rain in Tel Aviv, Israel

Dr. Florian Gerth - MBA911 - Quantitative Economics

Two events are independent if the occurrence of one has no impact on the occurrence of the other.

Probability Rules

• Which sets are independent?

1. (a) Your education (b) Your income level

2. (a) Draw a jack of hearts from a full 52-card deck (b) Draw a jack of clubs from a full 52-card deck

3. (a) Chicago Cubs win the National League pennant (b) Chicago Cubs win the World Series

4. (a) Snow in Santiago, Chile (b) Rain in Tel Aviv, Israel

•Dependent events • Independent

events

•Dependent events

•Independent events

Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Rules

• Independent one event has no effect on the other event P(A | B) = P(A)

P(A and B) = P(A)P(B) • For a fair coin tossed twice

A = event that a head is the result of the first toss B = event that a head is the result of the second toss

P(A) = 0.5 and P(B) = 0.5 P(AB) = P(A)P(B) = 0.5(0.5) = 0.25

Notes on the board Dr. Florian Gerth - MBA911 - Quantitative Economics

Independent Events

• A bucket contains 3 black balls and 7 green balls • Draw a ball from the bucket, replace it, and draw a second ball

1. The probability of a black ball drawn on first draw is:

P(B) = 0.30 2. The probability of two green balls drawn is:

P(GG) = P(G) × P(G) = 0.7 × 0.7 = 0.49

Dr. Florian Gerth - MBA911 - Quantitative Economics

Independent Events

• A bucket contains 3 black balls and 7 green balls • Draw a ball from the bucket, replace it, and draw a second ball

3. The probability of a black ball drawn on the second draw if the first draw is green is:

P(B |G) = P(B) = 0.30

4. The probability of a green ball drawn on the second draw if the first draw is green is:

P(G |G) = P(G) = 0.70

Dr. Florian Gerth - MBA911 - Quantitative Economics

Dependent Events

• An urn contains the following 10 balls: – 4 are white (W) and lettered (L) – 2 are white (W) and numbered (N) – 3 are yellow (Y) and lettered (L) – 1 is yellow (Y) and numbered (N)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Dependent Events

• An urn contains the following 10 balls: – 4 are white (W) and lettered (L) – 2 are white (W) and numbered (N) – 3 are yellow (Y) and lettered (L) – 1 is yellow (Y) and numbered (N)

P(WL) = 4/10 = 0.4 P(YL) = 3/10 = 0.3 P(WN) = 2/10 = 0.2 P(YN) = 1/10 = 0.1 P(W) = 6/10 = 0.6 P(L) = 7/10 = 0.7 P(Y) = 4/10 = 0.4 P(N) = 3/10 = 0.3

Dr. Florian Gerth - MBA911 - Quantitative Economics

Dependent Events • 4 balls White (W)

and Lettered (L)

• 2 balls White (W) and Numbered (N)

• 3 balls Yellow (Y) and Lettered (L)

• 1 ball Yellow (Y) and Numbered (N)

The urn contains 10 balls

4Probability 0

( ) = 1

WL

2Probability 0

( ) = 1

WN

3Probability 0

( ) = 1

WN

3Probability 0

( ) = 1

YN

Dr. Florian Gerth - MBA911 - Quantitative Economics

1

(YL)

Dependent Events • The conditional probability that the ball drawn is lettered, given

that it is yellow

( )( | ) (

0.3= = = 0.7 0)

5 .4

P YLP L Y P Y

• We can verify P(YL) using the joint probability formula P(YL) = P(L |Y) × P(Y) = (0.75)(0.4) = 0.3

See Excel File – “Session 1” – “Probability Rules”Dr. Florian Gerth - MBA911 - Quantitative Economics

• Until now: Concepts in Probability

• From now on: Probability in action  Probability Distributions

Dr. Florian Gerth - MBA911 - Quantitative Economics

Random Variables

• A random variable assigns a real number to every possible outcome or event in an experiment

X = number of refrigerators sold during the day

• Discrete random variables can assume only a finite or limited set of values

• Continuous random variables can assume any one of an infinite set of values; (lower value ≤ X ≤ upper value)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Random Variables EXPERIMENT OUTCOME RANDOM VARIABLES RANGE OF

RANDOM VARIABLES

Stock 50 Christmas trees

Number of Christmas trees sold

X = number of Christmas trees sold 0, 1, 2, . . . , 50

Inspect 600 items Number of acceptable items

Y = number of acceptable items 0, 1, 2, . . . , 600

Send out 5,000 sales letters

Number of people responding to the letters

Z = number of people responding to the letters

0, 1, 2, . . . , 5,000

Build an apartment building

Percent of building completed after 4 months

R = percent of building completed after 4 months

0 … R … 100

Test the lifetime of a lightbulb (minutes)

Length of time the bulb lasts up to 80,000 minutes

S = time the bulb burns 0 … S … 80,000

Dr. Florian Gerth - MBA911 - Quantitative Economics

Random Variables

EXPERIMENT OUTCOME RANGE OF RANDOM VARIABLES

RANDOM VARIABLES

Students respond to a questionnaire Strongly agree (SA)

Agree (A)

Neutral (N)

Disagree (D)

Strongly disagree (SD)

1, 2, 3, 4, 5

One machine is inspected Defective

Not defective

0, 1

Consumers respond to how they like a product

Good

Average

Poor

1, 2, 3

5 if SA 4 if A

= 3 if N 2 if D 1 if SD

X

      

  

0 if defective =

1 if not defective Y

3 if good = 2 if average

1 if poor Z

    

Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Distributions

• For discrete random variables, probability value assigned to each event – Statistics class of 100 students – Quiz with five problems with 1 point for each correct answer – Lowest score = 1, highest score = 5

• Three rules for all probability distributions: 1. Events are mutually exclusive and collectively exhaustive 2. Individual probability values between 0 and 1 3. Total probability sums to 1

Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Distributions Probability Distribution for Quiz Scores

RANDOM VARIABLE (X) SCORE

NUMBER PROBABILITY P(X)

5 10 0.1 = 10÷100

4 20 0.2 = 20÷100

3 30 0.3 = 30÷100

2 30 0.3 = 30÷100

1 10 0.1 = 10÷100

Total 100 1.0 = 100÷100

• Developed using relative frequency approach

Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Distributions

Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Distributions

• Central tendency of the distribution is the mean or expected value

• Amount of variability is the variance

Dr. Florian Gerth - MBA911 - Quantitative Economics

Expected Value of a Discrete Probability Distribution

• Expected value is a measure of the central tendency of the distribution

( ) ( ) =

=

= + + +

∑ 1

1 1 2 2

X X X

X (X ) X (X ) ... X (X )

n

i i i

n n

E P

P P P

where Xi = random variable’s possible values

P(Xi) = probability of each possible value of the random variable

= summation sign indicating we are adding all n possible values

E(X) = expected value or mean of the random variable

 Nothing else than a weighted average of the values of the random variable.Dr. Florian Gerth - MBA911 - Quantitative Economics

• For the quiz scores

( ) ( ) =

=

= + + + + = =

∑ 1

1 1 2 2 3 3 4 4 5 5

X X X

X (X ) X (X ) X (X ) X (X ) X (X ) (5)(0.1) + (4)(0.2) + (3)(0.3) + (2)(0.3) + (1)(0.1) 2.9

n

i i i

E P

P P P P P

Expected Value of a Discrete Probability Distribution

Dr. Florian Gerth - MBA911 - Quantitative Economics

Variance of a Discrete Probability Distribution

σ =

= = −∑2 2

1 Variance [X (X)] (X )

n

i i i

E P

where

Xi = random variable’s possible values E(X) = expected value of the random variable

[Xi − E(X)] = difference between each value of the random variable and the expected value

P(Xi) = probability of each possible value of the random variable

Dr. Florian Gerth - MBA911 - Quantitative Economics

• For quiz scores

=

= −∑ 2

1 Variance [X (X)] (X )

n

i i i

E P

Variance = (5 − 2.9)2(0.1) + (4 − 2.9)2(0.2) + (3 − 2.9)2(0.3) + (2 − 2.9)2(0.3) + (1 − 2.9)2(0.1)

= (2.1)2(0.1) + (1.1)2(0.2) + (0.1)2(0.3) + (−0.9)2(0.3) + (−1.9)2(0.1)

= 0.441 + 0.242 + 0.003 + 0.243 + 0.361 = 1.29

Variance of a Discrete Probability Distribution

Dr. Florian Gerth - MBA911 - Quantitative Economics

• Standard deviation is the square root of the variance

where

σ = =

square root standard deviation

Variance of a Discrete Probability Distribution

Dr. Florian Gerth - MBA911 - Quantitative Economics

• Standard deviation is the square root of the variance

where

σ = =

square root standard deviation

For this example

σ =

= =

Variance

1.29 1.14

Variance of a Discrete Probability Distribution

See notes on the board Dr. Florian Gerth - MBA911 - Quantitative Economics

Using Excel

See Excel File – “Session 1” – “2.1” Dr. Florian Gerth - MBA911 - Quantitative Economics

Using Excel

See Excel File – “Session 1” – “2.1” Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Distribution of a Continuous Random Variable • The fundamental rules for continuous random variables must be modified

1. The sum of the probability values must still equal 1 2. The probability of each individual value of the random variable occurring must

equal 0 or the sum would be infinitely large • The probability distribution is defined by a continuous mathematical

function called the probability density function or just the probability function represented by f (X)

• E.g., time, ounces, temperature, length, weight

Dr. Florian Gerth - MBA911 - Quantitative Economics

Probability Distribution of a Continuous Random Variable Probability Density Function  the area underneath the curve represents probability  to find any probability, we simply find the area under the curve associated with the range of interest

Most likely outcome

Probability Density Function, f(x)

Probability that weight is between 5.22 and 5.26

Dr. Florian Gerth - MBA911 - Quantitative Economics

Different kinds of probability distributions • Continuous Distributions

1. F-Distribution 2. Normal Distribution 3. Exponential Distribution

• Discrete Distributions 1. Poisson Distribution 2. Binomial Distribution

Dr. Florian Gerth - MBA911 - Quantitative Economics

The Normal Distribution • One of the most popular and useful continuous probability distributions

• The probability density function

2

2 ( ) 21( ) =

2

x

f X e µ

σ

σ π

− −

The normal distribution is specified completely when values for the mean, µ, and the standard deviation, σ, are known! I do not need to know anything about the other two moments (do you remember what they are?).Dr. Florian Gerth - MBA911 - Quantitative Economics

The Normal Distribution

Normal Distribution with Different Values for μ (mean)

Differing values of µ will shift the average or centre of the normal distribution  overall shape remains the same.

Dr. Florian Gerth - MBA911 - Quantitative Economics

The Normal Distribution Normal Distribution with Different Values for σ (standard deviation)

Differing values of σ will make the curve steeper and flatter.

Dr. Florian Gerth - MBA911 - Quantitative Economics

The Normal Distribution

• Symmetrical with the midpoint representing the mean • Shifting the mean does not change the shape • Values on the X axis measured in the number of standard deviations

away from the mean • As standard deviation becomes larger, curve flattens • As standard deviation becomes smaller, curve becomes steeper

Dr. Florian Gerth - MBA911 - Quantitative Economics

From normal to standard normal distribution Step 1 • Convert the normal distribution into a standard normal distribution

– Mean of 0 and a standard deviation of 1 – The new standard random variable is Z

= XZ µ σ −

where X = value of the random variable we want to measure μ = mean of the distribution σ = standard deviation of the distribution Z = number of standard deviations from X to the mean, μ

Dr. Florian Gerth - MBA911 - Quantitative Economics

From normal to standard normal distribution This is done because without a standard normal distribution a different table would be needed for each pair of µ and σ values  do you understand why?

Dr. Florian Gerth - MBA911 - Quantitative Economics

• For μ = 100, σ = 15, find the probability that X is less than 130

130 100= = 15

30= = 2 std dev 15

XZ µ σ − −

Normal Distribution Showing the Relationship Between Z Values and X Values

From normal to standard normal distribution

Dr. Florian Gerth - MBA911 - Quantitative Economics

Step 2 • Look up the probability from a table of normal curve areas • Use Appendix A or Table 2.10 • Column on the left is Z value • Row at the top has second decimal places for Z values

From normal to standard normal distribution

Dr. Florian Gerth - MBA911 - Quantitative Economics

AREA UNDER THE NORMAL CURVE Z 0.00 0.01 0.02 0.03

1.8 0.96407 0.96485 0.96562 0.96638 1.9 0.97128 0.97193 0.97257 0.97320 2.0 0.97725 0.97784 0.97831 0.97882 2.1 0.98214 0.98257 0.98300 0.98341 2.2 0.98610 0.98645 0.98679 0.98713

For Z = 2.00 P(X < 130) = P(Z < 2.00) = 0.97725 P(X > 130) = 1 − P(X ≤ 130) = 1 − P(Z ≤ 2)

= 1 − 0.97725 = 0.02275

From normal to standard normal distribution

Dr. Florian Gerth - MBA911 - Quantitative Economics

Example

• Company builds apartment buildings • Total construction time follows a

normal distribution • For triplexes, μ = 100 days

and σ = 20 days • Contract calls for completion in 125 days • Late completion will incur a severe

penalty fee • Probability of completing in 125 days?

Dr. Florian Gerth - MBA911 - Quantitative Economics

• Compute Z

125 – 100= = 20

25= =1.25 20

XZ µ σ −

• From Appendix A, for Z = 1.25 area = 0.89435

Example

Dr. Florian Gerth - MBA911 - Quantitative Economics

• Compute Z

125 – 100= = 20

25= =1.25 20

XZ µ σ −

• From Appendix A, for Z = 1.25 area = 0.89435

Example

The probability is about 0.89 that the company will not violate the contract

Dr. Florian Gerth - MBA911 - Quantitative EconomicsSee Excel File – “Session 1” – “2.3”

• If finished in 75 days or less, bonus = $5,000 • Probability of bonus?

75 – 100 20

–25 –1.25 20

XZ µ σ −

= =

= =

• Because the distribution is symmetrical, equivalent to Z = 1.25 so area = 0.89435

Example

Dr. Florian Gerth - MBA911 - Quantitative Economics

• If finished in 75 days or less, bonus = $5,000 • Probability of bonus?

75 – 100 20

–25 –1.25 20

XZ µ σ −

= =

= =

• Because the distribution is symmetrical, equivalent to Z = 1.25 so area = 0.89435

Example

P(X > 125) = 1.0 − P(X ≤ 125) = 1.0 − 0.89435 = 0.10565

The probability of completing the contract in 75 days or less is about 11%

Dr. Florian Gerth - MBA911 - Quantitative EconomicsSee Excel File – “Session 1” – “2.3”

• Probability of completing between 110 and 125 days? P(110 < X < 125) = P(X ≤ 125) − P(X < 110)

• P(X ≤ 125) = 0.89435

110 – 100 20

10 0.5 20

XZ µ σ −

= =

= =

For Z = 0.5 area = 0.69146

Example

Dr. Florian Gerth - MBA911 - Quantitative Economics

• Probability of completing between 110 and 125 days? P(110 < X < 125) = P(X ≤ 125) − P(X < 110)

• P(X ≤ 125) = 0.89435

110 – 100 20

10 0.5 20

XZ µ σ −

= =

= =

For Z = 0.5 area = 0.69146

Example

P(110 ≤ X < 125) = 0.89435 − 0.69146 = 0.20289

The probability of completing between 110 and 125 days is about 20%

Dr. Florian Gerth - MBA911 - Quantitative Economics

Standard Normal Distribution

AREA UNDER THE NORMAL CURVE Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.5 .69146 .69497 .69847 .70194 .70540 .70884 .71226 .71566 .71904 .72240

0.6 .72575 .72907 .73237 .73536 .73891 .74215 .74537 .74857 .75175 .75490

0.7 .75804 .76115 .76424 .76730 .77035 .77337 .77637 .77935 .78230 .78524

0.8 .78814 .79103 .79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327

0.9 .81594 .81859 .82121 .82381 .82639 .82894 .83147 .83398 .83646 .83891

1.0 .84134 .84375 .84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214

1.1 .86433 .86650 .86864 .87076 .87286 .87493 .87698 .87900 .88100 .88298

1.2 .88493 .88686 .88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147

1.3 .90320 .90490 .90658 .90824 .90988 .91149 .91309 .91466 .91621 .91774

1.4 .91924 .92073 .92220 .92364 .92507 .92647 .92785 .92922 .93056 .93189

1.5 .93319 .93448 .93574 .93699 .93822 .93943 .94062 .94179 .94295 .94408 Dr. Florian Gerth - MBA911 - Quantitative Economics

Using Excel Output for the Normal Distribution Example

See Excel File – “Session 1” – “2.3” Dr. Florian Gerth - MBA911 - Quantitative Economics

The Empirical Rule

• For a normally distributed random variable with mean μ and standard deviation σ

• Approximately 68% of values will be within ±1σ of the mean • Approximately 95% of values will be within ±2σ of the mean • Almost all (99.7%) of values will be within ±3σ of the mean

Dr. Florian Gerth - MBA911 - Quantitative Economics

The Empirical Rule

Dr. Florian Gerth - MBA911 - Quantitative Economics

The F Distribution

• It is a continuous probability distribution • The F statistic is the ratio of two sample variances • F distributions have two sets of degrees of freedom • Degrees of freedom are based on sample size and used to calculate the

numerator and denominator df1 = degrees of freedom for the numerator df2 = degrees of freedom for the denominator

• The probabilities of large values of F are very small

Dr. Florian Gerth - MBA911 - Quantitative Economics

The F Distribution

Dr. Florian Gerth - MBA911 - Quantitative Economics

The F Distribution

• Consider the example df1 = 5 df2 = 6 α = 0.05

From Appendix D, we get Critical Value = Fα, df1, df2

= F0.05, 5, 6 = 4.39 This means

P(F > 4.39) = 0.05

The probability is only 0.05 F will exceed 4.39

Significance level

F-Statistic (given through calculations)

Dr. Florian Gerth - MBA911 - Quantitative Economics

The F Distribution

Dr. Florian Gerth - MBA911 - Quantitative Economics

Using Excel

See Excel File – “Session 1” – “2.4” Dr. Florian Gerth - MBA911 - Quantitative Economics

What to do now…

1. MCQs (30 minutes) 2. Tutorial questions (60 minutes) 3. Come back and we discuss the tutorial questions (45 minutes) 4. Economics discussion (30 minutes) - Hope for Eurozone Rebound Dashed

5. Come back and we discuss the tutorial questions (15 minutes)

Dr. Florian Gerth - MBA911 - Quantitative Economics

Questions?

Dr. Florian Gerth - MBA911 - Quantitative Economics