Intro to Microeconomics 

What is efficiency?

Exam 1: Chapters 1­5 

Monday, October 1, 2018

Objectives

Chp 1

- Define economics and distinguish between micro and macro economics - Explain the notion of opportunity cost

- Identify the opportunity cost of a given action/choice

- Use marginal analysis to predict decisions

- Describe the benefit of allocating resources using economic markets and the limits of  such markets

Chp 2

- Recognize the importance of assumptions and model in economics

- Distinguish between positive and normative statements

- Describe the movement of inputs, outputs, and dollars in an economy using the circular flow diagram

- Relate the productions possibilities frontier to the concepts of scarcity, efficiency,  opportunity cost, and diminishing marginal returns

Chp 3

- Recognize how trade influence everyday life

What is inferior goods in marketing?

Don't forget about the age old question of gatech math

- Distinguish between absolute and comparative advantage

- Explain why trade occurs according to the Principle of Comparative Advantage - Identify areas of specialization, mutually beneficial terms of trade, and consumption  possibilities given a scenario

Chp 4

- Recall the laws of demand and supply

- Distinguish between changes in quantity demanded (supplied) and changes in demand  (supply)

- Explain the role of markets in determined prices and quantities sold

- Illustrate how changes in economic factors affect markets using the supply­and­demand  model

Chp 5

­ Define, calculate, and interpret price/income/cross­price elasticity of demand and price  elasticity of supply

­ Identify factors influencing demand and supply elasticities 

­ Relate price elasticity of demand to total revenue

Chp 1: Principles of Economics 

What is the meaning of quantity supplied?

Economics 

- The choices we make when we can’t get everything we want

- How society allocates scarce resources among competing uses

Microeconomics

- Ten Principles of Economics 1­7

How people make decisions

1. People face trade­offs

2. The cost of something is what you give up to get it

3. Rational people think at the margin

4. People respond to incentives

How people interact

5. Trade can make everyone better off

6. Markets are usually a good way to organize economic activity

7. Governments can sometimes improve market outcomes We also discuss several other topics like dq2 guide

- Production: output in individual industries and businesses

- Prices: prices of individual good and services

- Income: distributions of income and wealth

- Employment: employment by individual businesses or industries

Macroeconomics

- Ten Principles of Economics 8­10

How the Economy as a Whole Works

8. A country’s standard of living depends on its ability to produce goods and  services.

9. Prices rise when the government prints too much money.

10. Society faces a short­run trade­off between inflation and unemployment - Production: national output We also discuss several other topics like ger 2010 class notes

- Prices: aggregate price level

- Income: national income

- Employment: (un)employment in the economy

Some Fields of Economics

- Econometrics

- Development economics

- Labor economics

- Health economics

- Environmental economics

- Comparative economics

- Sports economics 

- Industrial organization

- Regional economics 

- Economics history

Societal Tradeoffs

- Most decisions we make are economic; we act with considering weighed tradeoffs. - Three key tradeoffs in society:

1. Resources: What gets produced?

Allocation of resources 

2. Producers: How is it produced?

Distribution of output/Mix of output 

3. Households: Who gets what is produced?

Opportunity cost

- opportunity cost: the value of the best alternative use of a resource; the value of the next  best thing; includes explicit & implicit costs

Ex: there is no such things as a free lunch because you would spend your time, the best  alternative, waiting for it

- explicit cost: direct payment made to others in the course of running a business Ex: wage, rent, materials Don't forget about the age old question of pinacocytes function

- implicit cost: any cost that results from using an asset instead of renting/selling it - opportunity gain: the value of the contribution of a resource

- sunk cost: the value of a cost that has already been made and cannot be recovered

Thinking at the Margin

- marginal change: a small incremental adjustment to an existing plan of action - A rational decision maker aims to get greatest benefit/satisfaction & compares marginal  benefits to marginal costs

- Take action IF marginal benefit greater/equal to marginal cost; then reevaluate for next  step

Incentive

- incentive: anything that induces you to act

- Can be positive (trying to get us to come to class for participation points) or negative  (trying to get us not to cheat with bad grades and disciplinary action) We also discuss several other topics like the process by which social structures are increasingly characterized by the most direct and efficient means to their ends is called rationalization.

Trade

- Mutually beneficial

- Enables specialization

- Promotes variety

The Role of Prices in Markets

- market: an exchange mechanism that allows buyer to trade with sellersDon't forget about the age old question of reinforcing contributory cause

- price: influences decisions of buyers and sellers and is likewise influenced by their  decisions

- A pure market economy relies only on the forces of supply and demand to set the prices  of goods and services (i.e. the invisible hand); no intervention by government - Economic spectrum

o Communism: planned system, high degree of government control, high level of  social services

o Socialism

o Capitalism: free market systems, low degree of government control, low level of  social services

o U.S. on economic spectrum: U.S. is a mixed economy (somewhere btw socialism  and communism). Markets do most of the work, but the government plays a role  in the allocation of many resources (education, roads, medicine, etc)

o Where should U.S. be on economic spectrum? Consensus of poll­ more towards  socialism

Efficiency vs. Equality

- efficiency: achieving the max benefit given available resources (size of economic pie) - equality: equal distribution of benefits

- Which to focus on is debatable

Ex: government safety net programs improve equality but reduce efficiency; balance­  unemployment can’t be too low or too high, people must be applying for jobs

The Role of Government

- Governments help to enforce the property rights necessary for markets to function - Property rights are important because if no one is enforcing them then people will steal - Property rights give you ownership of property and right to transfer ownership; trade­  involuntary exchange; no property rights = no trade

- Government can also improve efficiency when markets fail due to 

o externalities: failure of individuals/firms to internalize costs (ex­ pollution); no  efficient outcome = market failure; government can come in and help (ex: taxes  polluting firm, firm considers extra cost and proceeds)

 Benefits­ positively impacts bystander

 Costs­ negatively impacts bystander

o market power: ability of firms to exercise undue influence in a market

Review 

- Scarce resources force trade­offs 

- Our actions have explicit and implicit costs

- The best decisions are made at the margin; one step at a time, incremental - Allowing trade to be facilitated by markets is generally best, but government can  sometimes help to improve outcomes

Chp 2: Economists Wear Many Hats

Positive vs Normative Statements

- As scientists, economists use positive statements to describe the world as it is  - Positive statements can be confirmed or refuted; fact; can’t argue other side - As policy advisers, economists use normative statements to describe how the world  should be.

- Normative statements can’t be confirmed or refuted; opinion; can argue other side

Disagreements

- Economists may disagree regarding policy prescriptions due to differences in scientific  judgments and values

- Sometimes policy makers don’t follow the advice of economists; it’s complicated

Economists as Scientists

- Engage in an objective search for answers

- Some use experiments to gather data; but, many don’t, because experiments may be  impractical, costly, of unethical

- ask question  conduct background research  construct hypothesis  gather data  analyze data  draw conclusions

Assumptions and Models

- Assumptions help to simplify complex situations and direct attention to a specific aspect  of a problem

- models: simplified representations of reality often in the form of diagrams and equations Ex: maps, diagrams

- circular flow diagram: a simplified, visual representation of the economy that aims to  answer the questions: “How is the economy organized?” & “How do participants in the  economy interact?”

The Production Possibilities Frontier

Figure 1: The Circular Flow Diagram  (source: screenshots from lecture power  point)

- The Production Possibilities Frontier (PPF): a model that shows combinations of two  goods the economy can produce (output) given available resources and technology

Figure 2: PPF Example

- Points on PPF: feasible, efficient (produces  max possible using all resources)

- Points below PPF: feasible, inefficient  (resources are underutilized)

- Points above PPF: Infeasible (too few  resources available)

- The opportunity cost of an item is what must  be given up to obtain that item

- Moving along a PPF involves shifting  resources (Ex: labor) from the production of  one good to the other

- The slope (steepness; rise over run; change in y over change in x) of the PPF tells you the  opportunity cost of one good in terms of the  other; lower slope= lower opportunity cost

- Shape could be straight line (opportunity cost  remains constant) or bow­shaped curve  (opportunity cost rises with population; 

opportunity cost of production differs among goods or diminishing

        marginal returns); depends on the nature of the

        opportunity cost as the economy shifts resources from

        one industry to the other

Diminishing Marginal Returns

- Increasing one input, while holding all others constant, will eventually result in smaller  and smaller additions to output; increasing opportunity costs

- Marginal benefit/cost determined by difference in two points

Changes in the PPF

- PPF graphical representation of the productive capacity of a two­good economy - The PPF may shift or rotate depending on changes in the quantity and/or productivity of  the factors of production

o Shifting reflects changes that have the same impact on both goods

o Rotating reflects changes that impact one good (or, one good more than the other) - Economic growth shifts PPF outward­ can increase possibilities for production of both  products

- Economic growth specific for one product­ rotation of PPF; wouldn’t impact other  product

Review

- The PPF shows all combinations of two goods that an economy can possibly produce,  given its resources and tech

- PPF illustrates the concepts of trade­offs, efficiency, and economic growth - A bow­shaped PPF illustrates the concept of increasing opportunity cost

Cpt 3: Why do People Trade?

Trade in Everyday Life

- Goods and ideas (design) traded from different countries

PPF and Trade

- PPF shows various combinations of output that an economy can produce - Because the PPF reveals the tradeoffs faced in production, it can be used to explain  interdependence among people and nations

- Trade among companies, not just countries, so microeconomic 

- To determine why two people trade, we must determine who has the lower cost of  production

- We can use the PPF to examine differences in the cost of production using two methods: o absolute advantage: compares the productivity of producers – the number of  inputs required to produce one unit of a given good

o comparative advantage: compares the opportunity cost of production – what is  given up to produce an additional unit of a good

The Principle of Comparative Advantage

- Each good should be produced by the person that has the lower opportunity cost of  producing the cost of producing that good

- The games from specialization and trade are based on comparative advantage, not  absolute advantage

Terms of Trade

- terms of trade: amount of one good that must be given up to obtain another - Trade is mutually beneficial if each party can buy a good at a price lower than his/her  opportunity cost

- Acceptable terms of trade are those in which the “price” falls between the opportunity  costs of both parties.

Review

- Specializing and trading according to comparative advantage (not absolute advantage) is  mutually beneficial

- Though trade benefits society overall, some individual producers may “lose” in the  process. 

- Absolute advantage­ can make more of a product when producing only that product vs  competitor 

- Opportunity cost of producing product: not producing/producing

- Specialize dependent on differences in opportunity cost; lower opportunity cost­ should  specialize

- Mutually beneficial­ fall btw two opportunity costs; each country specializes in product  with lower opportunity cost; country selling want prices greater than cost of production - After trade­ leftover product is consumption possibilities 

Cpt 4: Talk is Cheap Because Supply Exceeds Demand

Perfectly Competitive Market

- Goods are homogeneous (exactly the same)

- So many buyers and sellers that non have an influence on price

- Buyers and sellers are price takers

The Supply­and­Demand Model

- The most powerful model in economics

- Used to describe how interactions between producers

and consumers in competitive markets determine the

quantities of a good/service sold and the price at which it

is sold & to analyze the response of markets to change in

economic conditions

Demand

- Consumer side

- Many factors influence what consumers buy, but economists tend to focus on price. - quantity demanded: amount of a good buyers are willing and able to purchase; the sum of individual demands 

- The Law of Demand: all else equal, there is an inverse relationship between price and  quantity demanded

- demand schedule: a table showing the quantity demanded of a good at a given price

- demand curve: the graph that corresponds to the demand schedule; inverse relationship  between price and quantity

- the ceteris paribus assumption (cp): both demand schedules and demand curves hold ALL other factors influencing demand constant

- change price  movement along the demand curve

- change in income, prices of related goods, tastes, expectations, number of buyers  shifts  in the demand curve (changes quantity demand at every price)

- If you want to increase the DEMAND, then change the price of a related good (shifts  line). 

- If you want to increase the QUANTITY DEMANDED, then increase the price of the  good itself (movement along line)

- normal goods: goods for which demand is directly related to income

o income and demand move in the same direction (cp)

- inferior goods: goods for which demand is inversely related to income o income and demand move in opposite directions (cp)

- substitutes: a good that can be used in the place of another good

o An increase in the price of one good leads to an increase in demand for the other  (cp)

Ex: increase price of butter, demand for margarine increases

- complements: goods used in conjunction with one another

o An increase in the price of one good leads to a decrease in demand for the other  (cp)

Ex: increase price of cereal, demand for milk decrease

- Review

o Each point on the demand curve represents the quantity demanded at a given  price.

o The downward slope of the demand curve illustrates the law of demand. o Changes in own­price result in movements along the demand curve.

o Changes in non­price variables result in shifts of the demand curve.

Supply

- Producer side

- quantity supplied: amount of a good sellers are willing and able to sell; the sum of  individual supplies

- Law of Supply: there is a direct relationship between quantity supplied and price (cp) - Similar to demand, the relationship between price and quantity supplied can be depicted  in a table (supply schedule) or in a graph (supply curve) (direct relationship between  price and quantity)

- change price  movement along the supply curve

- change in input prices, technology, expectations, number of sellers  shifts in the supply  curve (changes quantity demand at every price)

- If you want to increase the SUPPLY, then increase an ingredient (shifts line).  - If you want to increase the QUANTITY SUPPLIED, then increase the price of the good  (movement along line)

- Review

o Each point on the supply curve represents the quantity supplied at a given price. o The upward slope of the supply curve illustrates the law of supply.

o Changes in own­price result in movements along the supply curve.

o Changes in non­price variables result in shifts of the supply curve.

Markets

- It’s not OR demand, it’s supply AND

demand. Must have both to have an

exchange and for both consumers and

providers to be happy. 

- Quantity supplied = quantity demanded

(equilibrium) = stable market

- Buyers and sellers have different self

interest. Consumers want low prices

(downward push on price), and providers

want to maximize profit (upward push on

price); need to come to agreement

- Their actions drive the market toward equilibrium with the price of a good regulating the  quantities demanded and supplied.

- Disequilibruim

o Surplus: QS > QD  must lower price to increase demand and come to equilibrium o Shortage: QS < QD  must increase price to reduce demand and come to  equilibrium

- Analyzing Market Changes

1. Ask yourself: Does the supply and/or demand curves shift?

2. If so, in which direction does the curve shift? Show the change in using a supply and­demand diagram.

3. What is the effect of the change on equilibrium price and quantity? Identify the  new equilibrium point on the diagram. Use arrows to show the change in 

equilibrium price and quantity. 

- Examples: 

o If the demand suddenly goes up for a product, and both the equilibrium price and  quantity would increase.

o If the price of a product decreases, supply shifts right, the equilibrium quantity  increases.

o If the price of a substitute decreases, demand shifts down, the equilibrium  quantity and price decrease. 

- Changes in Equilibrium

Changes in Equilibrium: events that shift the supply and/or demand curves

No Change 

in Supply

An Increase 

in Supply

A Decrease 

in Supply

No Change in 

Demand

P same

Q same

P down

Q up

P up 

Q down

An Increase in 

Demand

P up 

Q up

P ambiguous

Q up

(right triangle)

P up 

Q ambiguous

(upper triangle)

A Decrease in 

Demand

P down

U down

P down

Q ambiguous

(lower triangle)

P ambiguous

Q down

(left triangle)

Review

- The laws of demand and supply explain how consumers and producers respond to  changes in price.

- The actions of self­interested buyers and sellers naturally drive markets to equilibrium. - Events affecting non­price variables cause market equilibriums to change. - Due to its simplicity and flexibility, the supply­and­demand model can be used to analyze many market outcomes. 

Cpt 5: Elasticity and Its Application

Elasticity 

­ How much consumers and producers respond to market changes; used to quantify  changes in quantity demanded and supplied 

Elasticity of Demand

Price Elasticity of Demand

­ Price elasticity of demand: how much quantity demanded responds to a change in price  (cp); will always be negative, so use absolute value 

­ %∆P 

o  %∆QD  Demand in Price Elastic

o  %∆QD  Demand in Price Inelastic 

­ Computing Price Elasticity of Demand

o Method 1: The Standard Method: PED= ∆Q D

∆ P

Where  ∆ y=∆ y

initial yx100

Easier way to remember it:  ∆=newvalue−initial value

initial valuex100

Ex: PED= ­1.5  1.5

So a 1% increase in price will result in 1.5% decline in quantity demanded (OR  10% increase = 15% decline)

o Method 2: The Midpoint Formula:

Easier way to remember it:  ∆=newvalue−initial value

midpointx100

­ The price elasticity of demand for a given good depends of whether it has close  substitutions, is classified as a necessity or a luxury, or is narrowly (or broadly) defined.  ­ The time elapsed since a price change (or time horizon) also affects the price elasticity of  demand.

­ Classifying Demand Curves

o Perfectly inelastic: vertical line; no change;  (∆Q D

∆ P=0)

o Relatively inelastic: steeper slope; small change;  (∆Q D

∆ P<1)

o Relatively elastic: less steep slope; large change;  (∆Q D

∆ P>1)

o Perfectly: elastic: horizontal line; extreme change – zero demand to any price  above P0;  (∆Q D 

∆ P=∞)

o Slope:  ∆ P 

∆Q

o Price Elasticity: | ∆Q D

∆ P| 

  ­     Total Revenue  

o (total expenditure): P x Q; the amount paid by buyers and received by sellers o A price increase has two effects on revenue: higher P mean more revenue on each unit you sell, but you sell fewer units (lower QD) due to the law of demand o If demand is price elastic, a price increase causes revenue to fall (inverse  relationship).

o If demand is price inelastic, a price increase causes revenue to rise (direct  relationship).

o Increase supply, lower equilibrium price, not large change in quantity demanded,  price inelastic good, revenue goes down.

Income Elasticity of Demand

­ Income elasticity of demand = percent change in QD/percent change in income o For normal goods, income elasticity > 0

o For inferior goods, income elasticity < 0

o For income elasticity of demand, the sign of the coefficient is important ­ Types of Goods

o Inferior: EI < 0

o Normal

 Necessity: 0 < EI < 1

 Luxury: EI > 1

Cross­Price Elasticity for Demand

­ Cross­price elast of demand  ¿change∈QDfor good 1

change∈price of good 2

­ For substitutes, cross­price elasticity > 0

­ For complement, cross­price elasticity < 0

­ Types of Goods

o Substitutes: EC > 0

o No relationship: EC = 0

o Complements: EC > 0

Elasticity of Supply

Price Elasticity of Supply

­ Price elasticity of supply = change∈QS 

change∈P

­ Elasticity 

o Perfectly inelastic: ES = 0

o Relatively inelastic: 0 < ES < 1

o Relatively elastic: ES > 1

­ Supply Curves

o Perfectly inelastic: PES = 0

o Inelastic: PES < 1

o Elastic: PES > 1

o Perfectly elastic: PES = ∞

­ The flatter the supply curve, the greater the PES; the steeper the supply curve, the lower  the PES. 

­ The price elasticity of supply depends on how easy it is for producers to change the  quantity supplied: time, spare production capacity, storage capacity/available reserves ­ Supply often becomes less elastic as Q rises due to production capacity limits. 

Microeconomics HW Notes Chp 01-05

Homework (Chp 01 & 02) Basic Concepts

∙ Microeconomics is the study of how prices and quantities are determined through  interactions between buyers and sellers (individuals and firms) in individual markets.  Therefore, microeconomists are more likely to create models to analyze the decisions of firms  (such as pricing) and those of consumers (such as shopping choices), as well as how  government policies affect those decisions.

∙ Macroeconomics is the study of factors that affect the entire economy. Therefore,  macroeconomists tend to create models to analyze how aggregate phenomena such as  growth, inflation, and unemployment respond to policy decisions of governments and central  banks, changes in aggregate spending or savings, and supply or demand shocks.

∙ Marginal benefit: an additional satisfaction or utility that a person receives from consuming  an additional unit of a good or service

∙ Opportunity cost: the value of the best alternative use of a resource; the value of the next  best thing; opp cost of a choice includes both the monetary amount paid and the value of your  time given up by making that choice over another  

∙ Law of increasing opportunity costs states that as you increase production of one good,  the opp cost to produce an additional good will increase

∙ A positive statement is one that seeks to describe the world as it is; can always be  supported or refuted by data

∙ A normative statement is one that offers an opinion as to the way the world should be;  require a larger philosophical framework to evaluate  

∙ Describing a statement as positive or normative does not mean true or false.  ∙ Households earn their income when firms purchase or rent factors of production in factor  markets to use them to produce goods and services

∙ Firms earn revenue when households buy goods and services in product markets ∙ Points inside the PPF represent inefficient output combinations where it is possible to increase  the population of both goods because some resources are employed.  

∙ Points on the PPF represent efficient output combinations where it is impossible to increase the production of one good without producing less of the other.

∙ Points outside the PPF represent output combinations that are unattainable given current  resources and technology.  

Homework (Chp 03)

∙ If the resources used in the production of two goods are not specialized and more of product  one is produced than product two, then the opp cost of producing each additional product two  remains constant as more of product two is produced.  

∙ The PPF of two non-specialized products would be a linear PPF instead of a bowed-out PPF. ∙ An individual has an absolute advantage in the production of a good if they can produce a  unit of output using fewer resources than someone else; who can produce more of that good if  both people devote all of their resources to making it

∙ An individual has a comparative advantage in the production of a good if they can produce  a good at a lower opp cost than someone else. A country will specialize in the production of  this good and trade it for other goods.  

∙ Reciprocal opp cost for producing one good is the opp cost for producing the other.  o Ex: Opp cost for producing Good 1 is 5 Good 2. Opp cost for producing Good 2 is 1/5  Good 1.  

∙ Possible for one person to have an absolute advantage in the production of both goods, but  impossible for one person to have a comparative advantage in the production of both goods ∙ When a country imports goods, the consumption of that good must be larger than what the  country produces itself.

∙ When a country exports goods, the consumption of that good must be smaller than what the  country produces itself.  

∙ Without engaging in international trade, any quantity outside a country’s original PPF is  infeasible.

Homework (Chp 04)

∙ Perfectly competitive markets: the goods and services bought and sold are all exactly the  same & there are large numbers of buyers and sellers, such that no single buyer or seller can  affect the market price

∙ In reality, most markets do not perfectly adhere to the assumptions of the perfectly  competitive markets

∙ The quantity demanded of any good is the amount of the god that buyers are willing and  able to purchase at a given price.

∙ The demand curve is a graph that shows the entire relationship between the price of a good  and the quantity of the good demanded; slopes downward

∙ A demand schedule is a table showing the relationship between the price of a good and the  amount that buyers are willing and able to purchase at various prices.

∙ The law of demand states that, other things being equal, the quantity demanded of a good  falls when the price of a good rises.

∙ change price  movement along the demand curve

∙ change in income, prices of related goods, tastes, expectations, number of buyers  shifts in  the demand curve (changes quantity demand at every price)

∙ The quantity supplied of a good is the amount of the good that sellers are willing and able to supply at a given price.  

∙ The supply curve shows the entire relationship between the price of a good and the quanity  of the good supplied; slopes upward

∙ A supply schedule is a table showing the relationship between the price of a good and the  amount of it that sellers are willing and able to supply at various prices.  

∙ The law of supply states that, other things being equal, the quantity supplied of a good  increases when the price of that good rises.

∙ change price  movement along the supply curve

∙ change in input prices, technology, expectations, number of sellers  shifts in the supply curve  (changes quantity demand at every price)

∙ normal goods: goods for which demand is directly related to income

o income and demand move in the same direction (cp)

∙ inferior goods: goods for which demand is inversely related to income

o income and demand move in opposite directions (cp)

∙ substitutes: a good that can be used in the place of another good

o An increase in the price of one good leads to an increase in demand for the other (cp) Ex: increase price of butter, demand for margarine increases

∙ complements: goods used in conjunction with one another

o An increase in the price of one good leads to a decrease in demand for the other (cp) Ex: increase price of cereal, demand for milk decrease

∙ When both the demand and supply curves shift, you can’t always determine the effect on price and quantity without knowing the magnitude of the shirts:

Changes in Equilibrium: events that shift the supply and/or demand curves

No Change  

in Supply

An Increase  

in Supply

A Decrease  

in Supply

No Change in Demand

P same

Q same

P down

Q up

P up  

Q down

An Increase in Demand

P up  

Q up

P ambiguous

Q up

(right triangle)

P up  

Q ambiguous

(upper triangle)

A Decrease in Demand

P down

U down

P down

Q ambiguous

(lower triangle)

P ambiguous

Q down

(left triangle)

∙ Surplus: QS > QD  must lower price to increase demand and come to equilibrium

o If a surplus exists in a market, then the current price must be higher than the  equilibrium price. For the market to reach equilibrium, you would expect buyers to  offer lower prices.

o Downward pressure

∙ Shortage: QS < QD  must increase price to reduce demand and come to equilibrium o If a shortage exists in a market, then the current price must be lower than the  equilibrium price. For the market to reach equilibrium, you would expect buyers to  offer higher prices.

o Upward pressure

Homework (Chp 05)

Don’t forget to do your hw kids.

See finished Chp 5 Notes for Week 5.