Teaching Economics Series

Arnold Wentzel

Overview

1. Knowing what to teach 2. Techniques of explaining concepts in Economics 3. Principles of explaining ideas in Economics 4. Explaining graphs and equations in Economics 5. Making ideas interesting in Economics 6. Making ideas memorable in Economics 7. Basics of assessment in Economics 8. Designing appropriate assessments in

Economics 9. Using PowerPoint slides appropriately

Teaching Economics Part 3: Explaining graphs and

equations

Arnold Wentzel

Basics

• Economics = cause-effect stories

• We tell it through:

– Graphs

– Equations

• How I realised it and refined it…

And then the buyer’s income went up and look how his demand

curve shifted! WOW!

We love story time!

Pixar’s 22 rules of storytelling

• Rule 4: Once upon a time there was ___. Every day, ___. One day ___. Because of that, ___. Because of that, ___. Until finally ___.

• Finding Equi: Once upon a time there was equilibrium. One day something happened that upset this equilibrium. Because of that, something else happened… Until finally equilibrium was found again.

FIRST, TELL THE STORY OF THE AXES

Axes as cause-effect framework

Cause/Effect

Effect/Cause

Price-Quantity AD-Y Cost-Quantity ConsumeA-ConsumeB

OutputA-OutputB

AD

Y

The story of the Keynesian axes

SECOND, TELL THE STORY OF THE CURVES

Curves as manifestations of agency

• Agency = ability to choose

• Curves represent cause-effect relationships for different agents or groups of agents

Story of a curve

P

Q

Those making choices about how much to buy – what is their story?

Story of a curve

P

Q

Those making choices about how much to sell – what is their story?

Story of a curve

AC

Q

Those making choices about how much to produce – what is their story?

THIRD, TELL THE STORY OF EQUILIBRIUM

Story of equilibrium and dis~

AD

Y

Story of why no change is needed… Story of how disequilibrium forces change…

Income

Production Spending

AS AD

AS AD AS

AD

Unemployment rises Inflation rises

Story of equilibrium

P

Q

Flea market negotiations…

Story of disequilibrium (Ice cream on the coldest day of the year)

P

Q

Items left on my table at the end of the day… What will change?

P

Q

Items on my table all gone at end of day, but people still in line What will change?

Story of disequilibrium (World Cup Final Match)

FOURTH, TELL THE STORY OF CHANGE

Understanding shifts

• Any change inside the framework = no shift

– i.e. if the inside-cause changes and the inside-effect responds – move along

– Everything else stays the same

• Any other cause outside the framework…

– …changes both the inside-cause and inside-effect

– Needs a third axis, or else…

– …the whole cause-effect relation needs to change

Principle

P QD

y x

Example: AA-curve cause-effect system

M P

M/P

R

L

M* P*

M*/P*

R*

L*

Ee

Exchange

rate

Foreign asset market Domestic asset market

Y Y*

Shows more clearly why we need ceteris paribus…

The story behind the shift

• Does the cause lead to…

– …more of the effect (usually right)?

– …less of the effect (usually left)?

• More = away from zero (hence right)

• Less = toward zero (hence left)

Every shift has a story

P

Q 0

Every day… …then one day… …and then… …and then… …until …

Use colours and animations

P

Q 0

FIFTH, FINDING EQUI AGAIN…

Approach

• Story of the axes frame everything

• Curves represent agents with their own story of how they make choices

• Equilibrium is the story of why change is not needed

• Shifts follow the Pixar story pattern:

– Equilibrium-change-equilibrium

Then as Q rose by 2 units, AC rose by 3.2 units… and the accountant cried out,

“Oh, no! We have diseconomies of scale!”

And there was great panic…

Basics

• Graphs are convertible into equations

• Both involve:

– Causes and an effect (variables)

– A starting point (intercept and equilibrium)

– Cause-effect change (coefficients and signs)

• Equations as effect factories…

Operators & symbols have meanings

• Multiply: interaction or inseparable

• Divide: comparison

• %: to judge size

Signs have meanings

• Plus: positive cause-effect relation

– Cause then Effect

– Cause then Effect

• Minus: negative cause-effect relation

– Cause then Effect

– Cause then Effect

• No problem if you know the story

Interest rate parity story

M P

M/P

r

L

M* P*

M*/P*

r*

L*

Ee

Exchange rate

Foreign asset market Domestic asset market

38

Y Y*

𝒓 = 𝒓∗ + 𝑬𝒆 − 𝑬

𝑬

Coefficients mean something • Link cause to effect

Time = B x Result

• Bigger is stronger (elasticity) Time = 0.2 x Result

Time = 1 x Result

Time = 3.5 x Result

Relate story to graph

• Demand story:

– Frame: price (cause) and quantity (effect)

– Start: price too high, nobody buys

– Cause: price falls

– Effect: quantity demanded rises

– Relation: negative

Relate story to equation

• Demand story:

– Frame: price (cause) and quantity (effect)

𝑷 = 𝑎 − 𝑏𝑸

Relate story to equation

• Demand story:

– Frame: price (cause) and quantity (effect)

– Start: price too high, nobody buys

𝑃 = 𝒂 − 𝑏𝑄

Relate story to equation

• Demand story:

– Frame: price (cause) and quantity (effect)

– Start: price too high, nobody buys

– Cause: price falls

– Effect: quantity demanded rises

– Relation: negative

𝑃 = 𝑎 − 𝒃𝑄

Relate equation to graph

P

Q 0

P=a-bQ

Manipulations are…

• …about isolating a cause or an effect

• Why 𝑷 = 𝒂 − 𝒃𝑸 or 𝑸 =𝟏

𝒃(𝒂 − 𝑷)?

• Don’t assume basic skills…

Interest rate parity story

M P

M/P

r

L

M* P*

M*/P*

r*

L*

Ee

Exchange rate

Foreign asset market Domestic asset market

46

Y Y*

𝒓 = 𝒓∗ + 𝑬𝒆 − 𝑬

𝑬

Interest rate parity story

M P

M/P

r

L

M* P*

M*/P*

r*

L*

Ee

Exchange rate

Foreign asset market Domestic asset market

47

Y Y*

𝑬 = 𝑬𝒆

𝟏 + 𝒓 − 𝒓∗

Most equations are stories

• Consumer equilibrium: 𝑀𝑈𝑎

𝑃𝑎=

𝑀𝑈𝑏

𝑃𝑏

• What is the story?

– As long as you have money, keep on spending. Buy those things that offer best value for money.

• What is value for money?

Which one?

Shop A Shop B Shop C

What you get from one battery

100 hours

5 hours

40 hours

Which one?

Shop A Shop B Shop C

What you pay for one R200 R2.50 R10

Which one?

Shop A Shop B Shop C

What you get from one battery

100 hours

5 hours

40 hours

What you pay for one R200 R2.50 R10

Value for money?

Most equations are stories

• What is value for money?

– What you get? (MU)

– What you pay? (P)

– Or what you get for what you pay?

– i.e. MU as compared to P?

• Value for money: 𝑀𝑈𝑎

𝑃𝑎

Story of equi and dis

• If (Value for money)a > (Value for money)b

– Buy A – no equilibrium

– Translate: 𝑀𝑈𝑎

𝑃𝑎>

𝑀𝑈𝑏

𝑃𝑏

• When are you satisfied?

– All money spent

– No product is more attractive

– Translate: 𝑀𝑈𝑎

𝑃𝑎=

𝑀𝑈𝑏

𝑃𝑏

Another example

• PPP: 𝐸 =𝑃

𝑃∗

• What is the story?

A tale of two islands

• A: 1 coconut = $1

• B: 1 coconut = R2

• They start to trade

• Exchange rate should be…?

• What if $1 = R1?

A B

Purchasing power parity

• Arbitrage corrects (sell ZAR and it depreciates)

• Or else: A gets all the money and B gets all the coconuts

=$1 =R2

$1

R2

$1=R1

$2

Exchange rate should reflect price

• ER/$ = P/P* = R2/$1 = 2 so R2=$1

• Exchange reflects relative price levels

=$1 =R2

$1

R2

$1=R2

$1

Derivation of PPP formula

• If for a hamburger PSA = R14 and PUS = $2 which one is more expensive?

• It depends…

• On what?

• To compare – convert into same currency

• How turn PUS into ZAR price?

• PUS in ZAR = PUS x EZAR/$

• PSA = R14 and PUS = $2 x R7/$ = R14

• We have equilibrium…

Absolute PPP

• PSA = PUS (in ZAR)

• PSA = PUS x EZAR/$

• Solve for EZAR/$

• EZAR/$ = PSA/PUS or E = P/P* • So if E = R7/$ it means…

• PPP: Prices of same basket of goods are equal

Approach

• Deconstruct an equation

– Cause, effect, relation and strength

– If there is a diagram, relate them

• Reconstruct it with a story

– Show how the story creates the equation

Challenge

• For a graph of your choice, develop an explanatory story

• For an equation of your choice, develop an explanatory story