Recitation VIII

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Recitation VIII

• Midterm review

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Disclaimer

• This is a brief overview
• Neither sufficient, nor indicative of the test
• This is what I think is the important bits,
• BUT
• It does not explain much, so youll have to refer
  back to your notes if you dont understand
  something
• This slideshow will be available
  atwww.columbia.edu/gpd2101/W3213

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Topics Covered
Growth
Facts about the World
Models
Solow-Swan
AK
Assumptions
Results and Graphs
Predictions
Comparison
Growth Accounting Technology
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Growth

• Facts about the World
• Unlikely to ask specific questions (i.e. poorest
  5 countries etc.)
• BUT likely to ask general questions about
  poverty, inequality and the experience over time

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Growth

• Models
• Solow-Swan
• What you need to know
• Assumptions
• Fundamental Equation(s)
• Graphs
• RELATIONSHIP between graphs and equations
• Predictions How do we test the model?
• What can it be used to predict?
• What cant it be used for?

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Solow Swan 1. Assumptions

• Production (Supply)
• YtF(At,Kt,Lt)
• Properties
• Constant Returns to Scale (CRS)
• Diminishing Returns to Capital
• Example Cobb Douglas function

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Solow Swan 1. Assumptions

• Production (Supply)
• YtF(At,Kt,Lt)
• Properties
• Constant Returns to Scale (CRS)
• Diminishing Returns to Capital
• Example Cobb Douglas function

Do you know what this means? Can you show
whether a function satisfies this? Can you
explain WHY we want to assume this?
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Solow Swan 1. Assumptions

• Demand
• YtCtIt
• Investment
• Two purposes
• Replace broken Capital
• Purchase new Capital
• Hence
• Saving
• Constant fraction s of income
• Combining yields

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Solow Swan 1. Assumptions

• Population
• Grows at constant rate n
• Technology
• Constant A WHY?
• We care about income per person, so divide
  everything by L, using lower case letters to
  denote per capita variables
• E.g.

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Solow Swan 2. Results

• Substituting for y and combining supply and
  demand
• The Fundamental Equation

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Solow Swan 2. Results

• Substituting for y and combining supply and
  demand
• The Fundamental Equation
• What does it mean?
• What does it predict?

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Solow Swan 2. Graph
Graph separately
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Solow Swan 2. Graph
What are on the axes?
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Solow Swan 2. Graph
What are on the axes?
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Solow Swan 2. Graph
What are on the axes?
Richer
Poorer
Why?
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Solow Swan 2. Graph
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Solow Swan 2. Graph
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Solow Swan 2. Graph
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Solow Swan 2. Graph
growth rate
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Solow Swan 2. Graph
growth rate
Of a country at this level of k
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Solow Swan 2. Graph
k
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Solow Swan 2. Graph
k
Steady state level of Capital per capita
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Solow Swan 2. Graph
Do you know what this means? How does a country
get there? What does it predict for growth of
rich vs poor countries?
k
Steady state level of Capital per capita
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Solow Swan 3. Predictions

• What does this model predict?
• Absolute convergence?
• Define
• Conditional convergence?
• Define
• What do we observe in the data?

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Solow Swan 3. Predictions

• Conditional convergence
• Suppose we have two groups of countries
• High savers sHigh
• Low savers sLow
• How would we represent them on the graph?
• What are the implications?

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Solow Swan 3. Cond. Conv.
What does it predict for growth of rich vs poor
countries? Rich high savers vs Poor high
savers? Rich low savers vs Poor low savers? Poor
low savers vs Poor high savers?
kHigh
kLow
Steady state level of Capital per capita
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AK 1. Assumptions

• Everything the same, except the production
  function
• Production Function
• YtF(At,Kt)
• Properties
• Constant returns to scale
• Constant returns to capital
• In per capita terms

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AK 2. Results

• What does the fundamental equation look like now?

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AK 2. Graph
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AK 2. Graph
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AK 2. Graph
growth rate
Of a country at this level of k
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AK 2. Graph
What does it predict for growth of rich vs poor
countries? If countries had different
characteristics?
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AK 3. Results
?
growth rate
growth rate
Poor country klow
Rich country khigh
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AK 3. Results
growth rate
growth rate

Poor country klow
Rich country khigh
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AK 3. Predictions

• What does this model predict?
• Absolute convergence?
• Define
• Conditional convergence?
• Define
• What do we observe in the data?

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Solow Swan vs AK

• Which model has more plausible assumptions?
• Which model comes closer to predicting the
  results we find in the data?

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Technology and Growth Accounting

• Technology, Aids and RD

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Topics Covered
Growth
Business Cycles
Keynesian
Classical
Facts about the World
Labour/Leisure 1 period
Models
Consumption/Saving - 2 periods
Solow-Swan
AK
Consumption/Saving AND Labour/Leisure Current
Period vs Future
Assumptions
Results and Graphs
Predictions
Demand and Supply
Comparison
Effects of Techonology shocks Temporary vs
Permanent
Growth Accounting Technology
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Business Cycles

• Basically, three models that build on each other
• Labor/Leisure choice in 1 period no possibility
  of saving Robinson Crusoe
• Consumption Decisions over two periods add the
  possibility of saving/borrowing
• Consumption over time Labor over time
• Demand and Supply

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Business Cycles

• Important concepts you MUST
• Understand
• Know how to show graphically
• Know the implications for decisions in the
  various periods
• In the first two models
• Wealth Effect
• Substitution Effect
• In the last
• Direct Effect
• Indirect Effect
• (both of these related to income and
  substitutions effects)
• And also
• Permanent vs Temporary changes

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Labour/Leisure choice

• Setup (assumptions)On Production (feasibility)
• No saving/borrowing
• Work for all the income you have, consume all of
  it
• CYwL
• w Wage
• L Hours worked

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Labour/Leisure choice

• Setup (assumptions)On Utility (desirability)
• Increasing in Leisure and Consumption
• Concave prefer the middle to extremes
• These imply indifference curves
• Optimal choice is The point
• On the budget constraint
• On the highest indifference curve
• Tangency point

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Labour/Leisure choice

• Feasible set
• CwL

What are on the axes?
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Labour/Leisure choice

• Feasible set
• CwL

C
L
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Labour/Leisure choice

• Feasible set
• CwL

What is the slope?
wL
C
L
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Labour/Leisure choice

• Feasible set
• CwL

What is the slope?
wL
C
w
1
L
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Labour/Leisure choice

• Indifference curves
• Prefer MORE C and LESS L

C
L
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Labour/Leisure choice

• Optimal decision

wL
C
L
24
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Labour/Leisure choice

• Effects of changes
• We analised 3
• Increase in overtime pay
• Increase in wealth
• Increase in wage
• All this to highlight the substitution and wealth
  effects
• Lets look at a wage increase

wL
C
L
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Labour/Leisure choice

• Wage increase w to w

wL
wL
C
L
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Labour/Leisure choice

• What are the effects?

wL
wL
C
L
24
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Digression Exam technique

• How to make sure your Substitution effect graph
  looks nice
• 1. Draw the initial budget line, and pick the
  point

wL
C
L
24
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Digression Exam technique

• How to make sure your Substitution effect graph
  looks nice
• 2. Draw the IMAGINARY budget line goes trough
  the old point, but has the new slope (steep
  enough)

wL
C
L
24
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Digression Exam technique

• How to make sure your Substitution effect graph
  looks nice
• 3. NOW Draw the indifference curve of the
  ORIGINAL point, so that the IMAGINARY budget line
  is partially above it

wL
C
L
24
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Digression Exam technique

• How to make sure your Substitution effect graph
  looks nice
• 4. Draw the new indifference curve of the
  substitution effect

wL
C
It has to touch In this region
L
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Digression Exam technique

• How to make sure your Substitution effect graph
  looks nice
• 4. Draw the new indifference curve of the
  substitution effect

wL
C
L
24
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Digression Exam technique

• How to make sure your Substitution effect graph
  looks nice
• 5. show the result of the substitution effect

wL
C
L
24
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Digression Exam technique

• How to make sure your Substitution effect graph
  looks nice
• 0. UNDERSTAND and KNOW the result of the
  substitution effect

wL
C
L
24
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Digression Exam technique

• 6. show the TRUE new budget line

wL
C
L
24
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Digression Exam technique

• 7. show the TRUE new optimal point and hence the
  wealth effect

wL
C
L
24
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Digression Exam technique

• 0. UNDERSTAND and KNOW the results of the wealth
  effect

wL
C
L
24
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Labour/Leisure choice

• What are the effects of a wage increase?
• The substitution effect INCREASES labor supply
• The wealth effect DECREASES labor supply
• End result ambiguous
• What do we assume for the macro economy?

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Consumption/Saving choice

• What is the decision we are considering?
• Consumption over time
• What is our budget constraint?
• c1 (c2 /1r) y1 ( y2 /1r)
• How did we derive it?
• WHAT DOES IT MEAN???

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Consumption/Saving choice

• What question do we ask in this model?

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Consumption/Saving choice

• What question do we ask in this model?
• The effect of an interest rate change, on current
  consumption
• What does it depend on?

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Consumption/Saving choice

• What question do we ask in this model?
• The effect of an interest rate change, on current
  consumption
• What does it depend on?
• Whether we are considering a borrower, lender
  (saver), or neither
• What effects are there?

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Consumption/Saving choice

• What question do we ask in this model?
• The effect of an interest rate change, on current
  consumption
• What does it depend on?
• Whether we are considering a borrower, lender
  (saver), or neither
• What effects are there?
• Wealth and Substitution
• What do we assume for the macro economy?

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Consumption/Saving choice

• What question do we ask in this model?
• The effect of an interest rate change, on current
  consumption
• What does it depend on?
• Whether we are considering a borrower, lender
  (saver), or neither
• What effects are there?
• Wealth and Substitution
• What do we assume for the macro economy?
• Only Substitution effect WHY?

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Consumption/Saving choice

• Effect of interest rate increase on the
  Macroeconomy

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Classical Macro interest change
Consumption/Saving choice

• Suppose the interest rate changes increases
• Effects?

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Consumption/Saving choice

• Suppose the interest rate changes increases
• Effects?
• C2 increases
• C1 decreases
• ESSENTIAL POINT

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Consumption/Saving choice

• Suppose the interest rate changes increases
• Effects?
• C2 increases
• C1 decreases
• ESSENTIAL POINT
• Relationship between CURRENT consumption and
  interest rate is

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Consumption/Saving choice

• Suppose the interest rate changes increases
• Effects?
• C2 increases
• C1 decreases
• ESSENTIAL POINT
• Relationship between CURRENT consumption and
  interest rate is NEGATIVE

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Consumption/Saving choice

• Suppose the income increases
• Effects? What does it depend on?

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Consumption/Saving choice

• Suppose the income increases
• Effects?
• Permanent vs Temporary increase

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Consumption/Saving choice

• Suppose the income increases
• Effects?
• Permanent vs Temporary increase
• What is the direction of the effect? (on what?)
• Permanent increase?
• Temporary increase?

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Consumption/Saving choice

• Suppose the income increases
• Effects?
• Permanent vs Temporary increase
• What is the direction of the effect? (on what?)
• Permanent increase positive
• Temporary increase positive
• What is the size of the effect?
• Permanent
• Temporary

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Consumption/Saving choice

• Suppose the income increases
• Effects?
• Permanent vs Temporary increase
• What is the direction of the effect? (on what?)
• Permanent increase positive
• Temporary increase positive
• What is the size of the effect?
• Permanent same size as the Y increase
• Temporary smaller increase than the Y inc.

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Consumption/Saving choice

• This implies a consumption function that depends
  on
• r
• PDV(Y)

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Consumption/Saving choice

• This implies a consumption function that depends
  on
• r NEGATIVELY
• PDV(Y) POSITIVELY

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Consumption/Saving choice
r
C
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Labor/Leisure choice over time

• How does our choice of when to work depend on
  wage?
• If our wage increases do we work more or less?
  Which wage?

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Labor/Leisure choice over time

• How does our choice of when to work depend on
  wage?
• If our wage increases do we work more or less?
  Which wage?
• If our current wage increases relative to our
  future wage, how is our CURRENT labor decision
  affected?

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Labor/Leisure choice over time

• We choose to work RELATIVELY more in periods
  where we are RELATIVELY more productive
• That is wt/wt1 matters, not wt alone
• Wage depends on how productive we are At, so we
  replace wt with At

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Labor/Leisure choice over time

• How does the interest rate influence how we
  allocate our labor?
• If the interest rate goes up, do we have an
  incentive to work more or less now RELATIVE to
  the future?

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Labor/Leisure choice over time

• This implies the Labor supply function is
• But we do not care about labor supply, we care
  about Y income (or consumption)
• What is our production function? (no firms)

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Labor/Leisure choice over time

• This implies the Labor supply function is
• But we do not care about labor supply, we care
  about Y income (or consumption)
• What is our production function? (no firms)

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Supply and Demand

• Production function
• Notice there are three possible things that can
  change

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Supply and Demand

• Production function - Graphically

r
C
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Equilibrium
r
r
C
C
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Equilibrium
r
Why doesr adjust to equilibratesupply
anddemand?
r
C
C
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Equilibrium
r
Why doesr adjust to equilibratesupply
anddemand?
r
C
C
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Supply and Demand - Shocks

• Suppose there is a
• Temporary increase in current technology
• How is Supply affected?
• How is Demand affected?

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Supply and Demand - Shocks

• Suppose there is a
• Temporary increase in current technology
• How is Supply affected?
• How is Demand affected?

Direct effect
Indirect effect
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Supply and Demand - Shocks
r
r
C
C
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Supply and Demand - Shocks
r
D
r
C
C
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Supply and Demand - Shocks
r
I
D
r
C
C
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Supply and Demand - Shocks
r
I
I
D
r
C
C
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Supply and Demand - Shocks
r
I
I
D
r
r
C
C
C
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Supply and Demand - Shocks

• Suppose there is an
• Expected increase in future technology
• How is Supply affected?
• How is Demand affected?

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Supply and Demand - Shocks

• Suppose there is an
• Expected increase in future technology
• How is Supply affected?
• How is Demand affected?

Indirect effect
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Supply and Demand - Shocks
r
r
C
C
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Supply and Demand - Shocks
r
r
C
C
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Supply and Demand - Shocks
r
r
C
C
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Supply and Demand - Shocks
r
r
r
C
C
C
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Keynesian

• VERY important should be questions about it
• Know the different responses and how to draw them
  (see Recitation VII)

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Good Luck!