Solow Growth Model (Part One) Flashcards

1
Q

Solow Growth

Notation:

A
  • Y: Measure Total Production (e.g. GNP/GDP)
  • K: Capital Stock (physical capital)
  • L: Labour (#workers)
  • A, alpha: technological parameters (shape, elasticity)
  • t: time
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2
Q

Production Function

What is the production fucntion, defined implicitly?

A

Yt = F(Kt, Lt)

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3
Q

Production Function

What is the Cobb-Douglas specification Production Function

Defined explicitly

A

Cobb-Douglas

For \alpha:

Output elasticity with respect to capital

  • Diminishing return to scale parameters
  • Measure return to scale
  • Factor share of capital (share output is capital)
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4
Q

Production Function

What is alpha in the production function?

A

For \alpha:

Output elasticity with respect to capital

  • Diminishing return to scale parameters
  • Measure return to scale
  • Factor share of capital (share output is capital)
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5
Q

Production Function

What is the Constant Return to Scale (CRS) Technology ?

A

Assumption: “If you double all inputs ⇒ exactly double outputs”

Any Constant: z: zYt = zF(Kt,Lt)

  • Want ot express in per/capita terms (per worker)
  • If multiply all imputs ame factor = same multiply outputs
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6
Q

National Income Accounting

Equation and Notation for National Income Accounting:

Now does savings and consumption relate to this?

A

Y=C+S

Note: Y=C+S (Consumption and Savings)

National output = Income = Consume + Save

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7
Q

Assumptions for Solow Growth Model

Key Assumptions

A
  1. Output produced to CRS technology
  2. Technology exogenous (function)
  3. Total savings are constant share income, s, S= sY (average savings rate)
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8
Q

Assumptions for Solow Growth Model

Simplifying Assumption

A
  • No governemnt expenditure/revenue: G=0
  • No trade (closed economy): NX = 0
  • Population (hence, labor L) grows at a constant rate n
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9
Q

Capital Accumulation

What is the equation and intuation for capital stock accumulation and depreciation over time

How does this relate to investment?

A
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10
Q

Production Function for Per worker

What is the Average Labour Productivity function

How can this be adjusted for a simplified function?

A

CRS Suppose: z = 1/L
Then: yt = F(kt, 1) = f(kt)

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11
Q

Solow Growth Model: Equilibrium

(1) National Income Accounting

A
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12
Q

Solow Growth Model: Equilibrium

(2) Savings relating to investing from national income accounting

A
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13
Q

Solow Growth Model: Equilibrium

(3)How does savings equals investment change whith Assumption three?

A
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14
Q

Solow Growth Model Equilibrium

(4) and (5): Show Capital Accumulation and the equation expressed in per capita terms.

A
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15
Q

Solow Growth Model: Equilibrium

(6) Growth in Full employment

Expressed in per worker terms when integrated with capital accumulation

A
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16
Q

Solow Growth Model: Equilibrium

(7) Capital Stock Per worker

A
17
Q

Sketch the graph for the solow growth model?

What are the equilibrium points

A

k(t+1) = kt =k*
y(t+1) = kt= y*

18
Q

How can equilibrium points be expressed in terms of the Capital Stock Per Worker Equation

A
19
Q

What happens when k’ is below equilibrium k*?

A

When k<k*:

More Capital Stock - accumulated from savings and investment - than need for the population

How much capital stock must increase to keep up with population growth

  • K must increase
20
Q

What happens when k’’ is above equilibrium k*?

A

When k > k*:
Population growing too fast for capital stock per worker → captial stock down trm) (K down)

21
Q

Implications

Implications for Growth:

A
  1. Output per workerr in equilibrium → constant
  2. Total output grows (Y) rate n
22
Q

Implications

Implications for Savings

A

Increased savings rate: higher steady state level $k$ and $y$

Positive relationship living standards and savings

s in numerator

23
Q

Implications

Implications for Population:

A

High population growth: leads lower steady state levels $k$ and $y$

n in denumerator