Solow Growth Model (Part One) Flashcards
Solow Growth
Notation:
- Y: Measure Total Production (e.g. GNP/GDP)
- K: Capital Stock (physical capital)
- L: Labour (#workers)
- A, alpha: technological parameters (shape, elasticity)
- t: time
Production Function
What is the production fucntion, defined implicitly?
Yt = F(Kt, Lt)
Production Function
What is the Cobb-Douglas specification Production Function
Defined explicitly
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)
Production Function
What is alpha in the production function?
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)
Production Function
What is the Constant Return to Scale (CRS) Technology ?
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
National Income Accounting
Equation and Notation for National Income Accounting:
Now does savings and consumption relate to this?
Y=C+S
Note: Y=C+S (Consumption and Savings)
National output = Income = Consume + Save
Assumptions for Solow Growth Model
Key Assumptions
- Output produced to CRS technology
- Technology exogenous (function)
- Total savings are constant share income, s, S= sY (average savings rate)
Assumptions for Solow Growth Model
Simplifying Assumption
- No governemnt expenditure/revenue: G=0
- No trade (closed economy): NX = 0
- Population (hence, labor L) grows at a constant rate n
Capital Accumulation
What is the equation and intuation for capital stock accumulation and depreciation over time
How does this relate to investment?
Production Function for Per worker
What is the Average Labour Productivity function
How can this be adjusted for a simplified function?
CRS Suppose: z = 1/L
Then: yt = F(kt, 1) = f(kt)
Solow Growth Model: Equilibrium
(1) National Income Accounting
Solow Growth Model: Equilibrium
(2) Savings relating to investing from national income accounting
Solow Growth Model: Equilibrium
(3)How does savings equals investment change whith Assumption three?
Solow Growth Model Equilibrium
(4) and (5): Show Capital Accumulation and the equation expressed in per capita terms.
Solow Growth Model: Equilibrium
(6) Growth in Full employment
Expressed in per worker terms when integrated with capital accumulation
Solow Growth Model: Equilibrium
(7) Capital Stock Per worker
Sketch the graph for the solow growth model?
What are the equilibrium points
k(t+1) = kt =k*
y(t+1) = kt= y*
How can equilibrium points be expressed in terms of the Capital Stock Per Worker Equation
What happens when k’ is below equilibrium k*?
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
What happens when k’’ is above equilibrium k*?
When k > k*:
Population growing too fast for capital stock per worker → captial stock down trm) (K down)
Implications
Implications for Growth:
- Output per workerr in equilibrium → constant
- Total output grows (Y) rate n
Implications
Implications for Savings
Increased savings rate: higher steady state level $k$ and $y$
Positive relationship living standards and savings
s in numerator
Implications
Implications for Population:
High population growth: leads lower steady state levels $k$ and $y$
n in denumerator
