# the elasticity of substitution

Capital Deepening and
Nonbalanced Economic Growth
Presenter: Dai, Qian
Introduction
• Kaldor Facts: a constant growth rate, a
constant capital-output ratio, and ect.
• A balanced growth consists with Kaldor
facts.
• Nonbalanced growth (approximately
consistent with Kaldor facts):
– Structural changes
– Engel’s law (demand side)
The Mechanism of the Paper
Nonbalanced
Growth
(output in the
sectoral level)
Capital
deepening
Two-sector
model
Price effect
(the elasticity
of substitution)
Kaldor Facts
Framework of the Paper
• Preference
• Population
• Two sectors and production function
• The elasticity of substitution
• Capital depreciation rate:
• Now consider the case
• Assumption1: Sector 1 is more labor
intensive,
• Technological progress:
• Capital and labor market clearing
Analysis
• Normalization: the price of final good
• A competitive equilibrium:
• Markets clearing, firms maximize profits,
and the households maximize their utility.
Technique to solute a competitive
equilibrium
How to characterize the equilibrium
• Step 1. Given K, L, M, the allocation
maximizes Y(t). (static equilibrium)
• Step 2: choosing the dynamics of K or c to
maximize the value function. (dynamics)
• Def. value function
Step 1
• In competitive equilibrium, capital and labor in
two sectors has the same marginal product.
• Define the capital share and labor share in
sector 1.
• Proposition 1: in the competitive
equilibrium,
Implications of proposition 1
• The elasticity of substitution
implies:
• An increase in K(t) causes an increase in
• An increase in M2, causes an increase in
• Factor prices in equilibrium:
Proposition2
Step 2: Dynamics
• Definition
• Proposition 3: Dynamic system
Nonbalanced growth rate, now
define asymptotic growth rate
Theorem 1
• The growth rate and values of all variables
Theorem 2
• We should review the dynamic system
theory.
Calibration
• The main logic of calibration
• To set up the economic system (based
agent behavior)
• To specify the parameters of the model
and run the model.
• To compare the outcome to the factual
parameters
How to apply calibration in the
paper?
• Calibration is based on a benchmark model,
which depicts agent’s behavior, economic
mechanism, and ect.. (the benchmark model in
the paper, section II)
• Specifying all related exogenous variables
(section III)
– Classification of industries
– Specifying variables
– Running the outcome and comparing the results to
the factual data.