Technology and Investment, 2013, 4, 24-26

Published Online Febr uary 2013 (http://www.SciRP.org/journal/ti)

Copyright © 2013 SciRes. TI

A Localization of Solow Growth Model with Labor Growth

Pattern in China

Wang Wanxin, Guo Zequn

Faculty of Business and Economics, The University of Hong Kong, Hong Kong, China

Department of Automation, Tsinghua University, Beijing, China

Email: einsteinw@126.com

Received 2012

ABSTRACT

This paper investigates the Solow Growth Model on a country-specific level by applying the demographic growth pat-

tern in China to it. To localize the neoclassic model, China population growth estimation function based on the Verhulst

Population Model is introduced to transform the population growth rate from a constant to a function, altering the orig-

inal model assumption. By inserting the population growth function into Solow's work, an economy growth phase dia-

gra m for China is obtained. MATLAB programming is used to depict the diagram in a three-dimensional space and to

show that the set of optimal cap ital-labor ratio values lies in the intersecting line of two planes rather than in the inter-

secting point of two curves in the ori ginal model setting. An neoclassical aggregate feasible growth path for China's

economy can be depicted based on a chosen optimal value. The dynamic equilibrium in this case should not be unique;

instead, capital-labor ratio together with population growth situation at a certain time point should be jointly taken into

consideration to solve t he optimization problem in the country's long term economy development.

Keywords: Solow Growth Model; China Population Growth; Optimal Economy Developmen t

1. Introduction

Researchers have been investigating on generalization of

the neoclassical Solow Growth Model [1] in different

directions by applying certain patterns or constraints to

different model factors. The standard neoclassic Solow

Growth Model has an essential assumption that the la-

bor(population) growth in the economy is constant. Ac-

cinelli and Brida [2], B ucci and Guerrini [3], Ferrara and

Guerr i ni [4] implemented several population (labor)

models, for example, Ramsey population model and

Uzawa-Lucase model [5] to Solow's work. However,

researches have not explored enough in terms of revising

the model to a regional level. China is a country worth

attention in terms of its demographical situation, with the

world's largest quantity and relatively high growing rate.

Solow's assumption about a constant population growth

does not suit in the case of China. By inserting a function

simulating China's population growth to the original

model set, a new phase diagram describing the country's

economy growth process can be depicted. The paper

helps study the dynamic equilibrium, namely the coun-

try's optimal growth pattern, in a more accurate stage,

with both the values of population growth and capi-

tal-labor ratio taken in to consideration.

2. The neoclassical Solow Growth Model

Consider the most general case: at time t, an economy

produces product called national product Yt with an ag-

gregate production function F

（

Lt

，

Kt

）

having two factors,

namely, labor (population) Lt and Kt capital. F is twice

differentiable and indicates the diminishing return of

each factor. By assuming population growths in a con-

stant continuous rate r we can get the neoclassical ag-

gregate feasible growt h path kt=f(k t)=(r+ s

µ

)kt–ct, where

µ

is the depreciation rate of capital, s is the propensity to

save. Also, the Solow's path (ksolow,csolow), which is called

the optimal balanced growth path, could be attained

through the formula:

. (1)

3. The localization to China Population

Growth Pattern

According to Luo's [6] modeling work of China's popu-

lation since year 2003, a function Pt, which simulates

annual demographical situation in China, is derived by

revising the Verhulst Population Model [8] with adjust-

ing to country-specific indexes and using Binary Bi-

nomial regression. The function is formulated as: