This paper proposes a one-sector multigroup growth model with endogenous labor supply in discrete time. Proposing an alternative approach to behavior of households, we examine the dynamics of wealth and income distribution in a competitive economy with capital accumulation as the main engine of economic growth. We show how human capital levels, preferences, and labor force of heterogeneous households determine the national economic growth, wealth, and income distribution and time allocation of the groups. By simulation we demonstrate, for instance, that in the three-group economy when the rich group's human capital is improved, all the groups will economically benefit, and the leisure times of all the groups are reduced but when any other group's human capital is improved, the group will economically benefit, the other two groups economically lose, and the leisure times of all the groups are increased.

The purpose of this study is to study an economic
growth model with heterogeneous households for providing insights into
relations between economic growth and income and wealth distribution. In the
economic growth literature, the Solow model is the starting point for almost
all analyses of economic growth [

First, we develop a multigroup
model in discrete time [

The production process is described by a neoclassical production function

Divide the two sides of the
above equation by

Consumers
make decisions on choice of consumption levels of services and commodities as
well as on how much to save. In order to provide proper description of
endogenous savings, we should know how individuals perceive the future.
Different from the optimal
growth theory in which utility defined over future consumption streams is used,
we assume that we can find preference structure of
consumers over leisure time, consumption,
and saving at the current state. The preference over current and future
consumption is reflected in the
consumer’s preference structure over leisure,
consumption and saving. This
study uses the approach to consumers’ behavior proposed by Zhang. Theoretical
and empirical implications and applications of the approach are examined in Zhang
[

As output is either consumed or saved, the sum of net
savings and consumption equals output, that is,

The
dynamics consist of

The dynamics of the economic system is governed by the
following

As it is difficult to find explicit conclusions about dynamic behavior of the system, in the remainder of this study we are concerned with a few special cases of the general model.

This section is concerned with the case that there are
two groups of labor force, and the production function takes on the Cobb-Douglas
form by

An equilibrium point of the system is given by

The two-group economy has a unique equilibrium.

It should be noted that as discussed in Appendix

This section examines effects of changes in some
parameters on the economic system. First, we study impact of change in group

From (

To study impact of preference change, we have to
specify change pattern as

This section simulates the
model when the economy consists of three different groups. For illustration, we
specify

At
equilibrium we have

Rather than further examining
these conditions, we simulate the model. To
simulate the model, we specify the groups’ human capital and preferences as
follows:

As the dynamic system has a
unique equilibrium, we can examine impact of changes in the parameters. First,
we examine impact of change in human capital. We fix the parameter values as in
(

We increase levels of human capital of the other two
classes as follows:

We now examine the impact of technological parameter
on the equilibrium values of the dynamic system. We list up the effects on the
variables as follows:

We also examine effects of change in the preferences. We
increase the propensity to save by

We
proposed a one-sector growth multigroup model with endogenous labor supply to
provide some insights into dynamics of wealth and income distribution in a
competitive economy with capital accumulation as the main engine of economic
growth. This study treats capital
accumulation as the main engine of economic growth. It is known that almost all
the contemporary growth models with microeconomic foundation are based on Ramsey’s 1928 paper. As the Ramsey [

We now prove Lemma

From
(

We now show that (

From

We now determine stability of the unique equilibrium.
The Jacobian matrix at equilibrium is given by

The author is grateful to important comments of Editor Huang Weihong and two anonymous referees.