Business Cycles with Spirit of Capitalism and Conspicuous Consumption in a Multi-Country Growth Model

This paper generalizes the global economic growth model with spirit of capitalism, social status, and conspicuous consumption recently proposed by Zhang (2016). Zhang’s model examines the role of spirit of capitalism, social status, and conspicuous consumption in national and international economic development, trade patterns, and distribution of income and wealth between countries. The multi-country growth model treats social status and wealth accumulation as endogenous variables. This paper generalizes the model by Zhang through making all exogenous constant parameters as exogenous time-dependent parameters. We demonstrate how the system reacts to exogenous periodic perturbations.


Introduction
The purpose of this study is to generalizes the global economic growth model with spirit of capitalism, social status, and conspicuous consumption recently proposed by Zhang (2016).We generalize Zhang's model by making all exogenous constant parameters as exogenous time-dependent parameters.With the generalized model we can show how the system reacts to any type of exogenous changes.This study emphasizes periodic perturbations in order to illustrate sources of business cycles.any exogenous influences.Many theoretical and empirical research about mechanisms and phenomena of economic fluctuations are published (e.g., Zhang, 1991Zhang, , 2005Zhang, , 2006;;Lorenz, 1993;Flaschel et al 1997;Chiarella and Flaschel, 2000;Shone, 2002;Gandolfo, 2005;Puu, 2011;Tian, 2015).These studies deal with economic business cycles on the basis of different economic theories.This study introduces real shocks to Zhang's model.The main difference between this study and Zhang (2016) is that this study deals with the exogenously fixed parameters as exogenous time-dependent parameters.Section 2 generalizes Zhang's model.In Section 3 we demonstrate that the movement of the global economy of J countries are described by J differential equations.The simulation shows some dynamic properties of the global economy of three national economies.Section 4 carries out comparative dynamic analysis with regard to exogenous periodic oscillations.Section 5 concludes the study.

The Multi-Country Trade Growth Model with Social Status
This section is to generalize Zhang's global growth model with spirit of capitalism and conspicuous consumption by making all exogenous constant parameters to be exogenous time-dependent (Zhang, 2016) ).Like Uzawa's two-sector growth model (Uzawa, 1961), each country has two -capital good and one consumer goodsectors.We describe the production sectors on the basis of neoclassical growth theory (e.g., Burmeister and Dobell, 1970;Azariadis, 1993;Barro and Sala-i-Martin, 1995).The modelling of international trade follows the Oniki-Uzawa trade model.As in Ikeda and Ono (1992), we assume that all the countries produce homogenous capital good.The consumer good sector produces goods and services and consumer goods are not tradable in the international markets.Households hold assets of the economy.Households distribute their incomes to consume and save.Exchanges are conducted in perfectly competitive markets.Only households undertake saving.All earnings of firms are distributed in the form of payments to factors of production.We measure prices in terms of the capital good, with the price of the capital good being unit.We denote wage and interest rates by respectively, in the j th country.Free trade implies that the interest rate is equal throughout the world economy, i.e.,    . to stand for the output level of sector m in country .j

The Capital Good Sectors
The production functions of the capital good sectors are specified as follows

The Consumer Good Sectors
We specify the production functions of the consumer good sectors as follows The per capita disposable income in each national economy is the sum of the current disposable income and the value of wealth.We have

Description of Social Status
To illustrate Zhang's approach, we illustrate a few approaches to social status in formal growth theory.By considering social status as a function of wealth, Chen and Guo (2009) assume that each household maximizes its lifetime utility where  measures the degree of the spirit of capitalism,   t c and  , stand for the consumption level and capital stock, respectively, and  implies the time discount rate.We also apply the idea that social status is measured with the level of capital ownership.Chen and Guo (2011) use the following utility function The household gets utility from the wealth-based social status.The status is measured by the physical-capital ownership   t k relative to the economy-wide level of physical capital stock  .

t K
They use 0   to measure the degree of the spirit of capitalism.Corneo and Jeanne (1999) apply the utility function as follows is an individual's social esteem.As in Zhang (2016), we specify social status function j as a function of wealth as follows The utility level is the propensity to consume consumer goods and the propensity to save.

Social Status and Propensities to Save and to Consume
Social status affects the propensities to consume and to save as follows  are time-dependent parameters which may be either positive, zero, or negative.The propensity to consume is increased by social status through conspicuous consumption.The propensity to save is affected by social status as social status is enhanced with rises in wealth.The spirit of capitalism may influence the propensity to save.

Optimal Household Behavior
Maximizing the utility subject to (8) yields

Wealth Accumulation
According to the definition of  , t s j we have the following equation to describe the change in the household's wealth The equation states that the change in wealth is savings minus dissaving.

Demand and Supply
Let   t K stand for the world's capital stocks.The total capital stock employed by country , j  ,

Equilibrium in Global Capital Markets
The world's total capital stock equals the world's wealth is the wealth owned by country .j

Demand and Supply
Equilibrium for consumer goods implies

Trade Balances
The world's output level of capital good is the world net savings where We completed the model.The model is structurally general.In formal economic growth literature some well-known models can be treated as its special cases.For instance, if we assume all the parameters to be constant over time, our model is the same as Zhang's model (Zhang, 2016).Our model is structurally similar to neoclassical growth theory (Solow, 1956;Uzawa, 1961) when the world economy is composed identical economies.It is structurally similar to the Oniki-Uzawa model (Oniki and Uzawa, 1965).

The World Economic Dynamics
The world economy consists of any (finite) number of national economies.Although the dynamic system contains many time-dependent parameters, we succeed in finding a computational procedure for plotting the movement of the world economy at any point in time.We first introduce new variables

Lemma
The dynamics of the world economy with J national economies is governed by the following  J dimensional differential equations system with  , as the variables t defined in the Appendix.The other variables are unique functions of  , By applying the computational procedure in the lemma we can follow the movement of the global economy.We simulate the global economy composed of 3 national economies.The rest of this section follows Zhang (2016) in examining the motion of the system when all the parameters are exogenously fixed.Parameter values specified as follows As in Zhang (2016), the initial conditions are as follows The motion of the variables is plotted in Figure 1.In Figure 1, the global income is We calculate the three eigenvalues as follows The equilibrium point is stable.The stability guarantees that comparative dynamic analysis can be effectively carried out.

Comparative Dynamic Analysis
As stated in the previous sector, when the parameters are specified as in (17), the economy is characterized of a stable equilibrium point.Zhang (2016) also showed how the economy is affected by once-for-all changes in some parameters.We examine how the economy is affected by time-dependent changes in parameters.We interpret the parameter values in (17) as the long-term average values.We allow small perturbations near these long-term parameter values.First, we introduce a variable

Perturbations in the Poor Country's Spirit of Capitalism
The spirit of capitalism refers to preference for owning more wealth.The measurement of spirit is the weight given to social status in the propensity to save.In our approach countries differ in human capital and spirits of capitalism.We study the effects of the periodic perturbations in the parameter measuring spirit of capitalism as follows    . 2 plots the simulation result.As the poor country experiences periodic changes in spirit of capitalism, the social status level of the poor and its propensity to save also experience oscillations.As they are globally connected, the capital good sectors of the global economies experience great changes due to the exogenous perturbations.The wage rates of the three economies experience similar periodic changes.The prices of consumer goods slightly change.With regard to microeconomic variables, the poor country's household experiences periodic changes in the wealth, consumption and preference.The households' behavior of the other two economies change slightly.
Figure 2. Perturbations in the poor country's spirit of capitalism

Perturbations in the Poor Country's Conspicuous Consumption
Conspicuous consumption is narrowly referred to show-off by making more consumption of consumer goods.In our modelling it is related to the weight given to social status in the function of the propensity to consume.We deal with the effects of the periodic changes in the parameter of measuring conspicuous consumption as follows    .
The simulation result is plotted in Figure 3.The economic system experience business cycles.The macroeconomic variables of the three economies oscillate due to the exogenous periodic shocks.The output levels of the consumer good sectors in countries 1 and 2 are slightly affected, even though the input factors are change greatly.
. Perturbations in the poor country's conspicuous consumption

Perturbations in the Rich Country's Propensity to Save
We consider the case that the rich country's propensity to save is perturbed as follows    .
The simulation result is plotted in Figure 4.The economic system experience business cycles.We now allow the poor country's population to be perturbed in the following way The simulation result is plotted in Figure 5.

Perturbations in the Depreciation Rate of Physical Capital in the Poor Country
We now allow the depreciation rate of physical capital in the poor country to be perturbed in the following way    .
The simulation result is plotted in Figure 6.

Perturbations in the Rich Economy's Total Factor Productivity of the Capital Good Sector
We examine the case that the rich country's total factor productivity of the capital good sector is perturbed as follows    .
The simulation result is plotted in Figure 7.
Figure 7.The total factor productivity of capital good sector rises

Conclusions
This paper generalized the global economic growth model with spirit of capitalism, social status, and conspicuous consumption recently proposed by Zhang (2016).Zhang's model examines the role of spirit of capitalism, social status, and conspicuous consumption in national and international economic development, trade patterns, and distribution of income and wealth between countries.The multi-country growth model treats social status and wealth accumulation as endogenous variables.Except the well-known growth models by Solow (1956), Uzawa (1961), and Oniki and Uzawa (1965), the model is based on by the literature on interdependence between economic growth and social status.This paper generalized Zhang's model by making all exogenous constant parameters as exogenous time-dependent parameters.We demonstrated how the system reacts to exogenous periodic perturbations.The study may be extended in different ways.For instance, we can also reveal motion of the model with some more general production functions and utility functions.It is also important to take account of different forms of taxation in the dynamic general equilibrium model.
We thus determine , r , where we apply 11) and (A7) we have .
From (A1) and ( 16), we obtain  With (A17) we take derivatives of (A15) with respect to t to obtain .
We confirmed the lemma.

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dependent positive parameters.The marginal conditions of the capital goods sectors are given by

Figure
Figure 1.The Motion of the economic system We identify the following equilibrium point , 107 .0 , 38 .196 , 95 .89    r K Y

Figure 4 .
Figure 4. Perturbations in the propensity to save 4.4 Perturbations in the Poor Country Population

Figure 5 .
Figure 5. Perturbations in the poor country population

Figure 6 .
Figure 6.Perturbations in the depreciation rate of physical capital A15)There are two solutions.As shown by simulation there is a meaningful solution as follows . The generalization allows us to analyze time-dependent shocks.The world economy consists any number of national economies, each We use subscript index, i and s to stand for capital good sector and consumer good sector, j  Capital is depreciated at an exponential rate  .j ,