Minimum Wage , Public Investment , Economic Growth

This paper considers the relationship between economic growth and minimum wage. Minimum wage helps reduce poverty and maintain a minimum standard of living. However, it is also claimed that minimum wage has a negative effect on employment and GDP. This paper develops a simple two-period overlapping generation model with three economic policies, minimum wage, unemployment benefit, and public investment that improves labor productivity. The government imposes tax on firms to finance public capital and unemployment benefit under a balanced budget. We show that economic growth is promoted with an increase in minimum wage and the ratio of public investment to tax revenue.


Introduction
Minimum wage is an economic policy that helps reduce poverty and maintain a minimum standard of living.However, it is also claimed that minimum wage has a negative effect on employment and GDP.Therefore, earlier studies consider the relationship between minimum wage and economic growth in a dynamic framework.Cahuc and Michel [1] introduce human capital accumulation in an endogenous growth model.Ravn and Sorensen [2] consider skill formation accumulated by schooling and training.Askenazy [3] develops endogenous growth model with an open economy and R&D sector.Irmen and Wigger [4] consider minimum wage with a two-country endogenous growth model.Tamai [5] discusses the interaction between inequality and economic growth from the view point of political economy.The above papers assume two sectors or heterogeneous agents.Fanti and Gori [6] consider the relationship between economic growth and minimum wage under a simple one-sector overlapping generation model with 1 homogeneous agents.It is 2 uncertain whether minimum wage promotes economic growth in earlier papers.
This paper introduces public investment that improves labor productivity, for example, infrastructure and medical service.Public investment is an economic policy with an important role in macroeconomic performance.Barro [7], Futagami, Morita and Shibata [8] examine economic growth with public investment that improves labor productivity.Glomm and Ravicumar [9] discuss economic growth including public investment and human capital accumulation.Yakita [10] considers public investment in an aging society.
Following Fanti and Gori [6], this paper introduces public investment that enhances labor productivity and considers the relationship between minimum wage and economic growth.The results obtained in this study are presented below.First, an increase in minimum wage always promotes economic growth.Second, an increase in the ratio of public investment to tax revenue promotes economic growth.
The remainder of this paper is organized as follows.Section 2 presents our model.Section 3 describes the equilibrium.Section 4 summarizes the paper.

Basic Structure
The economy in this paper is based on a basic two-period overlapping generations framework.There exist three agents, households, firms, and the government.
Households live two periods, young and old and supply one unit of labor to the labor market.If they are employed they receive wages, and if they are not employed, they receive unemployment benefit.The utility function in this paper is: , log log where , i y t c i is the young-period consumption of house- is the old-period consumption of household i; i is the index of both employment and unemployment , and is the constant discount factor.The budget constraint of households i is given as: where i t x is the income in young period, i t s is the savings, and is the interest rate.If the households are employed, they receive wags, and if they are not employed, they receive unemployment benefit.In this economy, minimum wages exist.Therefore the relation between minimum wage, and competitive wage, , is given as:.
where 1   is the constant mark-up rate that generates unemployment in the labor market.Households receive unemployment benefit when they are not employed, and is defined as: where is the constant replacement rate.Therefore unemployment benefit is fraction of minimum wage.The optimal allocations of household i are given by: 0,1

Firms
This paper assumes3 the production function as follows:   where t K is the capital stock, t is the public investment, is the labor input, A is the constant parameter, and is the constant parameter.This paper assumes neither depreciation nor population growth.Public investment and unemployment benefit are financed by tax revenue from firms.The profit maximizetion conditions are given as: where t  is the contribution rate for firms to finance public investment and unemployment benefit.In the competitive equilibrium, and hold.Using with Equation ( 5) and ( 9), is presented as: Because t is constant, the unemployment rate, L t L 1 t u   , is also constant for any period t.

Government
The government imposes tax on firms to finance public capital and unemployment benefit.Assuming a balanced budget, the budget constraint of the government is given by:    is the constant ratio of public investment to tax revenue, and is the constant ratio of unemployment benefit to tax revenue.Using Equation ( 5), ( 9), ( 10), ( 12), (14), and the budget constraint of the government is described as follows: is the total expenditure for unemployment benefit, and is the tax revenue.Hence t  is given by: From Equation ( 9), ( 10), ( 12), (13), and (15), is given by: Tax rate t  is an endogenous variable delivered by a balanced budget and this4 assumption is the same as in Fanti and Gori [4].Equation (15) shows that the tax rate is an5 increasing function of the unemployment rate and the ratio of public capital to tax revenue.The intuition is described as follows.If unemployment rate increases, then minimum wage increases and interest rate decreases because labor force becomes relatively scarce to capital.On the other hand, unemployment benefit t also increases with an increase , m t because unemployment benefit is fraction of minimum wage, and the total unemployment benefit t t increases.We assume the ratio of total unemployment benefit to tax revenue is constant and balanced budget.From Equation ( 12) and ( 14), the relationship between total expenditure of unemployment benefit and tax revenue is denoted as t t t t .To satisfy balanced budget when total expenditure of unemployment benefit, t t , increases and interest rate, t , decreases with an increase in unemployment rate, t b should increase.Hence tax rate is an increasing function of unemployment rate.From Equation ( 16), public investment is also an increasing function of unemployment rate; the reason for this is described as follows.When the unemployment rate increases, there are two effects to public investment.First, an increase in the unemployment rate increases t  from Equation (15), and this enlarges public investment because the tax revenue increases.Second, an increase in the unemployment rate decreases t because labor force becomes relatively scarce to capital, and this decrease public investment because the tax revenue decreases.Comparing the two effects, the first effect dominates the second effect.

Equilibrium
In a basic overlapping generations model, the capital stock in period is equal to the savings in period t.The relationship between capital and savings is: where 1 t K  is the capital in period , is the total savings of employees, and is the total savings of unemployment.The dynamics of this economy is shown as follows: because labor force becomes scarce and labor productivity is promoted.Comparing the two effects, the second effect dominates the first effect.Because the total income increases with an increase in  , the savings this economy also increase.Therefore economic growth is promoted with an increase in in  .
Finally, we focus on the effect of the ratio of public investment tax revenue on growth rate.Public investment increases with an increase in the constant ratio of public capital to tax revenue, from Equation ( 16).The derivative of growth rate with respect to  gives: Therefore the following proposition is established.Proposition 2 An increase in the ratio of public investment to tax revenue promotes economic growth.
An increase in the ratio of public investment to tax revenue,  , promotes public investment, and this increases the minimum wage and unemployment benefit, from Equation (5).Therefore both the total wage income and total unemployment benefit increase with an increase in the ratio of public investment.This means that the Copyright © 2013 SciRes.TEL total expenditure on unemployment benefit described as increases even if the ratio of unemployment benefit to tax revenue decreases.

Conclusion
This paper presents a simple endogenous growth model with minimum wage and public investment that improves labor productivity.Minimum wage is an economic policy that helps reduce poverty and maintain a minimum standard of living.However, it is also claimed that minimum wage has a negative effect on employment and GDP.The relationship between minimum wage and economic growth is uncertain in earlier papers.This paper shows that a rise in minimum wage always promotes economic growth.Moreover, this paper shows that a rise in the ratio of public investment to tax revenue promotes economic growth. r