We build a standard overlapping generations model with endogenous fertility and involuntary unemployment. Being different from a log utility function, the capital income tax affects saving at the model of constant relative risk-averse utility function (CRRA function). In the parameter condition, to have the case of non-substitution between consumption in different periods, the capital income tax raises saving to compensate for consumption in the future. Then, results show that a capital income tax improves fertility and unemployment with no social security system

Miyake, Yusuke

Watanabe, Minoru

Yasuoka, Masaya

Munich Personal RePEc Archive

Munich Personal RePEc Archive
Capital income taxation in endogenous
fertility model
Watanabe, Minoru and Miyake, Yusuke and Yasuoka,
Masaya
Hokusei Gakuen University, Kobe University, Kwansei Gakuin
University
20 December 2019
Online at https://mpra.ub.uni-muenchen.de/97721/
MPRA Paper No. 97721, posted 20 Dec 2019 14:07 UTC
1 
 
 
 
Capital income taxation in endogenous fertility model† 
 
 
Minoru Watanabe‡   Yusuke Miyake¶   Masaya Yasuoka§ 
 
 
Abstract 
We build a standard overlapping generations model with endogenous fertility and involuntary 
unemployment. Being different from a log utility function, the capital income tax affects saving at the 
model of constant relative risk-averse utility function (CRRA function). In the parameter condition, to 
have the case of non-substitution between consumption in different periods, the capital income tax 
raises saving to compensate for consumption in the future. Then, results show that a capital income 
tax improves fertility and unemployment with no social security system. 
 
Keywords: capital income tax, fertility, unemployment 
JEL Classifications: J13 J60 
  
                                                      
† We would like to thank seminar participants for helpful comments. Research for this paper was 
supported financially by JSPS KAKENHI Grant Numbers 17K03746 and 17K03791. Nevertheless, 
any remaining errors are the authors’ responsibility. 
‡ Hokusei Gakuen University email: m-watanabe@hokusei.ac.jp 
¶ Kobe University email: teatime567@gmail.com 
§ Correspondence to: School of Economics, Kwansei Gakuin University, 1-155, Uegahara Ichiban-
Cho, Nishinomiya, Hyogo 662-8501, Japan Tel.: +81-798-54-6993, E-mail: yasuoka@kwansei.ac.jp 
2 
 
1. Introduction 
Traditionally, a capital income tax is regarded as decreasing incentives for saving and as hindering 
economic growth if households exist infinitely, similarly to results reported by Chamly (1986). 
However, a capital income tax can contribute to macroeconomic performance within an overlapping 
generations model, as shown Uhlig and Yanagawa (1996). Kunze and Schuppert (2010) find that a 
capital income tax enhances not only economic growth but also employment. However, the impact of 
a capital income tax on fertility choice and unemployment under an overlapping generations model 
are considered only insufficiently in earlier studies. 
 
 
Fig. 1: Unemployment and Total Fertility Rate. 
(Data: OECD Statistics. However, fertility within the EU is based on Eurostat.) 
 
Following Fanti and Gori (2010), a decline of fertility and an increase in unemployment are 
crucially important issues in economically developed countries such as EU countries, as shown in Fig. 
1. Therefore, a child tax is recommended as a remedy for the issues in their study. Wang (2015) states 
that pensions and child subsidies increase fertility and employment. 
We extend Fanti and Gori (2010) and emphasize positive effects of a capital income tax. Results 
show that a capital income tax improves fertility and unemployment with no social security system 
such as one that provides a wage subsidy, child subsidy, and a pension. We assert the originality of the 
points in this paper as follows. For an endogenous fertility model, a logarithmic utility function is 
often assumed.1 However, in the logarithmic utility function, saving is unaffected by the change of 
the interest rate: in fact, the capital income tax has no effect on saving. However, considering the 
                                                      
1 Van Groezen, Leers and Meijdam (2003) and others assume a logarithmic utility function in the 
endogenous fertility model. 
France
Germany
Ita ly
Japan
Spain
U.S.
EU
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
0 5 10 15 20
Tot
al F
ert
ilit
y R
ate
Unemployment  Rate (%)
Unemployment and Total Fertility Rate (2017)
3 
 
constant relative risk averse (CRRA) utility function, the capital income tax raises the saving if it is 
complementary between present consumption and future consumption. Then, by virtue of an increase 
in saving, the capital stock per capita rises. 
The remainder of this article is constructed as follows. Section 2 builds our model. Section 3 derives 
the equilibrium of the model economy and examines the effect of a capital income tax on fertility and 
unemployment. The final section concludes our study. 
 
2. The model 
We construct a two-period overlapping generations (OLG) model with discrete time. The cohort born 
in period ݐ is regarded as generation ݐ, with agents living for two periods: one for the young period 
and the other for the old period. This model economy has agents of three types: households, firms, and 
a government. 
 
2.1.  Firm 
The production function in this model is assumed to have the following form: ௧ܻ ൌ ܣܭ௧ఈܮ௧ଵିఈ , 0 ൏ ߙ ൏ 1, 0 ൏ ܣ,  (1) 
where ௧ܻ represents total output. Here, ܭ௧ stands for capital stock, ܮ௧ denotes labor input, and ܣ 
expresses the technology level of the firm. 
Our paper presents consideration of unemployment with a minimum wage, as examined by Fanti 
and Gori (2010) and by Wang (2015). Particularly,Wang (2015) explain how a pension premium 
affects income per capita in the long run through capital markets. If the pension premium decreases, 
then the effect for capital accumulation is mitigated. This effect raises income per capita. An increase 
in income per capita can raise the pension benefit under the constant premium rate for pensions. 
In the unemployment model, labor input can be presented as ܮ௧ ൌ ሺ1 െ ݑ௧ሻ ௧ܰ ,  (2) 
where ݑ௧ signifies the unemployment rate and ௧ܰ is the population size. We define the fertility rate 
as ݊௧. Actually, ݊௧ can be regarded as the population growth rate and ௧ܰାଵ ൌ ݊௧ ௧ܰ can be reduced. 
The minimum wage is assumed in this model. We consider a model economy in which the minimum 
wage is higher than the competitive wage. We also assume that the capital stock is fully depreciated. 
We can obtain the following equation to maximize the firm profit as ݓ ൌ ሺ1 െ ߙሻܣ݇௧ఈሺ1 െ ݑ௧ሻିఈ ,   (3) 1 ൅ ݎ௧ ൌ ߙܣ݇௧ఈିଵሺ1 െ ݑ௧ሻଵିఈ .  (4) 
Therein, ݓሺ൐ 0ሻ represents the minimum wage, ݇௧ denotes the capital stock per capita ቀൌ ௄೟ே೟ቁ, and ݎ௧ is the interest rate. Because of (3), employment rate 1 െ ݑ௧ can be represented as 
4 
 
1 െ ݑ௧ ൌ ቆሺ1 െ ߙሻܣݓ ቇଵఈ ݇௧.  (5) 
By substitution of (5) into (4), the interest rate can be given as a constant level over time as ݎ௧ ൌ ݎ ൌ ߙܣଵఈ ൬1 െ ߙݓ ൰ଵିఈఈ െ 1.  (6) 
We assume that ݎ ൐ 0. 
 
2.2.  Household 
Households care for the consumption in both young and old period and the number of children 
(fertility). We assume the following Constant Relative Risk Averse (CRRA) utility function as ݒ௧ ൌ ܿ௬,௧ଵିఏ െ 11 െ ߠ ൅ ߚ ܿ௢,௧ାଵଵିఏ െ 11 െ ߠ ൅ ݊௧ଵିఏ െ 11 െ ߠ , 0 ൏ ߚ ൏ 1, 0 ൏ ߠ , (7) 
where ܿ௬,௧ and ܿ௢,௧ାଵ respectively denote consumption in the young and old period. With ߠ ൌ 1, a 
utility function (7) becomes a logarithmic utility function. Our paper presents consideration of 
equation (7), which is more of a general type than a logarithmic type. 
  In the young period, the household obtain wage income ሺ1 െ ݑ௧ሻݓ . 2  Here, ߝሺ൐ 0ሻ  and ݏ௧ 
respectively denote the childcare cost and saving. Then, the budget constraint in the young period can 
be shown as ܿ௬,௧ ൅ ߝ݊௧ ൅ ݏ௧ ൌ ሺ1 െ ݑ௧ሻݓ. (8) 
  Denoting ߬ as the capital income tax rate ሺ0 ൏ ߬ ൏ 1ሻ, the budget constraint in the old period can 
be presented as ܿ௢,௧ାଵ ൌ ሾ1 ൅ ሺ1 െ ߬ሻݎ௧ାଵሿݏ௧. (9) 
Subject to budget constraints (8) and (9), we derive the following allocations to maximize utility (7). ݊௧ ൌ ሺ1 െ ݑ௧ሻݓߝ ൅ ߝଵఏ ൅ ሺߝߚሻଵఏሾ1 ൅ ሺ1 െ ߬ሻݎ௧ାଵሿଵିఏఏ , (10) ݏ௧݊௧ ൌ ሺߝߚሻଵఏሾ1 ൅ ሺ1 െ ߬ሻݎ௧ାଵሿଵିఏఏ , (11) 
 
2.3. Government 
If one assumes the following government budget constraint with a balanced budget  τݎ௧ݏ௧ିଵ ௧ܰିଵ ൌ ܩ௧, (12) 
where ܩ௧  denotes non-productive government expenditure; then ܩ௧  does not contribute to the 
productivity of firms or marginal utility at all.3 Non-productive expenditure ܩ௧ is assumed because 
                                                      
2 We consider that the share of ݑ௧ remains unemployed in the young period. Then, the employment period is given as 1 െ ݑ௧. 3 This assumption is considered by Chamley (1986) and by others. It examines optimal taxation. 
5 
 
we can check the direct effect of the tax on the employment rate and on the fertility rate. 
 
3. Equilibrium 
 
 The equilibrium condition in capital markets is represented as ݇௧ାଵ ൌ ௦೟௡೟. Equations (6) and (11) can 
be derived as 
݇௧ାଵ ൌ ሺߝߚሻଵఏሾ1 ൅ ሺ1 െ ߬ሻݎ௧ାଵሿଵିఏఏ ൌ ሺߝߚሻଵఏ ቐ1 ൅ ሺ1 െ ߬ሻ ቎ߙܣଵఈ ൬1 െ ߙݓ ൰ଵିఈఈ െ 1቏ቑଵିఏఏൌ ݇. (13)
As shown by (13), the capital stock per capita is constant over time. If ߠ is larger than 1(ߠ ൐ 1ሻ, then 
the capital stock accumulation can be facilitated if the capital income tax rate rises because of a 
decrease in the interest rate. With ߠ ൌ 1 as the logarithmic utility function, the interest rate and the 
capital income tax rate do not affect the capital stock. 
Equilibrium in our model economy can be given as equilibrium in the capital stock market. In this 
section, we show that a decrease in capital income brought about by an increase in the capital income 
tax rate induces households to increase saving. Equations (5), (6) and (13) give the long-run 
employment rate as 1 െ ݑ ൌ ቆሺ1 െ ߙሻܣݓ ቇଵఈ ݇
ൌ ቆሺ1 െ ߙሻܣݓ ቇଵఈ ሺߝߚሻଵఏ ቐ1 ൅ ሺ1 െ ߬ሻ ቎ߙܣଵఈ ൬1 െ ߙݓ ൰ଵିఈఈ െ 1቏ቑଵିఏఏ 	. (14)
In general, the minimum wage raises unemployment because of a decrease in labor demand. Therefore, 
equation (14) shows ௗ௨ௗ௪ ൐ 0 ݂݋ݎ	ܽ݊ݕ 	ߠ ൐ 0. In addition, the following expression can be obtained 
because of equations (13) and (14) as ݀݇݀߬ ൐ 0	ܽ݊݀ ݀1 െ ݑ݀߬ ൐ 0 ݂݅ ߠ ൐ 1 . (15)
The output per capita can be shown as ൌ ݇ఈሺ1 െ ݑሻଵିఈ . 
Then, the following proposition can be established. 
 
Proposition 1 
With ߠ ൐ 1, a capital income tax improves long-term employment and output per capita. 
 
6 
 
Kunze and Schuppert (2010) show that an increase in the capital income tax facilitates capital stock 
accumulation and employment. Finally, the effect of capital income tax affects the fertility rate in the 
long run because the household income rises. Considering equations (10), (13), and (14), fertility can 
be derived as 
݊ ൌ ሺ1 െ ݑሻݓߝ ൅ ߝଵఏ ൅ ሺߝߚሻଵఏሾ1 ൅ ሺ1 െ ߬ሻݎሿଵିఏఏᇣᇧᇧᇧᇧᇧᇧᇤᇧᇧᇧᇧᇧᇧᇥୀ௞ ൌ
൬ሺ1 െ ߙሻܣݓ ൰ଵఈ ݇ݓߝ ൅ ߝଵఏ ൅ ݇ 	. (16)
Because of (13) and (16), one can obtain the following and the following proposition: ݀݊݀߬ ൌ ݀݊݀݇ ݀݇݀߬ ൐ 0 ݂݅ ߠ ൐ 1 . (17)
 
Proposition 2 
An increase in the capital income tax rate raises the fertility rate in the long-run if ߠ ൐ 1. 
 
Fanti and Gori (2010) show that a child tax raises the fertility rate. However, our manuscript shows 
that a tax only increases the fertility rate in the long-run, even if the child care cost does not change.4 
The case of ߠ ൐ 1 represents a complementary case or a non-substitution case. Then, an increase 
in capital income tax reduces consumption during the old period. Then, to avoid reduction of 
consumption in the old period, households raise saving to increase consumption in the old period. 
Then, the capital stock per capita increases. Income per capita increases. By virtue of an increase in 
income per capita, the household income rises and fertility increases. Moreover, marginal labor 
productivity rises and the labor demand increases. Consequently, the unemployment rate decreases. 
 
4. Conclusion 
Economically developed countries among the EU membership are confronting a common problem: a 
high unemployment rate and a low fertility rate. As described herein, we set an endogenous fertility 
model with a minimum wage and derive that the capital income tax can raise not only fertility but also 
income per capita. Based on results of our study, as future work we can assess aging population effects 
by considering the survival rate of elderly people. 
 
  
                                                      
4 Fanti and Gori (2010) consider taxation for child care. This taxation increases the child care cost. 
However, the child care cost used for our analyses does not change. Capital accumulation is facilitated 
by a capital income tax. Then income per capita raises fertility. In the setting by Fanti and Gori (2010), 
a child care tax reduces the fertility directly. Then, the capital stock accumulation per capita increases 
and income per capita rises. Finally, household income rises; also, the fertility rate rises indirectly. 
7 
 
References 
Chamley C. (1986) “Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives.” 
Econometrica, vol. 54, pp. 607-622. 
 
Fanti L. and Gori L. (2010) “Child policy solutions for the unemployment problem.” Economics 
Letters, vol. 109, pp. 147-149. 
 
Kunze L. and Schuppert C. (2010) “Financing social security by taxing capital income: A bad idea?” 
FinanzArchiv / Public Finance Analysis, vol. 66, pp. 243-266. 
 
Uhlig H. and Yanagawa N. (1996) “Increasing the capital income tax may lead to faster growth.” 
European Economic Review, vol. 40, pp. 1521-1540. 
 
Van Groezen B., Leers T. and Meijdam L. (2003) “Social security and endogenous fertility: pensions 
and child allowances as siamese twins.” Journal of Public Economics, vol. 87(2), pp. 233-251. 
 
Wang L. (2015) “Fertility and Unemployment in a social security system.” Economic Letters, vol. 133, 
pp. 19-23. 
 


Capital income taxation in endogenous fertility model

Munich RePEc Personal Archive

Munich Personal RePEc ArchiveCapital income taxation in endogenousfertility modelWatanabe, Minoru and Miyake, Yusuke and Yasuoka,MasayaHokusei Gakuen University, Kobe University, Kwansei GakuinUniversity20 December 2019Online at https://mpra.ub.uni-muenchen.de/97721/MPRA Paper No. 97721, posted 20 Dec 2019 14:07 UTC1    Capital income taxation in endogenous fertility model†   Minoru Watanabe‡   Yusuke Miyake¶   Masaya Yasuoka§   Abstract We build a standard overlapping generations model with endogenous fertility and involuntary unemployment. Being different from a log utility function, the capital income tax affects saving at the model of constant relative risk-averse utility function (CRRA function). In the parameter condition, to have the case of non-substitution between consumption in different periods, the capital income tax raises saving to compensate for consumption in the future. Then, results show that a capital income tax improves fertility and unemployment with no social security system.  Keywords: capital income tax, fertility, unemployment JEL Classifications: J13 J60                                                         † We would like to thank seminar participants for helpful comments. Research for this paper was supported financially by JSPS KAKENHI Grant Numbers 17K03746 and 17K03791. Nevertheless, any remaining errors are the authors’ responsibility. ‡ Hokusei Gakuen University email: m-watanabe@hokusei.ac.jp ¶ Kobe University email: teatime567@gmail.com § Correspondence to: School of Economics, Kwansei Gakuin University, 1-155, Uegahara Ichiban-Cho, Nishinomiya, Hyogo 662-8501, Japan Tel.: +81-798-54-6993, E-mail: yasuoka@kwansei.ac.jp 2  1. Introduction Traditionally, a capital income tax is regarded as decreasing incentives for saving and as hindering economic growth if households exist infinitely, similarly to results reported by Chamly (1986). However, a capital income tax can contribute to macroeconomic performance within an overlapping generations model, as shown Uhlig and Yanagawa (1996). Kunze and Schuppert (2010) find that a capital income tax enhances not only economic growth but also employment. However, the impact of a capital income tax on fertility choice and unemployment under an overlapping generations model are considered only insufficiently in earlier studies.   Fig. 1: Unemployment and Total Fertility Rate. (Data: OECD Statistics. However, fertility within the EU is based on Eurostat.)  Following Fanti and Gori (2010), a decline of fertility and an increase in unemployment are crucially important issues in economically developed countries such as EU countries, as shown in Fig. 1. Therefore, a child tax is recommended as a remedy for the issues in their study. Wang (2015) states that pensions and child subsidies increase fertility and employment. We extend Fanti and Gori (2010) and emphasize positive effects of a capital income tax. Results show that a capital income tax improves fertility and unemployment with no social security system such as one that provides a wage subsidy, child subsidy, and a pension. We assert the originality of the points in this paper as follows. For an endogenous fertility model, a logarithmic utility function is often assumed.1 However, in the logarithmic utility function, saving is unaffected by the change of the interest rate: in fact, the capital income tax has no effect on saving. However, considering the                                                       1 Van Groezen, Leers and Meijdam (2003) and others assume a logarithmic utility function in the endogenous fertility model. FranceGermanyIta lyJapanSpainU.S.EU11.11.21.31.41.51.61.71.81.920 5 10 15 20Total Fertility RateUnemployment  Rate (%)Unemployment and Total Fertility Rate (2017)3  constant relative risk averse (CRRA) utility function, the capital income tax raises the saving if it is complementary between present consumption and future consumption. Then, by virtue of an increase in saving, the capital stock per capita rises. The remainder of this article is constructed as follows. Section 2 builds our model. Section 3 derives the equilibrium of the model economy and examines the effect of a capital income tax on fertility and unemployment. The final section concludes our study.  2. The model We construct a two-period overlapping generations (OLG) model with discrete time. The cohort born in period  is regarded as generation , with agents living for two periods: one for the young period and the other for the old period. This model economy has agents of three types: households, firms, and a government.  2.1.  Firm The production function in this model is assumed to have the following form: , 0 1, 0 ,  (1) where  represents total output. Here,  stands for capital stock,  denotes labor input, and  expresses the technology level of the firm. Our paper presents consideration of unemployment with a minimum wage, as examined by Fanti and Gori (2010) and by Wang (2015). Particularly,Wang (2015) explain how a pension premium affects income per capita in the long run through capital markets. If the pension premium decreases, then the effect for capital accumulation is mitigated. This effect raises income per capita. An increase in income per capita can raise the pension benefit under the constant premium rate for pensions. In the unemployment model, labor input can be presented as 1 ,  (2) where  signifies the unemployment rate and  is the population size. We define the fertility rate as . Actually,  can be regarded as the population growth rate and  can be reduced. The minimum wage is assumed in this model. We consider a model economy in which the minimum wage is higher than the competitive wage. We also assume that the capital stock is fully depreciated. We can obtain the following equation to maximize the firm profit as 1 1 ,   (3) 1 1 .  (4) Therein, 0  represents the minimum wage,  denotes the capital stock per capita , and  is the interest rate. Because of (3), employment rate 1  can be represented as 4  1 1 .  (5) By substitution of (5) into (4), the interest rate can be given as a constant level over time as 1 1.  (6) We assume that 0.  2.2.  Household Households care for the consumption in both young and old period and the number of children (fertility). We assume the following Constant Relative Risk Averse (CRRA) utility function as , 11 , 11 11 , 0 1, 0 , (7) where ,  and ,  respectively denote consumption in the young and old period. With 1, a utility function (7) becomes a logarithmic utility function. Our paper presents consideration of equation (7), which is more of a general type than a logarithmic type.   In the young period, the household obtain wage income 1  . 2  Here, 0   and  respectively denote the childcare cost and saving. Then, the budget constraint in the young period can be shown as , 1 . (8)   Denoting  as the capital income tax rate 0 1 , the budget constraint in the old period can be presented as , 1 1 . (9) Subject to budget constraints (8) and (9), we derive the following allocations to maximize utility (7). 1 1 1 , (10) 1 1 , (11)  2.3. Government If one assumes the following government budget constraint with a balanced budget  τ , (12) where   denotes non-productive government expenditure; then   does not contribute to the productivity of firms or marginal utility at all.3 Non-productive expenditure  is assumed because                                                       2 We consider that the share of  remains unemployed in the young period. Then, the employment period is given as 1 . 3 This assumption is considered by Chamley (1986) and by others. It examines optimal taxation. 5  we can check the direct effect of the tax on the employment rate and on the fertility rate.  3. Equilibrium   The equilibrium condition in capital markets is represented as . Equations (6) and (11) can be derived as 1 1 1 1 1 1. (13)As shown by (13), the capital stock per capita is constant over time. If  is larger than 1( 1 , then the capital stock accumulation can be facilitated if the capital income tax rate rises because of a decrease in the interest rate. With 1 as the logarithmic utility function, the interest rate and the capital income tax rate do not affect the capital stock. Equilibrium in our model economy can be given as equilibrium in the capital stock market. In this section, we show that a decrease in capital income brought about by an increase in the capital income tax rate induces households to increase saving. Equations (5), (6) and (13) give the long-run employment rate as 1 11 1 1 1 1 	. (14)In general, the minimum wage raises unemployment because of a decrease in labor demand. Therefore, equation (14) shows 0 	  	 0. In addition, the following expression can be obtained because of equations (13) and (14) as 0	 1 0 1 . (15)The output per capita can be shown as 1  . Then, the following proposition can be established.  Proposition 1 With 1, a capital income tax improves long-term employment and output per capita.  6  Kunze and Schuppert (2010) show that an increase in the capital income tax facilitates capital stock accumulation and employment. Finally, the effect of capital income tax affects the fertility rate in the long run because the household income rises. Considering equations (10), (13), and (14), fertility can be derived as 1 1 11 	. (16)Because of (13) and (16), one can obtain the following and the following proposition: 0 1 . (17) Proposition 2 An increase in the capital income tax rate raises the fertility rate in the long-run if 1.  Fanti and Gori (2010) show that a child tax raises the fertility rate. However, our manuscript shows that a tax only increases the fertility rate in the long-run, even if the child care cost does not change.4 The case of 1 represents a complementary case or a non-substitution case. Then, an increase in capital income tax reduces consumption during the old period. Then, to avoid reduction of consumption in the old period, households raise saving to increase consumption in the old period. Then, the capital stock per capita increases. Income per capita increases. By virtue of an increase in income per capita, the household income rises and fertility increases. Moreover, marginal labor productivity rises and the labor demand increases. Consequently, the unemployment rate decreases.  4. Conclusion Economically developed countries among the EU membership are confronting a common problem: a high unemployment rate and a low fertility rate. As described herein, we set an endogenous fertility model with a minimum wage and derive that the capital income tax can raise not only fertility but also income per capita. Based on results of our study, as future work we can assess aging population effects by considering the survival rate of elderly people.                                                          4 Fanti and Gori (2010) consider taxation for child care. This taxation increases the child care cost. However, the child care cost used for our analyses does not change. Capital accumulation is facilitated by a capital income tax. Then income per capita raises fertility. In the setting by Fanti and Gori (2010), a child care tax reduces the fertility directly. Then, the capital stock accumulation per capita increases and income per capita rises. Finally, household income rises; also, the fertility rate rises indirectly. 7  References Chamley C. (1986) “Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives.” Econometrica, vol. 54, pp. 607-622.  Fanti L. and Gori L. (2010) “Child policy solutions for the unemployment problem.” Economics Letters, vol. 109, pp. 147-149.  Kunze L. and Schuppert C. (2010) “Financing social security by taxing capital income: A bad idea?” FinanzArchiv / Public Finance Analysis, vol. 66, pp. 243-266.  Uhlig H. and Yanagawa N. (1996) “Increasing the capital income tax may lead to faster growth.” European Economic Review, vol. 40, pp. 1521-1540.  Van Groezen B., Leers T. and Meijdam L. (2003) “Social security and endogenous fertility: pensions and child allowances as siamese twins.” Journal of Public Economics, vol. 87(2), pp. 233-251.  Wang L. (2015) “Fertility and Unemployment in a social security system.” Economic Letters, vol. 133, pp. 19-23.  

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Capital income taxation in endogenous fertility model

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