ict3 · title: ict3.nb author: fukito created date: 10/1/2008 3:51:08 pm

Information and Communication Technologies and the Income

Distribution : A Simulation through Gini Coefficient Approach

Toshitaka Fukiharu (Faculty of Economics, Hiroshima University)

September, 2008

In[1]:= Off@General::spell, General::spell1, Solve::svars, Solve::ifun, N:: meprec D

ICT3.nb 1

Introduction

In the traditional economics, the innovation was characterized by the modification in the production process: e.g. theshifts in the production functions. This paper focusses on the innovation in information and communication technolo-gies (ICTs). The special feature of the innovation in the ICTs implies the improvement in the quality of consumption ofgoods and services including leisure hours, as well as the modification in the production process. As an example of theanalysis on the traditional innovation, we may refer to Fukiharu [2007a], which examined the relationship between theGreen Revolution (GR) , one of the innovations, and the profit. It is not certain whether the farmers' profit rises due tothe GR, since it raises supply of grain, while reducing production cost. In Fukiharu [2007a] it was shown that when theproduction function is of CES (Constant Elasticity of Substitution) Type, the farmers' profit might fall with the assump-tion of positive substitution parameter. It has been argued that the innovation of ICTs expands the unfairness of income distribution. In the traditionalexpression, this may be rephrased that the wealthy capitalists class becomes relatively better off, while the poor work-ing class becomes relatively worse off. In this paper, assuming three social classes; the entrepreneurs, the capitalists,and the workers, how the relative shares of these classes in the national income changes due to the innovation of ICTs.Following the Classicals' framework, the capitalists have capital goods and do not work, while the workers have nocapital goods and earn income by providing his initial endowment of leisure for the other members. If the productionfunction is assumed to be under constant returns to scale, the payment of rent for the capital goods and the one of thewage for the labor supply occupies the whole revenue of products. In this paper, however, the production function isassumed to be under decreasing returns to scale, following Fukiharu [2007a]. This assumption guarantees the positiveprofit: surplus. Thus, in this paper, the entrepreneurs class exists. By computing the General Equilibrium (GE) prices,the comparative statics analysis is conducted. First, examining three cases on the assumption on the production func-tion, how the shares of three social classes change due to the innovation of the ICTs is analyzed. Second, the incomeiequality is examined in terms of Gini coefficient approach. We start with the Cobb-Douglas function case.

1: Cobb-Douglas Production Function Case

In this paper, it is assumed that there is only one firm, producing consumption good, q, utilizing the capital goods, K,and the labor input, L. The Cobb-Douglas production function with additive ICT innovation is assumed as in whatfollows:

q=f(K , L)=Hck KLa1 Hcl LLa2 a1 +a2 <1 (1-1)

where q is output, ck is the level of ICTs with respect to the capital input in the production process, K is the capitalinput, cl is the level of ICTs with respect to the labor input and L is the labor input. It is assumed that the production isconducted under decreasing returns to scale, so that the positive profit is guaranteed. By the profit maximization of thefirm, the capital demand function, Kd , the labor demand function, Ld , the supply function of the consumption good, qs ,and the profit, p0 , are computed. The profit accrues to the firm after paying the rental cost for capital goods and laborcost.

It is assumed that there is the (aggregate) household, who has the initial endowment of leisure hours, L0 =100, with noprofit distribution from the firm. This class aims at utility maximization subject to income constraint:

max u[x, l ]=xc1 b1 l c2 b2

s.t. px=w(L0 -l ) (2)

ICT3.nb 2

where u[x, l ] is the utility function, x is the quantity of consumption good, l is the leisure consumption, L0 is thehousehold's initial endowment of leisure hours, p is the commodity price, w is the wage rate. Note that the innovationof the ICTs causes the modification of the utility function. The level of ICTs with respect to the consumption good isexpressed by c1 , while the one with respect to leisure time is expressed by c2 .

It is assumed that the firm is owned by the (aggregate) entrepreneur, who receives the whole profit. This class aims atthe utility maximization subject to the income receipt, p0 , consuming the consumption good, x, and hiring a part of theworkers, L, for this class, without working itself outside the production process.

max u[x, L]=xc1 b1 L c2 b2

s.t. px+wL=p0 (3)

Note that the innovation of the ICTs causes the modification of the utility function in exactly the same way as in thecase of household. The level of ICTs with respect to the consumption good is expressed by c1 , while the one withrespect to leisure time is expressed by c2 .

It is assumed that there is the (aggregate) capitalist, who has the initial endowment of capital good, K0 =100, with noprofit distribution from the firm, consuming the consumption good, x, and hiring a part of the workers, L, for this classwithout working itself outside the production process. This class aims at the utility maximization subject to incomeconstraint:

max u[x, L]=xc1 b1 L c2 b2

s.t. px+wL=rK0 (4)

Note that the innovation of the ICTs causes the modification of the utility function in exactly the same way as in thecase of household. The level of ICTs with respect to the consumption good is expressed by c1 , while the one withrespect to leisure time is expressed by c2 .

The general equilibrium (GE) prices, p, r, and w are computed from the three equations, which stem from the threemarket equilibria.

Kd =K0 (capital market equilibrium) (5) xd =xdW +xdE +xdK =qs (commodity market equilibrium) (6) Ld +LdE +LdK =Ls (labor market equilibrium) (7)

Here, xdW is the commodity demand from the workers, xdE is the commodity demand from the entrepreneurs, xdK isthe commodity demand from the capitalists, LdE is the (domestic) labor demand from the entrepreneurs, LdK is the(domestic) labor demand from the capitalists, Ls is the total labor supply. Assuming that w=1, we compute GE prices,p*: commodity price, and r*: rental price of capital .

It was shown (Fukiharu [2007b]) that

w*Ls /p*qs = a2 , (8-1) p0 /p*qs = 1-a1 -a2 , (9-1) r*K0 /p*qs =a1 . (10-1) Thus, the innovation in ICTs causes no effect on the income distribution.

ICT3.nb 3

Thus, the Cobb-Douglas production function with structural ICT innovation is assumed as in what follows:

q=f(K , L)=Kck a1 Lcl a2 a1 +a2 <1 (1-2)

where q is output, ck is the level of ICTs with respect to the capital input in the production process, K is the capitalinput, cl is the level of ICTs with respect to the labor input and L is the labor input. In (1-2), the innovation may causethe modification of marginal rate of substitution between capital and labor, while it is not the case in (1-1). It isassumed, however, that the production is conducted under decreasing returns to scale, so that the positive profit isguaranteed.

It was shown (Fukiharu [2007b]) that

w*Ls /p*qs = a2 cl , (8-2) p0 /p*qs = 1-a1 ck -a2 cl , (9-2) r*K0 /p*qs =a1 ck . (10-2)

In the framework of this section, the altered production process causes the income distribution change, whereas themodification of utility function does not.

ü Income Distribution

Lorenzs curve can be constructed by the following functions, where the case for cl =ck =1 is depicted as a (piecewiselinear) red curve and the case for the other parameter is depicted as a blue (piecewise linear) curve, while the perfectlyequal income distribution case is depicted as a green line.

In[2]:= lorenz0@a1_, a2_, cl_, ck_, h0_D :=Module@8d1, d2, d3<, d1 = 8a2∗cl, 1 − a1∗ck − a2∗cl, a1∗ck<;

d2 = Sort@d1D; d3 = 880, 0<, 81ê3, d2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDL<,82ê3, Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL<, 81, 1<<;

ListPlot@d3, PlotJoined → True, PlotStyle → Hue@h0D, DisplayFunction → IdentityDD

When a1 =1/2, a2 =1/3, cl =1, and ck =1.2, the Lorenz curve for this parameter shows that the income distribution for thiscase is more unequal than the case of no ICTinnovations.

In[3]:= Show@8lorenz0@1ê2, 1ê 3, 1, 1, 0D, lorenz0@1, 1, 1 ê3, 1ê3, 1 ê3D,lorenz0@1ê2, 1ê 3, 1, 1.2, 2ê3D<, DisplayFunction → $DisplayFunctionD;

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

ICT3.nb 4

When a1 =1/5, a2 =1/3, cl =1.2, and ck =1, however, the Lorenz curve for this parameter shows that the social incomedistribution for this case is more equal than the case of no ICT innovations.

In[4]:= Show@8lorenz0@1ê5, 1ê 3, 1, 1, 0D, lorenz0@1, 1, 1 ê3, 1ê3, 1 ê3D,lorenz0@1ê5, 1ê 3, 1.2, 1, 2ê3D<, DisplayFunction → $DisplayFunctionD;

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Type 1 Gini coefficient is computed by the following function. Type 1 Gini coefficient is defined as the area betweengreen line and blue (or red) curve, devided by 1/2.

In[5]:= gini1@a1_, a2_, cl_, ck_D :=Module@8d1, d2, l1, l20, l2, l30, l3<, d1 = 8a2∗cl, 1 − a1∗ck − a2∗cl, a1∗ck<;

d2 = Sort@d1D; l1 = HHd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLLêH1ê3LL∗x;l20 = Hd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLL −HHHd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL −

Hd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLLLêH1ê3LL ∗H1ê3L;l2 = l20 + HHHd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL −

Hd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLLLêH1ê3LL ∗x;l30 = Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL −HH1 − Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDLLêH1ê3LL ∗H2ê3L;

l3 = l30 + HH1 − Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDLLêH1ê3LL∗x;Integrate@x − l1, 8x, 0, 1 ê3<D +

Integrate@x − l2, 8x, 1ê 3, 2 ê3<D + Integrate@x − l3, 8x, 2 ê3, 1<DD

Type 1 Gini coefficient for a1 =1/2, a2 =1/3, cl =1, and ck =1 is computed as in what follows.

In[6]:= N@gini1@1 ê2, 1ê 3, 1, 1DD

Out[6]= 0.111111

Type 1 Gini coefficient for a1 =1/2, a2 =1/3, cl =1, and ck =1.2 is computed as in what follows.

In[7]:= N@gini1@1 ê2, 1ê 3, 1, 1.2DD

Out[7]= 0.177778


In[8]:= N@gini1@1 ê5, 1ê 3, 1, 1DD

Out[8]= 0.0888889

Type 1 Gini coefficient for a1 =1/5, a2 =1/3, cl =1.2, and ck =1 is computed as in what follows.

ICT3.nb 5

In[9]:= N@gini1@1 ê5, 1ê 3, 1.2, 1DD

Out[9]= 0.0666667

Type 2 Gini coefficient is computed by the following function. Type 2 Gini coefficient is defined as the sum of thelengths of 2 points from the perfectly equal distribution points.

In[10]:= gini2@a1_, a2_, cl_, ck_D :=Module@8d1, d2, l1, l20, l2, l30, l3<, d1 = 8a2∗cl, 1 − a1∗ck − a2∗cl, a1∗ck<;

d2 = Sort@d1D; l1 = H1 ê3L − Hd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLL;l2 = H2ê 3L − Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL; l1 + l2D


In[11]:= N@gini2@1 ê2, 1ê 3, 1, 1DD

Out[11]= 0.333333

Type 2 Gini coefficient for a1 =1/2, a2 =1/3, cl =1, and ck =1.2 is computed as in what follows.

In[12]:= N@gini2@1 ê2, 1ê 3, 1, 1.2DD

Out[12]= 0.533333


In[13]:= N@gini2@1 ê5, 1ê 3, 1, 1DD

Out[13]= 0.266667

Type 2 Gini coefficient for a1 =1/5, a2 =1/3, cl =1.2, and ck =1 is computed as in what follows.

In[14]:= N@gini2@1 ê5, 1ê 3, 1.2, 1DD

Out[14]= 0.2

In order to examine whether there is a tendency for the social income distribution to become more equal, we construct1000 pairs of random parameters a1 , a2 , cl , and ck which satisfies 0§a1 §1, 0§a2 §1, 1§cl §2, and 1§ck §2 withpositive GE income shares for 3 social classes.

In[15]:= l0 = Table@f@e_D := If@He@@2DD∗e@@3DD > 0L && H1 − e@@1DD∗e@@4DD − e@@2DD∗e@@3DD > 0L,e, 8Random@Real, 80, 1<D, Random@Real, 80, 1<D,

Random@Real, 81, 2<D, Random@Real, 81, 2<D<D;FixedPoint@f, 8Random@Real, 80, 1<D, Random@Real, 80, 1<D,

Random@Real, 81, 2<D, Random@Real, 81, 2<D<D, 81000<D;

Among the 1000 pairs, the number of cases in which the social income distribution becomes more equal through ICTinnovation; i.e. type 1 Gini coefficient becomes smaller, is given as follows.

In[16]:= list1 = Table@gini1@l0@@i, 1DD, l0@@i, 2DD, 1, 1D −gini1@l0@@i, 1DD, l0@@i, 2DD, l0@@i, 3DD, l0@@i, 4DDD, 8i, 1, Length@l0D<D;

In[17]:= Length@Select@list1, # > 0 &DD

Out[17]= 519

ICT3.nb 6

Among the 1000 pairs, the number of cases in which the social income distribution becomes less equal through ICTinnovation; i.e. type 1 Gini coefficient becomes larger, is given as follows.

In[18]:= Length@Select@list1, # < 0 &DD

Out[18]= 481

Among the 1000 pairs, the number of cases in which the social income distribution becomes more equal through ICTinnovation; i.e. type 2 Gini coefficient becomes smaller, is given as follows. Note that we have the same result as in thetype 1 Gini coefficient approach.



Out[20]= 519

Among the 1000 pairs, the number of cases in which the social income distribution becomes less equal through ICTinnovation; i.e. type 2 Gini coefficient becomes larger, is given as follows. Note that we have the same result as in thetype 1 Gini coefficient approach.


Out[21]= 481

Repeating the same procedure, we may conclude that the probability of the case, in which the social income distribu-tion becomes less equal through ICT innovation, is almost 50%, while the probability of the case, in which the socialincome distribution becomes more equal through ICT innovation, is also almost 50%. In other words, when both cl andck rises through ICT innovation, we cannot conclude whether the income distribution becomes less equal.In what follows, we examine if the income distribution becomes less equal through ICT innovation, when only oneparameter, between cl and ck , becomes larger than 1. We start with the case in which only cl becomes larger than 1. Inorder to do so, we construct 1000 pairs of random parameters a1 , a2 , cl , and ck which satisfies 0§a1 §1, 0§a2 §1, 1§cl §2, and ck =1 with positive GE income shares for 3 social classes.

In[22]:= l01 = Table@f@e_D := If@He@@2DD∗e@@3DD > 0L && H1 − e@@1DD ∗e@@4DD − e@@2DD∗e@@3DD > 0L,e, 8Random@Real, 80, 1<D, Random@Real, 80, 1<D, Random@Real, 81, 2<D, 1<D;

FixedPoint@f, 8Random@Real, 80, 1<D, Random@Real, 80, 1<D,Random@Real, 81, 2<D, 1<D, 81000<D;

Among the 1000 pairs, the number of cases in which the social income distribution becomes more equal through ICTinnovation with effect solely on cl ; i.e. type 1 Gini coefficient becomes smaller, is given as follows.



Out[24]= 600

Among the 1000 pairs, the number of cases in which the social income distribution becomes less equal through ICTinnovation with effect solely on cl ; i.e. type 1 Gini coefficient becomes larger, is given as follows.

ICT3.nb 7


Out[25]= 400

Among the 1000 pairs, the number of cases in which the social income distribution becomes more equal through ICTinnovation with effect on cl ; i.e. type 2 Gini coefficient becomes smaller, is given as follows. Note that we have thesame result as in the type 1 Gini coefficient approach.



Out[27]= 600

Among the 1000 pairs, the number of cases in which the social income distribution becomes less equal through ICTinnovation with effect solely on cl ; i.e. type 1 Gini coefficient becomes larger, is given as follows. Note that we havethe same result as in the type 1 Gini coefficient approach.


Out[28]= 400

Repeating the same procedure, we may conclude that the probability of the case, in which the social income distribu-tion becomes more equal through ICT innovation with effect solely on cl , is greater than 50%, while the probability ofthe case, in which the social income distribution becomes less equal through ICT innovation with effect solely on cl , issmaller than 50%. In other words, when solely cl rises through ICT innovation, we may conclude that the socialincome distribution becomes more equal.We proceed to the case in which only ck becomes larger than 1. In order to do so, we construct 1000 pairs of randomparameters a1 , a2 , cl , and ck which satisfies 0§a1 §1, 0§a2 §1, 1§ck §2, and cl =1 with positive GE income shares for3 social classes.

In[29]:= l02 = Table@f@e_D := If@He@@2DD∗e@@3DD > 0L && H1 − e@@1DD ∗e@@4DD − e@@2DD∗e@@3DD > 0L,e, 8Random@Real, 80, 1<D, Random@Real, 80, 1<D, 1, Random@Real, 81, 2<D<D;

FixedPoint@f, 8Random@Real, 80, 1<D, Random@Real, 80, 1<D,1, Random@Real, 81, 2<D<D, 81000<D;

Among the 1000 pairs, the number of cases in which the social income distribution becomes more equal through ICTinnovation with effect solely on ck ; i.e. type 1 Gini coefficient becomes smaller, is given as follows.



Out[31]= 589

Among the 1000 pairs, the number of cases in which the social income distribution becomes less equal through ICTinnovation with effect solely on ck ; i.e. type 1 Gini coefficient becomes larger, is given as follows.


Out[32]= 411

ICT3.nb 8

Among the 1000 pairs, the number of cases in which the social income distribution becomes more equal through ICTinnovation with effect on ck ; i.e. type 2 Gini coefficient becomes smaller, is given as follows. Note that we have thesame result as in the type 1 Gini coefficient approach.



Out[34]= 589

Among the 1000 pairs, the number of cases in which the social income distribution becomes less equal through ICTinnovation with effect solely on ck ; i.e. type 1 Gini coefficient becomes larger, is given as follows. Note that we havethe same result as in the type 1 Gini coefficient approach.


Out[35]= 411

Repeating the same procedure, we may conclude that the probability of the case, in which the social income distribu-tion becomes more equal through ICT innovation with effect solely on ck , is greater than 50%, while the probability ofthe case, in which the social income distribution becomes less equal through ICT innovation with effect solely on cl , issmaller than 50%. In other words, when solely ck rises through ICT innovation, we may conclude that the socialincome distribution becomes more equal.

Thus, we have

Proposition 1 (Cobb-Douglas Type) :1. If only cl rises from c1 =c2 =cl =ck =1, the labor income share rises and the entreprenuers' income share declines,while the probability of social income distribution becoming more equal is higher.2. If only ck rises from c1 =c2 =cl =ck =1, the capitalists' income share rises and the entreprenuers' income share declines,while the probability of social income distribution becoming more equal is higher.3. If cl and ck rise from c1 =c2 =cl =ck =1, the labor income share rises, the capitalists' income share rises and theentreprenuers' income share declines, while it may be impossible to predict whether the social income distributionbecomes more equal or not.

2: CES Case with t=–1/2

In[36]:= Clear@l, list1, list2D

In this section, it is assumed that there is only one firm, producing consumption good, q, utilizing the capital goods, K,and the labor input, L.The production function is assumed as in what follows:

q=f(K , L)=HHck KL-t + Hcl LL-tL-nêt n<1, t= –1/2 (1-3)

where q is output, ck is the level of ICTs with respect to the capital input in the production process, K is the capitalinput, cl is the level of ICTs with respect to the labor input L is the labor input, n is the degree of homogeneity, and t isthe parameter on the elasticity of substitution. It is assumed that the production is conducted under decreasing returnsto scale, so that the positive profit is guaranteed. For ease of computation it is assumed that

ICT3.nb 9

b1 =b2 =1/3. (11)

ü 2.1 The Case when n=1/2

For further ease of computation, suppose that

n=1/2, t= –1/2 (1-3A)

When (1-3A) is assumed, it is possible to compute GE prices analytically. Here, n is the degree of homogeneity, and(1-3A) guarantees the positiveness of profit for the firm.

ü Income Distribution

It was shown (Fukiharu [2007b]) that {w*Ls /p*qs , p0 /p*qs , r*K0 /p*qs } is computed as the following data1, wherep0 /p*qs =1/2, and each element depends on c1 , c2 , cl , and ck .

In[37]:= data1 = 9 −c22 ck +è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

c22 ck Hc22 ck + c12 cl + 2 c1 c2 clL2 Ic1 c2 ck + c22 ck +

è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!c22 ck Hc22 ck + c12 cl + 2 c1 c2 clL M

,

1

2,

c2 Hc1 + 2 c2L ck

2 Ic1 c2 ck + c22 ck +è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

c22 ck Hc22 ck + c12 cl + 2 c1 c2 clL M=;

When c1 =c2 =cl =ck =1, {w*Ls /p*qs , p0 /p*qs , r*K0 /p*qs } is given by {1/8,1/2,3/8}

In[38]:= data2 = data1 ê. 8c1 → 1, c2 → 1, cl → 1, ck → 1<

Out[38]= 9 18

,12

,38=

Thus, Lorenz curve is depicted as a red curve in the following graph, while the perfectly equal income distribution isdepicted as a green line.

In[39]:= lorenz2@data_, k_D := Module@8d1, d2, d3<, d1 = data;d2 = Sort@d1D; d3 = 880, 0<, 81ê3, d2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDL<,82 ê3, Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL<, 81, 1<<;

ListPlot@d3, PlotJoined → True, PlotStyle → Hue@kD, DisplayFunction → IdentityDD

In[40]:= Show@8lorenz2@data2, 0D, lorenz2@81ê3, 1ê3, 1ê3<, 1ê3D<,DisplayFunction → $DisplayFunctionD;

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

ICT3.nb 10

If c1 , c2 , cl , and ck rises from c1 =c2 =cl =ck =1 separately, their effects on w*Ls /p*qs are given by the following.

In[41]:= 8D@data1@@1DD, c1D ê. 8c1 → 1, c2 → 1, cl → 1, ck → 1<,D@data1@@1DD, c2D ê. 8c1 → 1, c2 → 1, cl → 1, ck → 1<,D@data1@@1DD, clD ê. 8c1 → 1, c2 → 1, cl → 1, ck → 1<,D@data1@@1DD, ckD ê. 8c1 → 1, c2 → 1, cl → 1, ck → 1<<

Out[41]= 9 116

, −1

16, 9

128, −

9128

=

If c1 , c2 , cl , and ck rises from c1 =c2 =cl =ck =1 separately, their effects on r*K0 /p*qs are given by the following.

In[42]:= 8D@data1@@3DD, c1D ê. 8c1 → 1, c2 → 1, cl → 1, ck → 1<,D@data1@@3DD, c2D ê. 8c1 → 1, c2 → 1, cl → 1, ck → 1<,D@data1@@3DD, clD ê. 8c1 → 1, c2 → 1, cl → 1, ck → 1<,D@data1@@3DD, ckD ê. 8c1 → 1, c2 → 1, cl → 1, ck → 1<<

Out[42]= 9− 116

, 116

, −9

128, 9

128=

Thus, we have

Proposition 2A (CES Type, L0 =100 and t= –1/2) :1. If only c1 and/or cl rises from c1 =c2 =cl =ck =1, the labor income share, the lowest share in this society, rises (and thesecond lowest, capitalist's income share, declines on exactly the same amount) and the income distribution becomesmore equal.2. If only c2 and/or ck rises from c1 =c2 =cl =ck =1, the labor income share, the lowest share in this society, declines (andthe second lowest, capitalist's income share, rises on exactly the same amount) and the income distribution becomesmore unequal.3. If all the coefficients rise from c1 =c2 =cl =ck =1, there is a tendency for thr effects to cancel each other, and it may beimpossible to predict whether the income distribution becomes more equal or not.

In what follows, we conduct a simulation for Proposition 2A-3.

In[43]:= Clear@d1, d2, gini1D

Type 1 Gini coefficient for CES case is computed by the following function. Type 1 Gini coefficient is defined as theratio between the areas.

In[44]:= gini1@c10_, c20_, cl0_, ck0_D := Module@8d1, d2, l1, l20, l2, l30, l3<,d1 = data1 ê. 8c1 → c10, c2 → c20, ck → ck0, cl → cl0<; d2 = Sort@d1D;l1 = HHd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLLêH1ê3LL ∗x;l20 = Hd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLL −HHHd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL −

Hd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLLLêH1ê3LL ∗H1ê3L;l2 = l20 + HHHd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL −

Hd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLLLêH1ê3LL ∗x;l30 = Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL −HH1 − Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDLLêH1ê3LL ∗H2ê3L;

l3 = l30 + HH1 − Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDLLêH1ê3LL∗x;Integrate@x − l1, 8x, 0, 1 ê3<D +

Integrate@x − l2, 8x, 1ê 3, 2 ê3<D + Integrate@x − l3, 8x, 2 ê3, 1<DD

When c1 =c2 =cl =ck =1, Type 1 Gini coefficient is computed as in what follows.

ICT3.nb 11

In[45]:= N@gini1@1, 1, 1, 1DD

Out[45]= 0.125

When only ck rises from c1 =c2 =cl =ck =1, for example, Type 1 Gini coefficient is computed as in what follows and theincome distribution becomes more unequal as asserted by Proposition.

In[46]:= N@gini1@1, 1, 1, 1.1DD

Out[46]= 0.127207

In order to examine whether there is a tendency for income distribution to become more equal or not when all theparameters rise, we construct 1000 pairs of random parameters c1 , c2 , cl , and ck which satisfies 1§c1 §2, 1§c2 §2, 1§cl §2, and 1§ck §2.

In[47]:= l = Table@8Random@Real, 81, 2<D, Random@Real, 81, 2<D,Random@Real, 81, 2<D, Random@Real, 81, 2<D<, 81000<D;

In[48]:= table1 = Table@gini1@1, 1, 1, 1D −gini1@l@@i, 1DD, l@@i, 2DD, l@@i, 3DD, l@@i, 4DDD, 8i, 1, Length@lD<D;

Among the 1000 pairs, the number of cases in which the income distribution becomes more equal through ICT innova-tion; i.e. type 1 Gini coefficient becomes smaller, is given as follows.

In[49]:= Length@Select@table1, # > 0 &DD

Out[49]= 509

Among the 1000 pairs, the number of cases in which the income distribution becomes less equal through ICT innova-tion; i.e. type 1 Gini coefficient becomes larger, is given as follows.

In[50]:= Length@Select@table1, # < 0 &DD

Out[50]= 491

Repeating the same procedure, we may conclude that the probability of the case, in which the income distributionbecomes less equal through ICT innovation, is almost 50%, while the probability of the case, in which the incomedistribution becomes more equal through ICT innovation, is also almost 50%. In other words, when c1 , c2 , cl and ck

rises through ICT innovation, we cannot conclude whether the income distribution becomes less equal or not.This conclusion is achieved even if Type 2 Gini coefficient for CES case is used. Type 2 Gini coefficient for CES caseis computed by the following function. Type 2 Gini coefficient is defined as the sum of the lengths of 2 points from thecompletely equal distribution points.

In[51]:= gini2@c10_, c20_, cl0_, ck0_D := Module@8d1, d2, l1, l20, l2, l30, l3<,d1 = d1 = data1 ê. 8c1 → c10, c2 → c20, ck → ck0, cl → cl0<;d2 = Sort@d1D; l1 = H1 ê3L − Hd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLL;l2 = H2ê 3L − Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL; l1 + l2D

Among the 1000 pairs, the number of cases in which the income distribution becomes more equal through ICT innova-tion; i.e. type 2 Gini coefficient becomes smaller, is given as follows. Note that we have the same result as in the type 1Gini coefficient approach.

In[52]:= table2 = Table@gini2@1, 1, 1, 1D −gini2@l@@i, 1DD, l@@i, 2DD, l@@i, 3DD, l@@i, 4DDD, 8i, 1, Length@lD<D;

ICT3.nb 12

In[53]:= Length@Select@table2, # > 0 &DD

Out[53]= 509

Among the 1000 pairs, the number of cases in which the income distribution becomes less equal through ICT innova-tion; i.e. type 2 Gini coefficient becomes larger, is given as follows. Note that we have the same result as in the type 1Gini coefficient approach.

In[54]:= Length@Select@table2, # < 0 &DD

Out[54]= 491

We may conclude that if we examine whether the income distribution becomes less equal or not through ICT innova-tion, when only one parameter, among c1 , c2 , cl , and ck , becomes greater than 1, each separate examination exhibits100% probability of less-equalization or more-equalization. When all the parameters become greater than 1, however,separate tendency cancels each other, and the final conclusion is that the probability of the income distribution becom-ing less equal is 50% and the probability of the income distribution becoming more equal is 50%. In other words, wecannot say whether the income distribution becomes less equal or not through ICT innovation.

ü 2.2 The Case when n=2/3

Next, suppose that

n=2/3, t= –1/2 (1-3B)

When (1-3B) is assumed, it is not possible to compute general equilibrium prices analytically. Thus, in order to com-pute the general equilibrium prices, the Newton method must be utilized. The following function, gA[cl, ck, c1, c2],computes {w*Ls /p*qs , p0 /p*qs ,r*K0 /p*qs } when cl , ck , c1 , c2 , and the number of workers, L0 , are given arbitrarily.

In[55]:= Clear@gA, l, q, pi, f1, sol1A, sol1, ld, kd, qs, pi0, u, sol2, xdW,sol2E, xdE, sol2K, xdK, check1, sol3, data0, profit0, uL0, uE0, uK0D

ICT3.nb 13

In[56]:= gA@cl_, ck_, c1_, c2_, workers_D :=Module@8q, pi, f1, sol1A, sol1, ld, kd, qs, pi0, u, sol2, xdW, sol2E,

xdE, sol2K, xdK, check1, sol3, data0, profit0, uL0, uE0, uK0<,m = 2ê 3; t = −1ê 2;

q = HHck∗kL^H−tL + Hcl∗ lL^H−tLL^H−m êtL;pi = p∗q − r∗ k − w∗ l;f1 = Simplify@PowerExpand@8D@pi, kD 0, D@pi, lD 0<DD;sol1A = Solve@8D@pi, kD 0, D@pi, lD 0<, 8k, l<D;sol1 = sol1A@@1DD;ld = l ê. sol1;kd = k ê. sol1;qs = q ê. sol1;pi0 = pi ê. sol1;b1 = 1ê 3; b2 = 1ê3;l0 = workers;u = x^Hc1∗ b1L∗ le^Hc2∗ b2L;sol2 =

PowerExpand@Solve@8D@u, xDêD@u, leD pêw, p∗x w∗Hl0 − leL<, 8x, le<D@@1DDD;xdW = Simplify@x ê. sol2D; ls = Simplify@l0 − le ê. sol2D;u = x^Hc1∗ b1L∗ le^Hc2∗ b2L;sol2E =

PowerExpand@Solve@8D@u, xDêD@u, leD pêw, p∗x + w∗le pi0<, 8x, le<D@@1DDD;xdE = x ê. sol2E; ldE = le ê. sol2E;k0 = 100;u = x^Hc1∗ b1L∗ le^Hc2∗ b2L;sol2K =

PowerExpand@Solve@8D@u, xDêD@u, leD pêw, p∗x + w∗le r∗k0<, 8x, le<D@@1DDD;xdK = Simplify@x ê. sol2KD; ldK = Simplify@le ê. sol2KD;check1 = H8kd k0, Hxd = xdK + xdE + xdW ê. k → kdL qs< ê. w → 1L;sol3 = N@FindRoot@check1, 8p, 1<, 8r, 1 ê10<DD;data0 = N@Simplify@

PowerExpand@H8sW = w∗ ld, sE = pi0, sK = r∗kd<êHp∗qsLL ê. sol3 ê. w → 1DDDD

When c1 =c2 =cl =ck =1 and L0 =100, the share of entreprenuers's income=1/3=1–n holds, as exhibited by the followingcomputation.

In[57]:= gA@1, 1, 1, 1, 100D

Out[57]= 80.190476, 0.333333, 0.47619<

If c1 rises to 11/10, then Proposition 2A-1 holds. Proposition 2A-1 is independent of n so long as L0 =100 is guaranteed.

In[58]:= gA@1, 1, 11ê10, 1, 100D

Out[58]= 80.198198, 0.333333, 0.468468<

Now, let us raise L0 from 100 to 1000. The share of workers's income becomes the gretest share in this society.

In[59]:= gA@1, 1, 1, 1, 1000D

Out[59]= 80.421782, 0.333333, 0.244884<

In this situation, suppose that c1 rises to 11/10. Then, the share of workers's income rises. Since the share of workers'sincome is the gretest, however, the income distribution becomes more unequal, so that Proposition 2A-1 does not hold.

ICT3.nb 14

In[60]:= gA@1, 1, 11ê10, 1, 1000D

Out[60]= 80.427594, 0.333333, 0.239073<

Suppose that cl rises to 11/10. Then, the share of workers's income rises. Since the share of workers's income is thegretest, however, the income distribution becomes more unequal, so that Proposition 2A-1 does not hold.

In[61]:= gA@11ê10, 1, 1, 1, 1000D

Out[61]= 80.430173, 0.333333, 0.236494<

Suppose that ck rises to 11/10. Then, the share of workers's income declines. Since the share of workers's income is thegretest, however, the income distribution becomes more equal, so that Proposition 2A-2 does not hold.

In[62]:= gA@1, 11ê 10, 1, 1, 1000D

Out[62]= 80.413218, 0.333333, 0.253449<

Suppose that c2 rises to 11/10. Then, the share of workers's income declines. Since the share of workers's income is thegretest, however, the income distribution becomes more equal, so that Proposition 2A-2 does not hold.

In[63]:= gA@1, 1, 1, 11ê10, 1000D

Out[63]= 80.415666, 0.333333, 0.251<

Thus, we have

Proposition 2B (CES Type, L0 =1000 and t= –1/2) :1. If only c1 and/or cl rises from c1 =c2 =cl =ck =1, the labor income share, the highest share in this society, rises (andthe second lowest, entreprenuer's income share, remains the same) and the income distribution becomes more unequal.2. If only c2 and/or ck rises from c1 =c2 =cl =ck =1, the labor income share, the highest share in this society, declines(and the second lowest, entreprenuer's income share, remains the same) and the income distribution becomes moreequal.

Proposition 2A and Proposition 2B show that the labor income share rises if only c1 and/or cl rises, and it declines ifonly c2 and/or ck rises. This conclusion is independent of L0 . When L0 increases, however, the labor income sharerises. Therefore, if L0 increases sufficiently, then the labor income share becomes the highest so that the conclusion onthe income distribution for the society as a whole becomes completely opposite between Proposition 2A and Proposi-tion 2B.

3: CES Case with t=1/2

In this section, it is assumed that there is only one firm, producing consumption good, q, utilizing the capital goods, K,and the labor input, L.The production function is assumed as in what follows:

q=f(K , L)=HHck KL-t + Hcl LL-tL-nêt n=1/2, t= 1/2 (1-4)

It is assumed that the production is conducted under decreasing returns to scale, so that the positive profit is guaran-teed. For ease of computation (11) is assumed.

ICT3.nb 15

The aim of this section is to examine whether the conclusion in Section 2 holds when a parameter changes from t= –1/2to t= 1/2. When t= 1/2, however, the computation of GE is not easy. Thus, the Newton method is utilized in the computa-tion of general equilibrium, and the comparison is made between the case for c1 =c2 =ck =cl =1 and the cases in which (i)only c1 rises, (ii) only c2 rises, (iii) only ck rises, (iv) only cl rises from c1 =c2 =ck =cl =1. We start from the computa-tion of general equilibrium, proceeding to examine how the income distribution changes for each increase of ci

(i=l,k,1,2), while the other parameters remaining at 1. In order to do this, the following function, gB[cl , ck , c1 , c2 ] isconstructed. This function computes {w*Ls /p*qs , p0 /p*qs ,r*K0 /p*qs } when t= 1/2, while cl , ck , c1 , and c2 are givenarbitrarily. It is assumed in this section that

L0 =100. (12)

In[64]:= gB@cl_, ck_, c1_, c2_D :=Module@8q, pi, f1, sol1A, sol1, ld, kd, qs, pi0, u, sol2, xdW, sol2E,

xdE, sol2K, xdK, check1, sol3, data0, profit0, uL0, uE0, uK0<,m = 1ê 2; t = 1 ê2;

q = HHck∗kL^H−tL + Hcl∗ lL^H−tLL^H−m êtL;pi = p∗q − r∗ k − w∗ l;f1 = Simplify@PowerExpand@8D@pi, kD 0, D@pi, lD 0<DD;sol1A = Solve@8D@pi, kD 0, D@pi, lD 0<, 8k, l<D;sol1 = sol1A@@1DD;ld = l ê. sol1;kd = k ê. sol1;qs = q ê. sol1;pi0 = pi ê. sol1;b1 = 1ê 3; b2 = 1ê3;l0 = 100;u = x^Hc1∗ b1L∗ le^Hc2∗ b2L;sol2 =

PowerExpand@Solve@8D@u, xDêD@u, leD pêw, p∗x w∗Hl0 − leL<, 8x, le<D@@1DDD;xdW = Simplify@x ê. sol2D; ls = Simplify@l0 − le ê. sol2D;u = x^Hc1∗ b1L∗ le^Hc2∗ b2L;sol2E =

PowerExpand@Solve@8D@u, xDêD@u, leD pêw, p∗x + w∗le pi0<, 8x, le<D@@1DDD;xdE = x ê. sol2E; ldE = le ê. sol2E;k0 = 100;u = x^Hc1∗ b1L∗ le^Hc2∗ b2L;sol2K =

PowerExpand@Solve@8D@u, xDêD@u, leD pêw, p∗x + w∗le r∗k0<, 8x, le<D@@1DDD;xdK = Simplify@x ê. sol2KD; ldK = Simplify@le ê. sol2KD;check1 = H8kd k0, Hxd = xdK + xdE + xdW ê. k → kdL qs< ê. w → 1L;sol3 = N@FindRoot@check1, 8p, 10<,

8r, 1 ê100<, WorkingPrecision → 50, MaxIterations → 1000DD;data0 = N@Simplify@PowerExpand@H8sW = w∗ld, sE = pi0, sK = r∗kd<êHp∗qsLL ê. sol3 ê.

w → 1DDDD

When (11) and (12) hold, the shares of income distribution are computed by this function. For example, whenc1 =c2 =cl =ck =1, {w*Ls /p*qs , p0 /p*qs , r*K0 /p*qs } is given by {1/3,1/2,1/4}.

In[65]:= gB@1, 1, 1, 1D

Out[65]= 80.333333, 0.5, 0.166667<

ICT3.nb 16

Contrary to the case for t=–1/2, the capitalist's income share is the lowest and the labor income share is the secondlowest. First, suppose that c1 rises from 1 to 11/10 with other parameters remaining at 1. The share of workers' incomedeclines, while the one of capitalists rises, as shown in what follows. This result contradicts the former part in Proposi-tion 2A, while agreeing with the latter part.

In[66]:= data2 = gB@1, 1, 11ê 10, 1D

Out[66]= 80.329823, 0.5, 0.170177<

Indeed, the computation of Type 2 Gini coefficient shows that the income distribution becomes more equal when c1

rises from 1 to 11/10 with other parameters remaining at 1, as shown in what follows.

In[67]:= gini2A@data_D := Module@8d2, l1, l2<, d2 = Sort@dataD;l1 = H1ê 3L − Hd2@@1DDêHd2@@1DD + d2@@2DD + d2@@3DDLL;l2 = H2ê 3L − Hd2@@1DD + d2@@2DDLêHd2@@1DD + d2@@2DD + d2@@3DDL; l1 + l2D

In[68]:= 8gini2A@gB@1, 1, 1, 1DD, gini2A@gB@1, 1, 11ê10, 1DD<

Out[68]= 80.333333, 0.329823<

Secondly, suppose that cl rises from 1 to 11/10 with other parameters remaining at 1. The share of workers' incomedeclines, while the one of capitalists rises. This result contradicts the former part in Proposition 2A, while agreeingwith the latter part.

In[69]:= gB@11ê 10, 1, 1, 1D

Out[69]= 80.328602, 0.5, 0.171398<

Indeed, the computation of Type 2 Gini coefficient shows that the income distribution becomes more equal when cl


In[70]:= 8gini2A@gB@1, 1, 1, 1DD, gini2A@gB@11ê10, 1, 1, 1DD<

Out[70]= 80.333333, 0.328602<

Thirdly, suppose that c2 rises from 1 to 11/10 with other parameters remaining at 1. The share of workers' income rises,while the one of capitalists declines. This result contradicts the former part in Proposition 2A, while agreeing with thelatter part.

In[71]:= gB@1, 1, 1, 11ê10D

Out[71]= 80.336881, 0.5, 0.163119<

Indeed, the computation of Type 2 Gini coefficient shows that the income distribution becomes more unequal when c2


In[72]:= 8gini2A@gB@1, 1, 1, 1DD, gini2A@gB@1, 1, 1, 11ê10DD<

Out[72]= 80.333333, 0.336881<

Fourthly, suppose that ck rises from 1 to 11/10 with other parameters remaining at 1. The share of workers' incomerises, while the one of capitalists declines. This result contradicts the former part in Proposition 2A, while agreeingwith the latter part.

ICT3.nb 17

In[73]:= gB@1, 11ê 10, 1, 1D

Out[73]= 80.338014, 0.5, 0.161986<

Indeed, the computation of Type 2 Gini coefficient shows that the income distribution becomes more unequal when ck


In[74]:= 8gini2A@gB@1, 1, 1, 1DD, gini2A@gB@1, 11ê10, 1, 1DD<

Out[74]= 80.333333, 0.338014<

Thus, we have

Proposition 3 (CES Type, L0 =100 and t= 1/2) :1. If only c1 and/or cl rises from c1 =c2 =cl =ck =1, the labor income share, the second lowest share in this society,declines (and the lowest, capitalist's income share, rises, while the sum of the lowest and the second lowest remain thesame at 1/2) and the income distribution becomes more equal.2. If only c2 and/or ck rises from c1 =c2 =cl =ck =1, the labor income share, the second lowest share in this society, rises(and the lowest, capitalist's income share, declines, while the sum of the lowest and the second lowest remain the sameat 1/2) and the income distribution becomes more unequal.

In order to examine what would happen to the labor income share when arbitrary ICT innovation takes place, the set ofpoints, {cl , ck , c1 , c2 }, list1, where ci =1 or 11/10 (i=l,k,1,2), is constructed as follows.

In[75]:= d@n_, 1D := Table@i, 8i, 1, n<D;d@n_, 2D := Partition@Flatten@Table@8i, j<, 8i, 1, n<, 8j, 1, n<DD, 2D;d$aug@x_, n_D := Partition@Flatten@Table@8x@@iDD, j<, 8i, 1, Length@xD<, 8j, 1, n<DD,

Dimensions@xD@@2DD + 1D;d@n_, k_D := d$aug@d@n, k − 1D, nD

In[78]:= list1 = HHd@2, 4D ê. 81 → 0, 2 → 1<L + 10Lê10

Out[78]= 981, 1, 1, 1<, 91, 1, 1, 1110

=, 91, 1, 1110

, 1=, 91, 1, 1110

, 1110

=,

91, 1110

, 1, 1=, 91, 1110

, 1, 1110

=, 91, 1110

, 1110

, 1=, 91, 1110

, 1110

, 1110

=,

9 1110

, 1, 1, 1=, 9 1110

, 1, 1, 1110

=, 9 1110

, 1, 1110

, 1=, 9 1110

, 1, 1110

, 1110

=,

9 1110

, 1110

, 1, 1=, 9 1110

, 1110

, 1, 1110

=, 9 1110

, 1110

, 1110

, 1=, 9 1110

, 1110

, 1110

, 1110

==

In what follows, the difference between the Type 2 Gini coefficient corresponding to c1 =c2 =cl =ck =1and the onecorresponding to each element in list1 is computed. Here, the number with 10-15 is 0, so that out of 16 cases thenumber of "no change" (0) cases is 4, "more equality" cases (–) is 6 cases, while "more unequality" cases (+) is 6 cases.

In[79]:= list2A = Table@gini2A@gB@1, 1, 1, 1DD −gini2A@gB@list1@@i, 1DD, list1@@i, 2DD, list1@@i, 3DD, list1@@i, 4DDDD, 8i,1, Length@list1D<D

Out[79]= 80., −0.00354771, 0.00351033, 0., −0.00468114, −0.00817709,−0.001221, −0.00468114, 0.00473098, 0.00113379, 0.0082892,0.00473098, −1.38778× 10−15, −0.00354771, 0.00351033, −1.38778×10−15<

Thus, if all the coefficients rise from c1 =c2 =cl =ck =1, there is a tendency for thr effects to cancel each other, and it maybe impossible to predict whether the income distribution becomes more equal or not. In what follows, we conduct thissimulation.

ICT3.nb 18

In[80]:= TimeUsed@ D

Out[80]= 177.264

ICT3.nb 19

4: Conclusions

ICT3.nb 20

This paper examined the effects of four elements in innovation on the social income distribution. Traditional ele-ments in the innovation argument were restricted on the production process. In this paper, the production function hastwo factors of production: labor input and capital input. Thus, in this paper, the 1st element is the efficiency improve-ment of the labor input through ICT innovation, and the 2nd element the one of capital input. The special feature ofICTs consists in the fact that quality of life improves through ICT innovation. Thus, in this paper, since the utilityfunction has two variables: consumption good and leisure hours, the 3rd element is the improvement of the quality ofconsumption good through ICT innovation, and the 4th is the one of leisure hours through ICT innovation. In Section 1, first, the production function was specified by Cobb-Douglas type where the efficiency improvementimplies the additive type as in the traditional argument: i.e. one unit of input becomes c unit (c>1) after the innovation.Under this assumption, the innovation of ICTs cannot change the social income distribution at all. Thus, the productionfunction was modified to the Cobb-Douglas type where the efficiency improvement implies the structural type in thesense that the improvement implies the increased parameter of the Cobb-Douglas production function. It was shownthat the 3rd and 4th elements have no effect on the social income distribution. The 1st and 2nd elements can influencethe social income distribution. Firstly, due to the 1st element the labor income share rises and the probability of socialincome distribution becoming more equal is higher. Secondly, due to the 2nd element the labor income share declinesand the probability of social income distribution becoming more equal is higher. When the 1st and 2nd elements aretaken into account at the same time, however, the total effect is that the probabilities of social income distributionbecoming more equal and more unequal are 50% each, so that we cannot predict at all whether through ICT innova-tions the social income distribution becomes more equal or more unequal. In Section 2, the production function was specified by CES type with negative substitution parameter. It was shownthat all the four elements influence the income distribution structure, while the income share of the entrepreneurs isconstant. For example, firstly, the 1st and/or 3nd elements contribute to the rise of workers' income share. Meanwile,secondly, the 2nd and/or 4th elements contribute to the rise of capitalists' income share. When the number of workers(or initial leisure hours) is relatively small, worker's income share is the lowest in the society, so that the above effectcontributes to the equalization of social income distribution in the first case, while it contributes to the unequalizationof social income distribution. When the number of workers (or initial leisure hours) is relatively large, however,worker's income share is the greatest in the society, so that the above effect contributes to the unequalization of socialincome distribution in the first case, while it contributes to the equalization of social income distribution. When all theelements are taken into account, however, the effects from these elements tend to cancel with each other, and conclu-sion from the simulation is that we cannot predict at all whether through ICT innovations the social income distributionbecomes more equal or more unequal. In Section 3, the production function was specified by CES type with positive substitution parameter. It was shownthat all the four elements influence the income distribution structure, while the income share of the entrepreneurs isconstant. The results, however, contradict those in the previous section in many aspects. For example, firstly, the 1stand/or 3nd elements contribute to the decline of workers' income share. Meanwile, secondly, the 2nd and/or 4thelements contribute to the decline of capitalists' income share. Since the number of workers (or initial leisure hours) isassumed to be relatively small in this section, worker's income share is the greatest in the society, so that the aboveeffect contributes to the equalization of social income distribution in the first case, while it contributes to the unequaliza-tion of social income distribution. When all the elements are taken into account, however, the effects from theseelements tend to cancel with each other, and conclusion from the simulation is that we cannot predict at all whetherthrough ICT innovations the social income distribution becomes more equal or more unequal. The local stability is guaranteed for CES type production functions. Thus, it was shown by these simulations, thattheoretically, no definite relation holds between the innovation of ICTs and the social income distribution. In order toderive the definite relation, one must examine what type of production function the economy has and how great are theparameters in the production function.

ICT3.nb 21

References

Fukiharu, T. [2007a], "The Green Revolution and the Water Crisis in India: an Economic Analysis", Farming Systems Design 2007, Int. Symposium on Integrated Analysis on Farm Production Systems, M. Donatelli, J. Hatfield, A. Rizzoli, Eds., Catania (Italy), 10-12, September 2007, Book1, pp.153-4

Fukiharu, T. [2007b], "Information and Communication Technologies and the Income Distribution: A General Equilibrium Simulation", Miquel Sànchez-Marrè, Javier Béjar, Joaquim Comas, Andrea E. Rizzoli, Giorgio Guariso (Eds.) Proceedings of the iEMSs Fourth Biennial Meeting: International Congress on Environmental Modelling and Software (iEMSs 2008). International Environmental Modelling and Software Society, Barcelona, Catalonia, July 2008, vol1, pp.240-247.

ICT3.nb 22

ict3 · title: ict3.nb author: fukito created date: 10/1/2008 3:51:08 pm

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