Urban unemployment, privatization policy, and a differentiated mixed oligopoly

Transcription

1 Urban unemployment, privatization policy, and a differentiated mixed oligopoly University of Tokyo Industrial Organization Workshop 2014 Feb. 5 th Tohru aito (The University of Tokushima) Outline 1. Motivation 2. Previous literature 3. Model Household Rural Sector Urban Sector 4. Migration and unemployment 5. Conclusion 2014/2/5 2 1

2 Motivation(1) 1. Recently some public firms have been privatized in many countries. 2. Since it is possible that the privatization of public firm affects the various kinds of market in the economy; Labor, goods, capital, and so on. 3. Particularly, the change of labor market in urban area affects the migration between rural area and urban area. 4. Since it is not desirable that the urban unemployment increases in the economy, we need consider the privatization of public firm more carefully. 5. Though the traditional dualistic models analyze the relationship between unemployment in urban area and labor migration, most of setting does not necessarily express reality. 2014/2/5 3 Motivation(2) 5. The 1 st purpose of this paper is to construct the model to analyze the relationship between urban unemployment and the privatization of public firm. 6. The 2 nd purpose of it is to analyze the effect of public firm of privatization on labor demand, urban unemployment, and social welfare. 2014/2/5 4 2

3 The share of public firm in regions of China (2003) 2014/2/5 5 The share of public firm in regions of China (2009) 2014/2/5 6 3

4 Jan. 13 th 2014 from The ikkei 2014/2/5 7 Unemployment in China (%) ( 年 ) Country Urban area Rural area 2014/2/5 8 4

5 Dualistic economy model 1. Harris and Todaro (1970) conceived a mechanism by which unemployment occurred endogenously in the framework of a dualistic economy in development economics. 2. Corden and Findlay (1975) relax this assumption, and analyze a model with free mobility of capital between the urban area and the rural area. 3. (1998) considers the partial privatization and shows that partial privatization is optimal in a mixed duopoly when a public firm is as productive as its private competitor. 4. Matsumura and Kanda (2005) generalize Matsumura (1998) to a mixed oligopoly setting with more than two private firms and show that at least partial privatization is socially preferable in the short run. 5. Fujiwara (2007 ) considers the differentiated goods in the mixed oligopoly and investigate the effect of goods differentiation on optimal privatization of public goods in short-run and long-run 2014/2/5 9 Mixed oligopoly model 1. De Fraja and Delbono (1989) show that when public firms compete with many private firms, they should maximize profits rather than welfare in order to improve overall social welfare. 2. Matsumura (1998) considers the partial privatization and shows that partial privatization is optimal in a mixed duopoly when a public firm is as productive as its private competitor. 3. Matsumura and Kanda (2005) generalize Matsumura (1998) to a mixed oligopoly setting with more than two private firms and show that at least partial privatization is socially preferable in the short run. 4. Fujiwara (2007 ) considers the differentiated goods in the mixed oligopoly and investigate the effect of goods differentiation on optimal privatization of public goods in short-run and long-run 2014/2/5 10 5

6 Spatial economics model 1. The monopolistic competition model by Dixit and Stiglitz (1977) has been applied to many regional science and urban studies. A salient study by Krugman (1991) is the pioneering work in core-periphery models. 2. Pfluger (2004) substitutes quasi-linear utility function with logarithmic sub utility for Dixit and Stiglitz type utility function to solve the model analytically. 3. Ottaviano, Tabuchi, and Thisse (2002) introduce the competition effect into the Core-periphery model and construct the Core-periphery which is solved analytically. 2014/2/5 11 Previous works Development economics Lewis (1954) Mixed oligopoly De Fraja and Delbono (1990) Spatial economics Krugman (1991) Harris & Todaro (1970) aito (2012) aito (2013) 2014/2/5 (many studies) Matsumura (1998) Matsumura & Kanda (2005) Fujiwara (2007) This paper Pfluger (2004) Ottaviano, Tabuchi, & Thisse (2002) 12 6

7 The model Urban area Public firms Urban sector Q 0 ;Q 1 ;ááá;q Private firms Differentiated products Mixed oligopoly Rural area Rural sector Z Homogeneous products Competitive market Capital Capital Unemployment households Labor Households employed by urban sector Capital Labor Households employed by rural sector 2014/2/5 13 Households (1) Utility function The quasi-linear utility function as well as Ottaviano, Tabuchi, and Thisse (2002) Differentiated manufactured goods All households in an economy have common preference ò U l = ë q 0l + P i=1 qil ó ìàí à 2 ò [q 0l ] 2 + P i=1 [qil ] 2 ó ô à í 2 q 0l + P i=1 qil õ 2 + z (l = c; r; u) q 0l q il z : consumption of goods produced by public firm : consumption of goods produced by i th private firm : consumption of agricultural goods : the number of private manufactured goods 2014/2/5 14 7

8 Households (2) Budget constraint w l + rk ö = p 0 q 0l + P i=1 pi q il + z (l = c; r; u) w l p i p 0 kö r : the wage rate of household l : price of goods produced by i th private firm : price of goods produced by public firm : endowment capital : capital rent Urban minimum wage rate w c = wö Unemployment households w u = /2/5 15 Households (3) Utility maximization problem ò max ë q 0l + P q 0l ;á á á;q l i=1 qil ó ìàí à 2 ò [q 0l ] 2 + P i=1 [qil ] 2 ó ô à í 2 q 0l + P i=1 qil õ 2 + z subject to w l + rk ö = p 0 q 0l + P i=1 pi q il + z (l = c; r; u) the first order condition of q 0l and q il ë à (ì à í)q 0l à í q 0l + P i=1 ë à (ì à í)q il à í q 0l + P i=1 ô ô qil qil õ à p 0 = 0 õ à p i = 0 (i = 1; á á á; ) 2014/2/5 16 8

9 Households (4) Demand function q ã 0l = a à [b + c( + 1)]p 0 + cp q ã il = a à [b + c( + 1)]p i + cp a = ë [ì+í] 1 ; b = [ì+í] ; c = (ìàí)[ì+í] í (l = c; r; u) w l p i p 0 kö r : the wage rate of household l : price of goods produced by i th private firm : price of goods produced by public firm : endowment capital : capital rent 2014/2/5 17 Households (5) Price index manufactured goods " # P ñ p 0 + P i=1 p i Indirect utility function of household i v l = ë q ã 0l + P i=1 q ã il! ìàí à 2 [q ã 0l ]2 + P i=1 [q ã il ]2! à 2 í " # 2 q ã 0l + P i=1 q ã il à p 0 q ã à P 0l i=1 p i q ã + w il l + rk ö a = 2 (+1) 2b à a p 0 + P i=1 pi! b+c(+1) + 2 [p 0 ] 2 + P i=1 [pi ] 2! à 2 c " p 0 + P # 2 pi + w l + rk ö i=1 2014/2/5 18 9

10 Migration between urban area and rural area Urban unemployment Population constraint L õ ñ u Lc +L u L c + L u + L r = 1 Substituting λ into population constraint, L c + (1 à õ)l r = 1 à õ 2014/2/5 19 Production (1) Agricultural goods sector competitive only labor input numeraire Production function of agricultural goods Z = (L r ) û ; û 2 (0;1) L r : Labor input Wage in rural area w r = û(l r ) ûà1 2014/2/

11 Production (2) Manufactured goods sector mixed oligopoly (One public firm and private firms) The large number of private firm labor input and (fixed ) capital input Total demand of manufactured goods in a economy Q 0 = (L c + L u + L r )(q 0c + q 0u + q 0r ) = a à [b + c( + 1)]p 0 + cp Q i = (L c + L u + L r )(q ic + q iu + q ir ) = a à [b +c( + 1)]p i + cp; (i = 1;ááá;) Production function of manufactured goods Q j = m L j c (j = 0; á á á; ) 2014/2/5 21 Production (3) Cost function of manufactured goods sector C(Q 0 ) = mwöq 0 à r C i (Q i ) = mwöq i à r (i = 1;ááá;) Profit function of public firm and private firms in a economy ù 0 = (a à [b + c( + 1)]p 0 + cp)(p 0 à mwö) à r ù i = (a à[b + c( + 1)]p i + cp)(p i à mwö) à r (i = 1; á á á; ) Social welfare function a W = 2 (+1) 2b à a p 0 + P i=1 pi! b+c(+1) + 2 [p 0 ] 2 + P i=1 [pi ] 2! à 2 c " p 0 + P # 2 pi + ù 0 + P ùi + wö(l 0 c + P L i c ) + ù r + w r L r + ( + 1)r i=1 i=1 i=1 2014/2/

12 Production (4) Maximize the weighted average of social welfare and its profit V(ò) ñ ù 0 + (1 à ò)w = (a à [b + c( + 1)]p 0 + cp)(p 0 à mwö) à r pi! + (1 à ò) â a 2 (+1) 2b à a p 0 + P i=1 + [p 0 ] 2 + P! [pi ] 2 c à 2 p 0 + P i=1 i=1 b+c(+1) + 2 " # 2 pi + P ùi + wö(l 0 c + P L i c )w r L r + r( + 1) ã i=1 i=1 The first order condition for the objective function of public @p 0 = + ( P i 0 + wö 0 i=1 = a à(1 +ò)[b + c( + 1)]p 0 + cp + òmwö[b + c( +1)] = 0 (*)The behavior of each firm does not affect price index of j = 0 (j = 0; á á á; ) 23 Production (5) Assuming the symmetry of private firms, p ñ p 1 = ááá = p The equilibrium price of manufactured goods produced by public firm ð ñ a c ò p 0 = (1+ò)[ b+c(+1) ] + (1+ò)[ b+c(+1) ] P + 1+ò mwö The equilibrium price of manufactured goods produced by private firm a p = 2[ b+c(+1) ] c + 2[ b+c(+1) ] mwö P + 2 Inserting p 0 and p into P, the following equation is hold. P = p 0 + p ð 2+(1+ò) = 2(1+ò)[b+c(+1)] ñ ð ñ ð 2+(1+ò) a + 2(1+ò)[b+c(+1)] cp + 2ò+(1+)ò 2(1+ò) ñ mwö 2014/2/

13 Production (6) Solving this equation with respect to price index P, P* is given by ð P ã = 2 1+ò 2+(1+ò) ( )b+[ 2ò+(1+ò)]c the equilibrium price of each firm ð p ã 0 = p ã = 2 1+ò 2b+(+3)c ( b+(+1)c )( 2( 1+ò)b+ [( 1+ò)+2ò ]c) ( ò+1)a ( )b+c[ + ( +2)ò] ñ c + 2[ b+c(+1) ] the market clear condition of capital market h + 1 = k ö ñ ð a ò 2[ 2ò+(1+ò) ] ( )b+[ 2ò+(1+ò)]c h ð c a + (1+ò)( b+c(+1) ) ð 4ò+2(1+ò) 2( 1+ò)b+ ( 2ò+ ( 1+ò))c ñ mwö: 2( 2ò+(1+ò) ) 2( 1+ò)b+ ( 2ò+(1+ò))c ñ i mwö ñ ò + 1+ò i mwö 2014/2/5 25 Migration between urban area and rural area (1) Q ö : the total production of manufactured goods Q ö h ð ñi ð ñ 3+ò 2(1+3ò) = ( + 1) à b 2(1+ò)+(2ò+(1+ò))c a à b 2(1+ò)+(2ò+(1+ò))c mw @m < < 0 The productivity of manufactured goods sector (m) Q ö The minimum wage in urban area (wö) Q ö 2014/2/

14 Migration between urban area and rural area (2) The labor demand of manufactured goods sector L ö c = mq h ö ð ñi ð ñ 3+ò 2(1+3ò) = ( + 1) à b 2(1+ò)+(2ò+(1+ò))c am à b 2(1+ò)+(2ò+(1+ò))c m 2 wö Comparative statics (the effect of privatization of public firm on labor demand of manufactured goods = [ 2+(3+)c ]aà2[ 2+(à1)c ] ( 2ò+2cò+c+cò+2 ) 2 R0 2014/2/5 27 Migration between urban area and rural area (3) ì = 0:8;í = 0:2; > 1 > 0 4+2(à1)c 2+(3+)c a 1.4 < /2/

15 Lemma 1 When the intensity of preference for differentiated manufactured goods is large relatively and a is larger Than [4 + 2( à 1)c]=[2 + (3 + )c], progress of privatization leads to increase the labor demand of manufactured goods sector 2014/2/5 29 Migration between urban area and rural area (4) The labor demand of agricultural goods 1 L r = (1 à õ) ûà1 ð ñ wö û 1 ûà1 The revised population constraint in an economy h ð ñi ð ñ ð ñ 3+ò 2(1+3ò) ( + 1) à b 2(1+ò)+(2ò+(1+ò))c am à b 2(1+ò)+(2ò+(1+ò))c m 2 û wö w + (1 à õ) ûà1 û 1 ûà1 = 1 à õ From implicit function theorem dõ dò = à 2bm( [ 2+ ( +3)c]aà2[ 2+ ( à1)c]mwö ) ô à á [( 2+(2+)c)ò+ ( 2+c) ] 2 û w 1 ûà1 ( ) 1àõ û 1àû 1 ( ) ûà1 +1 õr0 2014/2/

16 Migration between urban area and rural area (5) ì = 0:8;í = 0:2; > 1;mwö = 1: [4+2(à1)c]mwö 2+(3+)c 4+2(à1)c 2+(3+)c 1.6 a < > > /2/5 31 Proposition 1 When the intensity of preference for differentiated manufactured goods is large (small) relatively and a and is larger(smaller) than [4 + 2c ( à 1)]mwö=[c ( + 3) + 2], the progress of public firm's privatization improves (makes a worse) urban unemployment. 2014/2/

17 The effect of privatization on social welfare (1) W ã : the equilibrium social welfare òh i 2 ó W ã b+c(+1) = + [p ã ] 2 a 2 (+1) 2b à 2 The effect of privatization of public firm on social welfare ã = à [b + c( + p ã ã 0 p ã + c 2 [ P ã ] 2 + (L r ) û ó + p + cp Price Price Index effect ((L r ) û ) Migration effect Proposition 2 a is large enough and the price effect and the employment effect exceed the price index effect, the progress of privatization of public firm improves the social welfare. 2014/2/5 33 Concluding remarks This paper considers the model to analyze the relationship between urban unemployment and the privatization of public firm. We apply the dualistic economy model to differentiated mixed oligopoly by combining Harris and Todaro (1970) with Fujiwara (2007). The effect of privatization of public firm on labor demand depends on the intensity of preference for differentiated manufactured goods. When the intensity of preference for differentiated manufactured goods is large relatively and some condition is held, the progress of public firm's privatization improves (makes a worse) urban unemployment. 2014/2/

18 Concluding remarks The large enough and the price effect and the employment effect exceed the price index effect, the progress of privatization of public firm improves the social welfare. 2014/2/