The Merger of Airline Companies: Chamberlin-Type Monopolistic Competition Approach

JAL3.nb 1 The Merger of Airline Companies: Chamberlin-Type Monopolistic Competition Approach December, 200 Toshitaka Fukiharu (Faculty of Economics, Hiroshima University) December, 200 Introduction In Fukiharu and Yamada [200], authors examined the merger of Japanese airline companies; JAL (Japan Air Line) and JAS (Japan Air System). There were three major airline companies; i.e. above two air line companies and ANA (All Nippon Airline), until 2002. JAL and ANA werw efficient firms with high revenues, and JAS was less efficient firm with less revenue. Japanese Fair Trade Commission (FTC) intervened in the merger of 2002. While admitting the merger, FTC set the condition for the merger: the lowering of air fare of the merged company and sustaining of lowered air fare for three years. After the merger, the Japanese airline industry consitsts mainly of two firms; JAL System and ANA. Constructing the Cournot oligopoly model, the authors showed that if the merger of two firms is profittable, the air fare must be higher in this two-firm-cournot equilibrium, compared with-three-firm Cournot equilibrium. As the conclusion of the paper, FTC's condition may be regarded as the remedial measure against this harmful consequence. The model in Fukiharu and Yamada [200], however, cannot explain why ANA opposed the merger. ANA expressed the opposition to the merger [http://...]. In the analysis of the Cournot model, ANA has no incentive to oppose this merger: it can secure higher profit after the merger of JAL and JAS, since the same high air fare prevails in the Cournot-type perfect substitutability framework. In the present paper, to explain the reason for the opposition by ANA, Chamberlin type monopolistic competition model is constructed. In this model, goods (airline services) are differentiated, so that different air fares are determined. Thus, in this paper, utility function is specified by CES function, where imperfect substitutability emerges. Using simulation approarch, the merger of JAL and JAS is examined. In Section I, three-firm Chamberlin type monopolistic competition model is constructed. It is assumed that JAL, ANA, and JAS provide air travel services, where those services are differentiated. In the short-run equlibrium, profits and prices of those airlines ate computed, by specifying the parameters of utility and cost functions. In Section II, two-firm Chamberlin type monopolistic competition model is constructed, and it is examined what

JAL3.nb 2 conditions are required for the merger of the two firms, such as JAL and JAS, to be feasible. With this conclusion, the financial situation of the third firm, such as ANA, is examined by simulation approarch. In[1]:= Off@General::"spell", General::"spell1"D I: Three-Firm Chamberlin Type Monopolistic Competition Model Suppose that there are three firms, such as JAL, ANA, and JAS, in a industry, such as air travel service. Services, provided by those airlines are differentiated for the consumers, thus services are imperfect substitutes. One of the utility functions which give rise to the imperfect substitutability in the demand function for these services is CES (constsnt elasticity of substitution) function: H k 1 x 1 -t + k 2 x 2 -t + k 3 x 3 -t L -nêt, where n is the degree of homogeneity. In this paper, it is assumed that n=1 and t=-1/2. In the first place, the case of k 1 =k 2 =k 3 =1 is examined. In[2]:= k1 = 1; k2 = 1; k3 = 1; m = 100; Let u[x 1,x 2,x 3 ] be the utility function of the society, where x 1 is the service of JAS, x 2 is the service of JAL, and x 3 is the service of ANA, with the following functional form. In[3]:= Out[3]= u = Hk1 x1^h1 ê 2L + k2 x2^h1 ê 2L + k3 x3^h1 ê 2LL^2 I è!!!!!! x1 + è!!!!!! x2 + è!!!!!! x3 M 2 This society maximizes the utility subject to the budget constraint: max u[x 1,x 2,x 3 ] subject to p 1 x 1 +p 2 x 2 +p 3 x 3 =m where p 1 is the service charge of JAS, p 2 is the service charge of JAL, and p 3 is the service charge of ANA and m is fixed budget of the society. Assuming that m=100, the demand function for each travel service is derived by the following function: In[]:= sol10 = Solve@D@u, x1dêd@u, x2d p1 ê p2, D@u, x2dêd@u, x3d p2 ê p3, p1 x1 + p2 x2 + p3 x3 m<, x1, x2, x3<d@@1dd Out[]= 9x1 x2 100 p2 p3 p1 Hp1 p2 + p1 p3 + p2 p3l, 100 p1 p3 p2 Hp1 p2 + p1 p3 + p2 p3l,x3 100 p1 p2 p3 Hp1 p2 + p1 p3 + p2 p3l = As remarked above, the gross substitutability prevails in the demand functions. To apply this demand function for Chamberlin type monopolistic competition model, inverse demand function, p 1 = f 1 [x 1,x 2,x 3 ] for JAS p 2 = f 2 [x 1,x 2,x 3 ] for JAL p 3 = f 3 [x 1,x 2,x 3 ] for ANA must be derived as in what follows. In[5]:= sol11 = Simplify@Solve@x1 m Hq1^2LêHq1 k1 + q2 k2 + q3 k3l, x2 m Hq2^2LêHq1 k1 + q2 k2 + q3 k3l, x3 m Hq3^2LêHq1 k1 + q2 k2 + q3 k3l<, q1, q2, q3<d@@3ddd;

JAL3.nb 3 In[]:= Out[]= sol12 = Solve@k1 ê p1 Hq1 ê. sol11l, k2 ê p2 Hq2 ê. sol11l, k3ê p3 Hq3 ê. sol11l<, p1, p2, p3<d@@1dd 100 100 I è!!!!!! x1 + è!!!!!! x2 M 9p3,p1, x3 + $%%%%%%%%%%%%%%%% I è!!!!!! x1 + %%%%%%%%%%%%%%%% è!!!!!! x2 M 2 i %%%%%%% è!!!!!! è!!!!!! x3 x1 x1 + 2 x1 è!!!!!! x2 + x2 + $%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% I è!!!!!! x1 + è!!!!!! x2 M 2 y %%%%%%% x3 j z k { 100 I è!!!!!! x1 + è!!!!!! x2 M p2 = i è!!!!!! è!!!!!! x2 x1 + 2 x1 è!!!!!! x2 + x2 + $%%%%%%%%%%%%%%%% I è!!!!!! x1 + %%%%%%%%%%%%%%%% è!!!!!! x2 M 2 y %%%%%%% x3 j z k { For JAS, profit function, pi 1 [x 1,x 2,x 3 ], is defined by f 1 [x 1,x 2,x 3 ] x 1 -c1[x 1 ], where c1[x 1 ]=c 1 x 1 is the linear cost function. As in Fukiharu and Yamada [200], assume that c 1 =2. pi 1 [x 1,x 2,x 3 ] is derived as follows. In[7]:= pi1 = Hp1 ê. sol12l x1 2 x1 100 è!!!!!! x1 I è!!!!!! x1 + è!!!!!! x2 M Out[7]= 2 x1+ x1 + 2 è!!!!!! x1 è!!!!!! x2 + x2 + $%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% I è!!!!!! x1 + è!!!!!! x2 M 2 %%%%%%% x3 For JAL, profit function, pi 2 [x 1,x 2,x 3 ], is defined by f 2 [x 1,x 2,x 3 ] x 2 -c2[x 2 ], where c2[x 2 ]=c 2 x 2 is the linear cost function. As in Fukiharu and Yamada [200], assume that c 2 =1.5. pi 2 [x 1,x 2,x 3 ] is derived as follows. In[]:= pi2 = Hp2 ê. sol12l x2 1.5 x2 100 I è!!!!!! x1 + è!!!!!! x2 M è!!!!!! x2 Out[]= 1.5 x2 + x1 + 2 è!!!!!! x1 è!!!!!! x2 + x2 + $%%%%%%%%%%%%%%%% I è!!!!!! x1 + %%%%%%%%%%%%%%%% è!!!!!! x2 M 2 %%%%%%% x3 For ANA, profit function, pi 3 [x 1,x 2,x 3 ], is defined by f 3 [x 1,x 2,x 3 ] x 3 -c3[x 3 ], where c3[x 3 ]=c 3 x 3 is the linear cost function. As in Fukiharu and Yamada [200], assume that c 3 =1.5. pi 3 [x 1,x 2,x 3 ] is derived as follows. In[9]:= pi3 = Hp3 ê. sol12l x3 1.5 x3 Out[9]= 1.5 x3 + 100 x3 x3 + $%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% I è!!!!!! x1 + è!!!!!! x2 M 2 %%%%%%% x3 Traditional approach is, first, to derive reaction function, x 1 =R 1 [x 2,x 3 ], by solving pi 1 @x 1, x 2, x 3 D/ x 1 =0 with respect to x 1. After deriving these reaction functions, by solving the following simultaneous equations the short-run equilibrium for Chamberlin type monopolistic competition is computed. x 1 =R 1 [x 2,x 3 ] x 2 =R 2 [x 1,x 3 ] x 3 =R 3 [x 1,x 2 ] Unfortunately, however, Mathematica cannot derive these reaction functions. Thus, the system of simultaneous equations is solved numerically utilizing Newton method as in what follows. In[10]:= sol13 = FindRoot@ D@pi1, x1d 0, D@pi2, x2d 0, D@pi3, x3d 0<, x1, 10<, x2, 10<, x3, 10<D Out[10]= x1 5.1322, x2 7.2522, x3 7.2522<

JAL3.nb Profits for JAS, JAL, and ANA at this short-run equilibrium for Chamberlin type monopolistic competition are computed as in what follows. In[11]:= pi1 ê. sol13, pi2 ê. sol13, pi3 ê. sol13< Out[11]= 1.23, 23.97, 23.97< Total profit for the airline industry is.7979. In[12]:= Apply@Plus, pi1 ê. sol13, pi2 ê. sol13, pi3 ê. sol13<d Out[12]=.7979 Utility level for this society at the short-run equilibrium for Chamberlin type monopolistic competition is computed as in what follows. In[13]:= u ê. sol13 Out[13]= 0.725 Finally, air fares for ANA, JAS, and JAL at the short-run equilibrium for Chamberlin type monopolistic competition are computed as in what follows. In[1]:= sol12 ê. sol13 Out[1]= p3.575, p1 5.575, p2.575< In what follows, the above program is collected as the function, check3[c 1,c 2,k 1,k 2,k 3,m], which computes the shortrun equilibrium for Chamberlin type monopolistic competition, given c 1, c 2, k 1, k 2, k 3, and m. In[15]:= Clear@u, c2, k1, k2, x2, x3, m, fig2, fig3, sol1, sol2, sol3, sold In[1]:= check3@c1_, c2_, k1_, k2_, k3_, m_d := Module@u, sol10, sol11, sol12, pi1, pi2, pi3, sol13<, u = Hk1 x1^h1 ê 2L + k2 x2^h1 ê 2L + k3 x3^h1 ê 2LL^2; sol10 = Solve@D@u, x1dêd@u, x2d p1 ê p2, D@u, x2dêd@u, x3d p2 ê p3, p1 x1 + p2 x2 + p3 x3 m<, x1, x2, x3<d@@1dd; sol11 = Simplify@Solve@x1 m Hq1^2LêHq1 k1 + q2 k2 + q3 k3l, x2 m Hq2^2LêHq1 k1 + q2 k2 + q3 k3l, x3 m Hq3^2LêHq1 k1 + q2 k2 + q3 k3l<, q1, q2, q3<d@@3ddd; sol12 = Solve@k1 ê p1 Hq1 ê. sol11l, k2ê p2 Hq2 ê. sol11l, k3 ê p3 Hq3 ê. sol11l<, p1, p2, p3<d@@1dd; pi1 = Hp1 ê. sol12l x1 c1 x1; pi2 = Hp2 ê. sol12l x2 c2 x2; pi3 = Hp3 ê. sol12l x3 c2 x3; sol13 = FindRoot@ D@pi1, x1d 0, D@pi2, x2d 0, D@pi3, x3d 0<, x1, 10<, x2, 10<, x3, 10<D; sol13, ":utility" Hu ê. sol13l, Hsol12 ê. sol13l, ":profit 1" Hpi1 ê. sol13l, ":profit 2" Hpi2 ê. sol13l, ":profit 3" Hpi3 ê. sol13l<d It is ascertained first of all that the same result is obtained when c 1 =2, c 2 =1.5, k 1 =1, k 2 =1, k 3 =1, and m=100. In[17]:= check3@2, 1.5, 1, 1, 1, 100D Out[17]= x1 5.1322, x2 7.2522, x3 7.2522<, 0.725 :utility, p3.575, p1 5.575, p2.575<, 1.23 :profit 1, 23.97 :profit 2, 23.97 :profit 3<

JAL3.nb 5 Next, it is examined what would happen when k 1, k 2, and k 3 are changed proportionately. As is expected, the same result is obtained since the demand functions are the same as before, except for the utility level of the society. In[1]:= check3@2, 1.5, 1 ê 3, 1 ê 3, 1 ê 3, 100D Out[1]= x1 5.1322, x2 7.2522, x3 7.2522<,.75139 :utility, p3.575, p1 5.575, p2.575<, 1.23 :profit 1, 23.97 :profit 2, 23.97 :profit 3< As JAS becomes more inefficient; higher c 1, air fares of all the airlines become higher, and profits for JAL and ANA rises, while the profit for JAS is lowered. In[19]:= check3@3, 1.5, 1, 1, 1, 100D Out[19]= x1 3.005, x2 7.93, x3 7.93<, 53.935 :utility, p3.51, p1 7.51, p2.51<, 1.59 :profit 1, 2.3932 :profit 2, 2.3932 :profit 3< In[20]:= Clear@u, v, c2, k1, k2, k3, x2, x3, m, pi2, pi3, sol0, sol1, sol2, sol3, fig2, fig3, sold In[21]:= II: Two-Firm Chamberlin Type Monopolistic Competition Model Suppose that the merger between JAS and JAL is admitted by FTC. Crews of JAS can provide the air travel service under JAL system. Thus, the merger implies the disappearance of JAS from the market and the creation of new airline company; JAL System. In this section, it is examined why the merger is attempted at all. The merger is attemted since it is profitable, in the sense that the profit of JAL System is at least as great as the sum of profits of JAL and JAS. In Fukiharu and Yamada [200], it was shown that the merger in Cournot oligopoly is profitable so long as the difference of efficiency; the difference of c 1 and c 2, is large. Is it possible that the merger in Chamberlin type monopolistic competition model is profitable when the difference of efficiency is large. In order to examine this problem, the two-firm Chamberlin type monopolistic competition model is constructed in what follows. The utility function, v[x 2,x 3 ], is of CES type: H k 2 x 2 -t + k 3 x 3 -t L -nêt, where it is assumed that n=1 and t=-1/2. As in Section I, the case of k 2 =k 3 =1 is examined. In[22]:= c2 = 1.5; k2 = 1; k3 = 1; m = 100; In[23]:= Out[23]= v = Hk2 x2^h1 ê 2L + k3 x3^h1 ê 2LL^2 I è!!!!!! x2 + è!!!!!! x3 M 2 This society maximizes the utility subject to the budget constraint: max v[x 2,x 3 ] subject to p 2 x 2 +p 3 x 3 =m where p 2 is the service charge of JAL System, and p 3 is the service charge of ANA and m is fixed budget of the society. Assuming that m=100, the demand function for each travel service is derived by the following function: In[2]:= sol0 = Solve@D@v, x2dêd@v, x3d p2 ê p3, p2 x2 + p3 x3 m<, x2, x3<d@@1dd Out[2]= 9x2 100 p3 p2 Hp2 + p3l,x3 100 p2 p3 Hp2 + p3l =

JAL3.nb As remarked above, the gross substitutability prevails in the demand functions. To apply this demand function for Chamberlin type monopolistic competition model, inverse demand function, p 2 =g 2 [x 2,x 3 ] for JAL System p 3 =g 3 [x 2,x 3 ] for ANA must be derived as in what follows. In[25]:= sol1 = Solve@x2 Hx2 ê. sol0l, x3 Hx3 ê. sol0l<, p2, p3<d@@2dd Out[25]= 9p2 100 è!!!!!! x2 I è!!!!!! x2 + è!!!!!! x3 M,p3 100 I è!!!!!! x2 + è!!!!!! x3 M è!!!!!! x3 = For JAL System, profit function, pi 2 [x 2,x 3 ], is defined by g 2 [x 2,x 3 ] x 2 -c2[x 2 ], where c2[x 2 ]=c 2 x 2 is the linear cost function. As in Section I, we assume that c 2 =1.5. pi 2 [x 2,x 3 ] is derived as follows. In[2]:= pi2 = Hp2 ê. sol1l x2 c2 x2 è!!!!!! 100 x2 Out[2]= 1.5 x2 + è!!!!!! x2 + è!!!!!! x3 For ANA, profit function, pi 3 [x 2,x 3 ], is defined by g 3 [x 2,x 3 ] x 3 -c3[x 3 ], where c3[x 3 ]=c 3 x 3 is the linear cost function. As in Section I, we assume that c 3 =1.5. pi 3 [x 2,x 3 ] is derived as follows. In[27]:= Out[27]= pi3 = Hp3 ê. sol1l x3 c2 x3 100 è!!!!!! x3 è!!!!!! x2 + è!!!!!! 1.5 x3 x3 Traditional approach is, first, to derive reaction function, x 2 =R 2 [x 3 ], by solving pi 2 @x 2, x 3 D/ x 2 =0 with respect to x 2. After deriving these reaction functions, by solving the following simultaneous equations the short-run equilibrium for Chamberlin type monopolistic competition is computed. x 2 =R 2 [x 3 ] x 3 =R 3 [x 2 ] Mathematica can derive the reaction function of JAL System as in what follows. In[2]:= Out[2]= sol2 = Solve@D@pi2, x2d 0, x2d@@3dd 9x2 0.7 x3 0.037 H3200. x3 1. x3 2 L I2.17 10 7 x3 1.79 10 x3 2 15. x3 3 + 70. x3 H1.7 + x3l è!!!!!!!!!!!!!!!!!!!!! 225. + x3 M 1ê3 + 0.029393 I2.17 10 7 x3 1.79 10 x3 2 15. x3 3 + 70. x3 H1.7 + x3l è!!!!!!!!!!!!!!!! 225. + x3!!!!! M 1ê3 = The reaction function of JAL System is depictedas in what follows.

JAL3.nb 7 In[29]:= fig2 = Plot@x2 ê. sol2, x3, 0, 10<, AxesLabel "x3", "x2"<d; x2 7 5 2 10 x3 Mathematica can derive the reaction function of ANA as in what follows. In[30]:= Out[30]= sol3 = Solve@D@pi3, x3d 0, x3d@@3dd 9x3 0.7 x2 0.037 H3200. x2 1. x2 2 L I2.17 10 7 x2 1.79 10 x2 2 15. x2 3 + 70. x2 H1.7 + x2l è!!!!!!!!!!!!!!!!!!!!! 225. + x2 M 1ê3 + 0.029393 I2.17 10 7 x2 1.79 10 x2 2 15. x2 3 + 70. x2 H1.7 + x2l è!!!!!!!!!!!!!!!! 225. + x2!!!!! M 1ê3 = The reaction function of ANA is depictedas in what follows. In[31]:= list1 = Table@x3 ê. sol3 ê. x2 0.01 i, 0.01 i<, i, 1, 1000<D; fig3 = ListPlot@list1, PlotJoined True, PlotStyle Dashing@0.01<D, AxesLabel "x3", "x2"<d; 10 x2 2.5 7 7.5 x3 The equilibrium of short-run two-firm Chamberlin type monopolistic competition model is derived as the intersection of two reaction functions as depicted in the following diagram.

JAL3.nb In[33]:= Show@fig2, fig3<, PlotRange 0, 10<, 0, 10<<D; x2 10 2 2 10 x3 To derive the equilibrium, the system of simultaneous equations is solved numerically utilizing Newton method as in what follows. In[3]:= sol = FindRoot@x2 Hx2 ê. sol2l, x3 Hx3 ê. sol3l<, x2, 10<, x3, 10<D Out[3]= x2.33333, x3.33333< The profit, which accrues to JAL System, is computed as in what follows. In[35]:= pi2 ê. sol Out[35]= 37.5 The profit, which accrues to ANA, is computed as in what follows. In[3]:= pi3 ê. sol Out[3]= 37.5 In Section I, JAS's profit was 1.23, while JAL's profit was 23.97. Thus, the merger of JAS and JAL, or the creation of JAL System is not profitable, since the profit of JAL System cannot surpass the sum of profits of JAL and JAS. Utility for the society is computed as in what follows. In[37]:= v ê. sol Out[37]= 33.3333 Air fares of JAL System and ANA are given as in what follows, which are higher than in the three-firm Chamberlin type monopolistic competition model. In[3]:= sol1 ê. sol Out[3]= p2., p3.< As remarked, in Fukiharu and Yamada [200], it was shown that the merger in Cournot oligopoly is profitable so long as the difference of efficiency; the difference of c 1 and c 2, is large. The aim of this section is to examine if it is possible that the merger in Chamberlin type monopolistic competition model is profitable when the difference of efficiency is large. Using check3, constructed in Section I, if c 1 =10 and c 2 =1.5, equilibrium for the three-firm Chamberlin type monopolistic competition model is computed as in what follows.

JAL3.nb 9 In[39]:= check3@10, 1.5, 1, 1, 1, 100D Out[39]= x1 0.09, x2.2351, x3.2351<, 1.373 :utility, p3 5.12, p1 22.12, p2 5.12<, 5.97032 :profit 1, 32.255 :profit 2, 32.255 :profit 3< JAS's profit is 5.97032, while JAL's profit is 32.255. Thus, the merger of JAS and JAL, or the creation of JAL System is not profitable, since the profit of JAL System cannot surpass the sum of profits of JAL and JAS. If c 1 =100 and c 2 =1.5, equilibrium for the three-firm Chamberlin type monopolistic competition model is computed as in what follows. In[0]:= check3@100, 1.5, 1, 1, 1, 100D Out[0]= x1 0.0070799, x2.3311, x3.3311<, 3.305 :utility, p3 5.91503, p1 202.915, p2 5.91503<, 0.720 :profit 1, 3.73 :profit 2, 3.73 :profit 3< JAS's profit is 0.720, while JAL's profit is 3.73. Thus, the merger of JAS and JAL, or the creation of JAL System is not profitable, since the profit of JAL System cannot surpass the sum of profits of JAL and JAS. If c 1 =1000 and c 2 =1.5, equilibrium for the three-firm Chamberlin type monopolistic competition model is computed as in what follows. In[1]:= check3@1000, 1.5, 1, 1, 1, 100D Out[1]= x1 0.000075532, x2.33331, x3.33331<, 33.33 :utility, p3 5.99105, p1 2002.99, p2 5.99105<, 0.07772 :profit 1, 37.25 :profit 2, 37.25 :profit 3< JAS's profit is 0.07772, while JAL's profit is 37.25. Thus, the merger of JAS and JAL, or the creation of JAL System is not profitable, since the profit of JAL System cannot surpass the sum of profits of JAL and JAS. In this way, it is impossible that the merger in Chamberlin type monopolistic competition model is profitable when the difference of efficiency is large. What is required in order for the merger to be profitable in Chamberlin type monopolistic competition model? In order to examine this problem, the above series of program is collected as check2[c 2,k 2,k 3,m], which computes the equilibrium with the gragh of reaction functions, given c 2,k 2,k 3, and m. In[2]:= check2@c2_, k2_, k3_, m_d := Module@v, sol0, sol1, pi2, sol2, fig2, pi3, sol3, list1, fig3, fig, sol, pi20, pi30, v0, p0<, v= Hk2 x2^h1 ê 2L + k3 x3^h1 ê 2LL^2; sol0 = Solve@D@v, x2dêd@v, x3d p2 ê p3, p2 x2 + p3 x3 m<, x2, x3<d@@1dd; sol1 = Solve@x2 Hx2 ê. sol0l, x3 Hx3 ê. sol0l<, p2, p3<d@@2dd; pi2 = Hp2 ê. sol1l x2 c2 x2; sol2 = Solve@D@pi2, x2d 0, x2d@@3dd; fig2 = Plot@x2 ê. sol2, x3, 0, 10<, DisplayFunction IdentityD; pi3 = Hp3 ê. sol1l x3 c2 x3; sol3 = Solve@D@pi3, x3d 0, x3d@@3dd; list1 = Table@x3 ê. sol3 ê. x2 0.01 i, 0.01 i<, i, 1, 1000<D; fig3 = ListPlot@list1, PlotJoined True, PlotStyle Dashing@0.01<D, DisplayFunction IdentityD; fig = Show@fig2, fig3<, PlotRange 0, 10<, 0, 10<<D; sol = FindRoot@x2 Hx2 ê. sol2l, x3 Hx3 ê. sol3l<, x2, 10<, x3, 1<D; pi20 = pi2 ê. sol; pi30 = pi3 ê. sol; v0 = v ê. sol; p0 = sol1 ê. sol; Show@fig, DisplayFunction $DisplayFunctionD; sol, ":utility" v0, p0, ":profit 2" pi20, ":profit 3" pi30<d First, it is ascertained that the function computes same equilibrium when the same parameters are given.

JAL3.nb 10 In[3]:= check2@1.5, 1, 1, 100D 10 2 2 10 Out[3]= x2.33333, x3.33333<, 33.3333 :utility, p2., p3.<, 37.5 :profit 2, 37.5 :profit 3< Suppose, next, that after the merger of JAL and JAS, evaluation of services for JAL System and ANA rises proportionately, essentially the same result obtains, except for utility level. In[]:= check2@1.5, 2, 2, 100D 10 2 2 10 Out[]= x2.33333, x3.33333<, 133.333 :utility, p2., p3.<, 37.5 :profit 2, 37.5 :profit 3< Finally, suppose that after the merger of JAL and JAS, evaluation of service for JAL System rises proportionately greater than for ANA, the merger may become profitable, as shown by the following simulation. In[5]:= check2@1.5, 3, 2, 100D 10 2 2 10 Out[5]= x2., x3.<, 200. :utility, p2 7.5, p3 5.<,. :profit 2, 2. :profit 3<

JAL3.nb 11 Note, however, that the profit for ANA declines, and the air fare of JAL System rises, while the air fare of ANA declines. This point is what makes ANA oppose the merger of JAL and JAS. In its opinion on the merger, ANA remarked that combined air route system makes JAL System more attractive than ANA. The toal profit for the airline industry after the merger is 7, which is greater than the one before the merger. The intevention by Japanese FTC; the directive of air fare decline on JAL System, may be regarded as the remedial measure againt this situation. Finally, it must be noted that the change of utility levels before and after the merger cannot determine whether the merger makes the society better off, since the utility function differs by the merger; disappearance of x 1. Conclusion Constructing the Cournot oligopoly model, Fukiharu and Yamada [200] showed that if the merger of JAL and JAS is profitable, the air fare after the merger must be higher. As the conclusion of their paper, FTC's condition for the merger may be regarded as the remedial measure against this harmful consequence. Their model, however, cannot explain why ANA opposed the merger, since ANA can obtain higher profit than before the merger in the Cournot oligopoly model. This stems from one of the assumptions in the Cournot oligopoly model, the assumption of perfect substitutability of goods and services. In this paper, it is assumed that goods and services are differentiated, and they are imperfect substitutes. For this purpose, the Chamberlin-type monopolistic competition model under CES utility function is utilized. In Fukiharu and Yamada [200], it was shown that the large difference of efficiency of the merging two companies may make the merger profitable. In this paper, it was shown that that factor alone cannot make the merger profitable. The increased attractiveness of merged companies is required for making the merger profitable. Furthermore, the profit for ANA declines, and the air fare of JAL System rises, while the air fare of ANA declines. This point is what makes ANA oppose the merger of JAL and JAS. In its opinion on the merger, ANA remarked that combined air route system makes JAL System more attractive than ANA. Finally, the toal profit for the airline industry after the merger is greater than the one before the merger. Thus, the intevention by Japanese FTC; the directive of air fare decline on JAL System, may be regarded as the remedial measure againt this situation, as in Fukiharu and Yamada [200]. REFERENCES (1) Fukiharu, T, and Hidenori Yamada [200], A Case Study of Anti-Monopoly Law Application: Merger of JAL and JAS, (in Japanese), Discussion Paper (http://home.hiroshima-u.ac.jp/fukito/index.htm)