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\title{Delegations In The Presence Of Foreign Competition}
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             \author[1]{Dr. Najiba  Benabess}

             \affil[1]{  Norwich University}

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\date{\small \em Received: 23 June 2010 Accepted: 22 July 2010 Published: 3 August 2010}

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\begin{abstract}
        


Previous research examining mixed duopoly shows that the use of an incentive contract for the public firm increases welfare and that privatization reduces welfare. This paper is built from Barros (1995) model by investigating and deriving the optimal incentive contracts when the public domestic firm competes not with domestic private firm but instead with a private foreign firm. We show that by giving the public manager an incentive contract based on linear combination of welfare and profit, welfare increases. Indeed, for less weight on profit given that the private firm is foreign instead of domestic, the optimal delegation contract is actually lower than that in the traditional duopoly (Barros 1995). On the other hand, the effect of privatization in this case is more complex, it depends on marginal cost.

\end{abstract}


\keywords{duopoly, privatization, optimal delegation, }

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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
he mixed oligopolies literature has been used to examine the welfare consequences of strategic trade policies, privatization, open-door policies, and international acquisitions and location decisions (DeFraja and Delbono, 1989; Fjell and Pal, 1996; Pal and White, 1998; \hyperref[b3]{Matsushima and Matsumura, 2003}; \hyperref[b1]{Dadpay and Heywood, 2006)}. A few previous studies integrate incentive contracts in mixed oligopoly and they deserve reconsideration. \hyperref[b0]{Barros (1995)} examined a duopoly with a public firm and one private domestic firm. The public firm maximizes an incentive contract combining profit and sales although the results are unchanged if instead it maximizes a combination of profit and welfare. He draws two conclusions: the use of an incentive contract increases welfare and privatization of the public firm decreases welfare. We reproduce these conclusions for the duopoly by considering the public firm competes with a foreign private firm instead of domestic firm. We found out that incentive contract increases welfare even when the public firm competes with a foreign firm instead of domestic firm. More importantly, the optimal incentive contract (?) is lower than the one when the public firm competes with a domestic private firm. On the other hand, the effect of privatization on welfare is more complicated in this case than in the traditional mixed duopoly model (DeFraja and Delbono 1989). The effect of privatization depends on the marginal cost (k). This paper is motivated by the fact that in many actual cases, About : 158 harmon drive , northfield vt 05663 norwich university business school. state-owned firms compete with foreign firms due to globalization and international integration. The next section describes the model and present equilibria. The third section compares social welfare with and without incentive contract for public firm managers; and privatization is also examined in this section. Section 4 draws conclusions. 
\section[{II.}]{II.} 
\section[{MODEL AND EQUILIBRIA}]{MODEL AND EQUILIBRIA}\par
There exists one public firm indexed by 0 competing with one private foreign firm. Private owners maximize profit and public owners maximize welfare. Managers maximize the objective function as specified in their respective incentive contracts. All firms produce homogenous goods and share the quadratic cost function typically used in the literature , where is a constant. As we are ignoring entry issues, we set without loss of generality.\par
Let be the output of the public firm and be the output of the private foreign firm. A linear inverse demand curve, , gives consumer surplus as . 
\section[{The private foreign firm's profit is}]{The private foreign firm's profit is}\par
The public firm's profit is\par
Social welfare, the sum of consumer surplus and producer surplus, is the public owner's (the government's) objective function:\par
(\par
The public owner offers its manager an incentive contract that is linear combination of welfare and the public firm's profit:\par
There are a total of three cases: (a) public firm maximizes welfare and private foreign firm maximizes its profit; (b) the public firm provides its manager with an incentive contract; (c) the public firm maximizes its profit instead of welfare. Thus in each comparison we identify the change in social welfare that results from the public incentive contract. The equilibrium for case a and c, without any strategic contracts, have only one stage; while for the remaining case (b), the structures of the games have two stages. The public owner and private firm owner play a game over the incentive proportions in stage one and the public and private firms play a Cournot game in quantity in stage two. Backward induction yields the subgame perfect Nash equilibrium in each case.\par
Equilibrium for Case a:\par
The optimal output for the public firm and foreign private firm are presented respectively:(5) (6)\par
The optimal welfare resulting from this case is presented as follows:\par
(7)\par
Equilibrium for Case b:\par
The equilibrium when only the public firm faces an incentive contract yields the following:\par
(8)(9)\textbf{(10)}\par
The optimal welfare resulting from case b is presented in equation (  {\ref 11}):\par
(11) Thus, in the next section, comparing (7) and (11) yields the welfare difference associated with the public incentive contract. 
\section[{Case c: Privatization}]{Case c: Privatization}\par
In this case, the public firm maximizes its profit instead of social welfare. The equilibrium yields:(12) (13)\textbf{(14)}\par
III. 
\section[{COMPARISON}]{COMPARISON}\par
This section draws comparisons across the equilibria derived above.\par
1. The effect of incentive contract on social welfare:\par
First, we compare case (a) with case( b). The government is able to set an objective function for the public firm other than simply maximizing welfare. This ability actually results in a higher eventual welfare. The fundamental proposition follows from comparing a public firm that maximizes welfare with one that maximizes incentive contract.\par
PROPOSITION 1: In a mixed duopoly in which public firm competes with a foreign profit maximizing firm, the public firm can always improve welfare by using an incentive contract.\par
PROOF: Subtracting (7) from (11) respectively yields: <0 Next, we compare the optimal extent of incentive contract when the public firm competes with foreign firm with the one when the public firm competes with a domestic private firm. We found out that the less the weight or the emphasis on profit given that the private firm is foreign and not domestic, the optimal extent of delegation actually exceeds that of the case of \hyperref[b0]{Barros (1995)} only when the marginal cost is lower than value one.\par
PROPOSITION 2: When a public firm competes with a foreign firm, the optimal extent of delegation exceeds that of the case when a public firm competes with a domestic firm but only when the marginal cost is lower than value one. 
\section[{PROOF:}]{PROOF:}\par
The optimal extend of delegation for the traditional mixed duopoly is as follows \hyperref[b0]{(Barros 1995}):\par
(15) Subtracting (  {\ref 9}) from (16) yields:\par
Figure  {\ref 1} : Shows the change of the optimal extent of delegation resulting from the cases when the public firm competes with a foreign firm and when it competes with a domestic private firm.\par
The figure above shows that:? k<1, ?\textbf{k=1, ; ? k>1, . 2.} 
\section[{PROPOSITION 3: In mixed duopoly in which the public}]{PROPOSITION 3: In mixed duopoly in which the public}\par
The effect of privatization on welfare: Next, we determine the effect of privatization on welfare when a public firm competes with a foreign private firm. I found out that when the public firm competes with a foreign firm instead domestic one, the effect of privatization on welfare in undetermined, it depends on the marginal cost; which is in contrast with the traditional mixed duopoly in which DeFraja and Delbono  {\ref (1989)} showed that privatization increases welfare.\par
firm competes with a foreign private firm, privatization may increase social welfare but only if the marginal cost is sufficiently high; otherwise, if the marginal cost is low (less than k*) avoiding privatization is the optimal. 
\section[{PROOF:}]{PROOF:}\par
Subtracting equation (  {\ref 7}) from ( \hyperref[formula_5]{14}) yields: We conclude that, at higher k, it is optimal for the public firm to maximize profit instead of social welfare.\par
3.\par
PROPOSITION 4: In Mixed duopoly in which a public firm competes with a foreign private firm, privatization decreases welfare and delegation improves it.\par
Privatization versus delegation:\par
In this section, we compare the optimal welfare when a public firm maximizes its profit with the one when it provides its manager an incentive contract. 
\section[{PROOF:}]{PROOF:}\par
Subtracting equations ( \hyperref[formula_5]{14}) from (11) yields:\par
Figure  {\ref 4} : Represents the three optimal welfares resulting from the three cases presented above .\par
Green curve refers to , the red curve is the and the yellow curve represents . We conclude that the optimal welfare with incentive contract is superior to both privatization and nationalization.\par
IV. 
\section[{CONCLUSION}]{CONCLUSION}\par
Previous work from duopoly examining public managerial incentive contracts reached unambiguous conclusions. Such contracts always improve welfare and privatization decreases welfare. This paper investigates the optimal extent of delegation when a public firm competes with a foreign private firm instead of domestic private firm. A series of important conclusions emerge. First, when only the public firm has the possibility of an incentive contract, the contract continues to increase welfare. Second, the extent of optimal delegation when a public firm competes with a domestic private firm exceeds that one resulting from the case when a public firm competes with a foreign private firm instead. Third, the effect of privatization on social welfare depends on the specifics of the market structure and the cost function.\par
V.\begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{figure3}}\end{figure}
 			\footnote{Global Journal of Management and Business Research Volume XI Issue V Version I ©2011 Global Journals Inc. (US) April} 			\footnote{Delegations In The Presence Of Foreign Competition©2011 Global Journals Inc. (US)} 			\footnote{©2011 Global Journals Inc. (US)} 			\footnote{©2011 Global Journals Inc. (US) April 2011} 		 		\backmatter   			 
\subsection[{ACKNOWLEDGEMENTS}]{ACKNOWLEDGEMENTS}\par
The author is very thankful to John Heywood for his help, support and guidance in this research. 			  			  				\begin{bibitemlist}{1}
\bibitem[Defraja and Delbono ()]{b2}\label{b2} 	 		‘Alternative strategies of a public enterprise in oligopoly’.  		 			G Defraja 		,  		 			F Delbono 		.  	 	 		\textit{Oxford Economic Papers}  		1989. 41 p. .  	 
\bibitem[Barros ()]{b0}\label{b0} 	 		‘Incentive schemes as strategic variables: an application to a mixed duopoly’.  		 			F Barros 		.  	 	 		\textit{International Journal of Industrial Organization}  		1995. 13 p. .  	 
\bibitem[Matsushima and Matsumura ()]{b3}\label{b3} 	 		‘Mixed oligopoly and spatial agglomeration’.  		 			N Matsushima 		,  		 			T Matsumura 		.  	 	 		\textit{Canadian Journal of Economics}  		2003. 36 p. .  	 
\bibitem[Dadpay and Heywood ()]{b1}\label{b1} 	 		‘Mixed Oligopoly in a single international market’.  		 			A Dadpay 		,  		 			J S Heywood 		.  	 	 		\textit{Australian Economic Papers}  		2006. 45 p. .  	 
\bibitem[Pal and White ()]{b4}\label{b4} 	 		‘Mixed oligopoly, privatization, and strategic trade policy’.  		 			D Pal 		,  		 			M D White 		.  	 	 		\textit{Southern Economic Journal}  		1998. 65 p. .  	 
\bibitem[The Presence Of Foreign Competition ©2011 Global Journals Inc. (US)]{b5}\label{b5} 	 		\textit{The Presence Of Foreign Competition ©2011 Global Journals Inc. (US)},  				 	 
\end{bibitemlist}
 			 		 	 
\end{document}
