mathsperts3

# mathsperts3 - &nd the Cournot (Nash) equilibrium. Let q...

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Mathsperts II. The Extended Cournot Game. Suppose in the world market for cars, there are two competitors, Volkswagen and Toyota. Suppose both have the same unit costs of production c and the world demand for cars is given p = 1 q where q q V ; q T respectively, show V = [1 q V q T c ] q V T = [1 q T q V c ] q T : As it plays no role in what follows, simplify by assuming c = 0 : (i) If Toyota produces q T ; let q BR V denote the level of output which maximises Volkswagen pro&t; i.e. q BR V ( q T ) = arg max q V [1 q V q T ] q V : Show q BR V = 1 2 [1 q T ] and q BR T = 1 2 [1 q V ] Find the Cournot equilibrium where both &rms are playing best responses; i.e. solve for q V ; q T where q V = q BR V ( q T ) and q T = q BR T ( q V ) : (ii) Suppose Angela Merkel decides to subsidise Volkswagen with a small pro- duction subsidy s: V = [1 q V q T + s ] q V T = [1 q T q V ] q T :
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Unformatted text preview: &nd the Cournot (Nash) equilibrium. Let q & V ( s ) ; q & T ( s ) denote those equilibrium choices. How does this subsidy a/ect outputs and the equilbrium market price? (iii) Assume Volkswagen is entirely owned by German shareholders. Also Angela Merkel can use lump sum taxation to recover the production subsidy. The surplus accruing to the German nation is then & V = [1 & q & V ( s ) & q & T ( s )] q & V ( s ) : Show this surplus is increasing in s; while Toyota±s surplus is decreasing in s: How might this explain why EU trading rules restrict individual governments from subsidising companies in their own countries? 1...
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## This note was uploaded on 12/31/2011 for the course ECON MR 102 taught by Professor Huyduong during the Winter '11 term at RMIT Vietnam.

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