In a given market their are two firms each of which has the same dema.pdf

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In a given market their are two firms each of which has the same demand curves, for i{a,b} and j=i it is: qi=abpi+2bpj they also have the same cost function: ci(q)=cqi. (a) (4 points) (Differentiated Bertrand or Price Competition) Assuming both firms maximize over price: i. (1 point) Set up the objective function of a representative firm. ii. (2 points) Find the firm's best response. iii. (1 point) Find the Nash equilibrium - you may assume symmetry. Also find the equilibrium profits of both firms..

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