Consider a differentiated Bertrand model with demands for firms 1 and 2 given, re- spectively, by: x_(1)=10-p_(1)+p_(2) x_(2)=10-p_(2)+p_(1) (a) The costs of each firm are given by c_(1)=c_(2)=3. Plot the best responses. Solve for the equilibrium prices and profits for each firm. (b) Suppose now that firm 1 succeeds in increasing 2's cost from c_( solutionspile.com

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Consider a differentiated Bertrand model with demands for firms 1 and 2 given, re- spectively, by:

x_(1)=10-p_(1)+p_(2)
x_(2)=10-p_(2)+p_(1)

(a) The costs of each firm are given by

c_(1)=c_(2)=3

. Plot the best responses. Solve for the equilibrium prices and profits for each firm. (b) Suppose now that firm 1 succeeds in increasing 2's cost from

c_(2)=3

to

c_(2)=6

, and this is costless for firm 1. Compute the new equilibrium prices, quantities, and profits, and draw the change in the best responses. (c) Assume that firm 1 can raise firm 2's marginal cost as in part (b) but that this action is costly - that is, firm 1 faces an increase of its marginal cost

c_(1)

when attempting to raise its rival's cost. How high can

c_(1)

rise before it becomes un- profitable for firm 1 to raise its rival's cost to

c_(2)=6

?

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