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Suppose that Pepsi and Coke are competing in a horizontally differentiated Bertrand market and setting prices. The demand curves are as follows:
Qc = 40-5Pc + 4Pp
Qc = 100-2Pp + Pc
Coke face marginal cost MCc = 12 and Pepsi faces marginal cost MCp = 8.
(a) Write the equation for the demand for coke in terms of price Pc as a function of Pp and Qc.
(b) Determine the marginal revenue for Coke as a function of Pp and Qc.
(c) Find the equation that tells how much Coke would produce for any price Pp using the above.
(d) Find the reaction function for Coke (Pc as a function of Pp ) using your answer above.
(e) Find the reaction function for Pepsi.
(f) Determine the Bertrand equilibrium.
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