Consider Bertrand competition but with differentiated products. The products are

Question

Consider Bertrand competition but with differentiated products. The products are Mishka’s coffee and Temple coffee. The demand for Mishka’s coffee is given by qM = 12 2pM + pT where pM is the own price of coffee and pT is Temple’s price of coffee. Demand for Temple’s coffee is qT = 12 2pT + pM. Note that because the products are differentiated, if one coffee shop sets a lower price it does not capture the entire coffee market. Assume the marginal cost of each coffee shop is 3.

(a) Find the best response functions of each coffee shop.

(b) Solve for the equilibrium prices of each coffee shop.

Explanation / Answer

a) The best response is to make a collission and set a combined price and behave like a monopoly. Since demand curve and marginal cost for both the firms is identical, the best way iis to behave like a monopoly by making collusive oligopoly.

b) In that case Market demand will be given by Qd = 24 - 2p

Deman si nothing but AR

TR = 24q -2q2

MR = 24-4q

Equilibrium where MR = MC

24-4q = 3

4q = 21

q = 5.25

5.25 = 24 -2p

2p = 18.75

p = 9.375

both the firms should sell equal quantties and at same price.

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