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3. please answer the following question fully and in detail consider...

# Question: please answer the following question fully and in detail consider...

###### Question details

Please answer the following question fully and in detail!

Consider a Bertrand duopoly with two firms 1,2 who sell the same good. The demand curve of the good is given by Q = 30 − p if p < 30 and Q = 0 if p ≥ 20. Both firms have the same constant unit cost 5.

Firms 1,2 set prices p1, p2. If firms set different prices, then the firm which sets the minimum price of the two, receives the demand at that price while its rival receives zero demand. If both firms set the same price, they equally split the demand at that price.

(a) Determine the profit functions of firms 1,2.

(b) Find best response of firm 2 to p1 = 9

(c) Find best response of firm 1 to p2 = 4.

(d) Show that (p1 = 4, p2 = 4) is a Nash Equilibrium (NE) of the Bertrand duopoly.

(e) Show that (p1 = 8, p2 = 8) is a not an NE of the Bertrand duopoly.