c)If the two firms compete on price (Bertrand model without collusion), will both firms serve the market? If not, which one will serve? Compute the market price, the quantity served in the market and the firm’s profit.(7 marks) Since MCB= 1 < MCA=> Only firm B serves the market under Bertrand. The market price will be 1.99 and the quantity supplied is 28.01 Firm B profit is then 21.74 d)If instead, the two firms compete on quantity with firm A (as it is in the market first) has the right to choose the quantity first (and then firm B will choose its quantity –Stackelberg model). Compute the market price, quantity supplied by firm A and firm B. (7 marks)Firm B’s problem:Max B = (30 - QA–QB) QB- 5 - QBFOC => 30 - QA -2QB –1 = 0 => Firm B’s best response is: QB = (29 –QA)/2 And firm A’s problem is:Max A = [30 - QA–(29 –QA)/2] QA- 5 - 2QAThe FOC implies that QA= 13.5 And QB= 7.75 And P = 8.75
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