Question

ECON M/C is this correct?

A duopoly faces the inverse demand curve p = 10 – 4, where q is the sum of firm 1's output 91 and firm 2's output (2 (q = 41 +92). Firm 1's total cost function is given by Ci(91) 2q1 and firm 2's total cost function is given by C2(92) 8q2. Suppose firms engage in price competition (Bertrand competition). Which of the following statements is correct? Select one: a. Bertrand equilibrium of this duopoly coincides with competitive equilibrium. b. P1 = P2 = 2 in Bertrand equilibrium. c. P1 = P2 = 8 in Bertrand equilibrium. O d. Pı = 2 and p2 = 8 in Bertrand equilibrium. e. Total output in Bertrand equilibrium of this duopoly coincides with monopoly equilibrium output having firm 1 as the monopolist

Answer 1

where each firms Simual taneou L 10-q 2 lo-q Bertrand Price competition ( that is from 1 and from -2) decides Their Prices cously Demand function of firm if pis p Di (bi, bi)= if bi= p; if bil bů in Bertrand con firm in indus Incentive To charge price for its product Less Than of its rivalls frice in order to get entire market demand that is if firm- Charges then Demand of Firm - will be entire market dem and due to this each firm tries To set its Price Less Than of its rival's frice. But this also has one exception that is can charge it's frice Less Than of its marginal cost Petition each sustry have bi LP2 - 1 neither from

marginal costs of firom-1 mc(91) = dollall 2 dai of firm-2 mc(ar) = dca (921 8 marginal cost of from is Less Than of Firm-2's marginal Cost which gives cost advantage to from-1. charging Than o of P2 = 8 and Now in rival's uncler conting.com letition that is Price of Product Less rivals Price. Firm-2 can charge minimum Price for its Product is by slightly below this Charging p2=8 from-y is able To capture entire market for example P2 = bire where Ero. Since e is and can be ignored in Calculations So The Bertrand equilibrium Ans: (c) bi = pz = 8 Bertrand equilibrium 8-e very small Term

why (a) is not correct competitive equilibrium required That is Bertrand competitive Symmetry in costs mci = MC₂ Then we will have equilinnum Not Why (b) is Correct Because be can not be Less Than 8. = mc2 Why (d) is Not correct Because firm- I can charge even pi=7 To get an entire demand why it Charge pi=2 which is voilation of rationality of producers. why (e) is from-1 as monopolist Not correct oftimal: MR Mc 10-29 2 -2 8 29 9 - 4 where as in Bertrand duolay with either with 8 2 cannot gives 9=4