Ch12 - Monopolistic Competition and Oligopoly

If firms can collude then in this case they should

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If firms can collude, then in this case they should each produce half the quantity  that maximizes total industry profits (i.e. half the monopoly profits).  If on the other  hand the two firms had different cost functions, then it would not be optimal for  them to split the monopoly output evenly. Joint profits will be (300-3Q)Q - 2(30(Q/2) + 1.5(Q/2) 2 ) = 270Q - 3.75Q 2  and will be  maximized at Q = 36.  You can find this quantity by differentiating the above profit  function with respect to Q, setting the resulting first order condition equal to zero,  and then solving for Q. Thus, we will have q 1  = q 2  = 36 / 2 = 18 and  P = 300 - 3(36) = $192. Profit for each firm will be 18(192) - (30(18) + 1.5(18 2 )) = $2,430. c. The managers of these firms realize that explicit agreements to collude are illegal.  Each firm must decide on its own whether to produce the Cournot quantity or the  cartel quantity.   To aid in making the decision, the manager of WW constructs a  payoff matrix like the real one below.   Fill in each box with the (profit of WW,  profit of BBBS).  Given this payoff matrix, what output strategy is each firm likely  to pursue? If WW produces the Cournot level of output (22.5) and BBBS produces the collusive  level (18), then: Q = q 1  + q 2  = 22.5 + 18 = 40.5 P = 300 -3(40.5) = $178.5. Profit for WW = 22.5(178.5) - (30(22.5) + 1.5(22.5 2 )) = $2581.88. Profit for BBBS = 18(178.5) - (30(18) + 1.5(18 2 )) = $2187. 211
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Chapter  12:  Monopolistic Competition and Oligopoly Both firms producing at the Cournot output levels will be the only Nash Equilibrium  in this industry, given the following payoff matrix. Given the firms end up in any  other cell in the matrix, one of them will always have an incentive to change their  level of production in order to increase profit.  For example, if WW is Cournot and  BBBS is cartel, then BBBS has an incentive to switch to cartel to increase profit.  (Note: not only is this a Nash Equilibrium, but it is an equilibrium in dominant  strategies.) Profit Payoff Matrix BBBS (WW profit, BBBS profit) Produce Cournot q Produce Cartel q WW Produce Cournot q 2278,2278 2582, 2187 Produce Cartel q 2187, 2582 2430,2430 d. Suppose WW can set its output level  before  BBBS does.  How much will WW choose  to produce in this case?  How much will BBBS produce?  What is the market price,  and what is the profit for each firm?  Is WW better off by choosing its output first?  Explain why or why not.  WW is now able to set quantity first.  WW knows that BBBS will choose a quantity  q 2  which will be its best response to q  or: q 2 = 30 - 1 3 q 1 .
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