Chapter 14

  1. 2.2 The profit-maximizing cartel output is the monopoly output. Setting MR=MC[&MR|=|MC&] yields 1004Q=20,[&100|-|4Q|=|20,&] so Q=20.[&Q|=|20.&] Each of the four firms produces q=20/4=5.[&q |eq|&][&20/4|=|5.&]

  2. 3.1 The inverse demand curve is p=10.001Q.[&p|=|1|-|0.001Q.&] The first firm’s profit is π1=[10.001(q1+q2)]q10.28q1.[&|pi|_{1}|=|[1|-|0.001(q_{1}|+|q_{2})]q_{1} |minus|&][&0.28q_{1}.&] Its first-order condition is dπ1/dq1=10.001(2q1+q2)0.28=0.[&~rom~d|pi|_{~normal~1}/~rom~d~normal~q_{1}|=|1 |minus|&][&0.001(2q_{1}|+|q_{2})|-|0.28|=|0.&] If we rearrange the terms, the first firm’s best-response function is q1=36012q2.[&q_{1}|=|360|-|*cf*{1}{2}|thn|q_{2}.&] Similarly, the second firm’s best-response function is q2=360

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