# Chapter 14

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

3.1 The inverse demand curve is $p=1-0.001Q.$[&p|=|1|-|0.001Q.&] The first firm’s profit is ${\pi}_{1}=[1-0.001({q}_{1}+{q}_{2})]{q}_{1}-0.28{q}_{1}.$[&|pi|_{1}|=|[1|-|0.001(q_{1}|+|q_{2})]q_{1} |minus|&][&0.28q_{1}.&] Its first-order condition is $\text{d}{\pi}_{1}/{\text{d}q}_{1}=1-0.001(2{q}_{1}+{q}_{2})-0.28=0.$[&~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 ${q}_{1}=360-\frac{1}{2}{q}_{2}.$[&q_{1}|=|360|-|*cf*{1}{2}|thn|q_{2}.&] Similarly, the second firm’s best-response function is ${q}_{2}=360$

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