Managerial Economics and Strategy, 2/e

Chapter 11

1. 1.4 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.&] There are four firms, so each firm produces $20/4=5.$ [&20/4|=|5.&]

2. 2.2 The inverse demand function is $p=1-0.001Q.$ [&p|=|1|-|0.001Q.&] The first firm’s profit is ${\pi }_1=[1-0.001(q_1+q_2)]q_1-0.28q_1.$ [&|pi|_{1}|=|[1|-|0.001(q_{1 }|plus|&][&q_{2})]q_{1}|-|0.28q_{1}.&] Its first-order condition is $\text{d}{\pi }_1/\text{d}{q}_1=1-0.001\left(2q_1+q_2\right)-0.28=0.$ [&~rom~d|pi|_{~normal~1}/~rom~d~normal~q_{1}|=|1|-|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}.&] ...