Microeconomics: Theory and Applications with Calculus, 4e

Chapter 14

1. 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.&]

2. 3.1 The inverse demand curve is $p=1-0.001Q.$[&p|=|1|-|0.001Q.&] The first firm’s profit is ${\pi }_1=[1-0.001(q_1+q_2)]q_1-0.28q_1.$[&|pi|_{1}|=|[1|-|0.001(q_{1}|+|q_{2})]q_{1} |minus|&][&0.28q_{1}.&] Its first-order condition is $\text{d}{\pi }_1/{\text{d}q}_1=1-0.001(2q_1+q_2)-0.28=0.$[&~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 $q_2=360$