$334$

$28\mathrm{.}3(0)$ Suppose that Carl and Simon sign a marketing agreement. They decide to determine their total output jointly and to each produce the same number of pumpkins. To maximize their joint profits, how many pumpkins should they produce in toto?

$q,$ How much does each one of them produce? $q,$ How much profit does each one of them make? $q,$

a$)$

$28\mathrm{.}4(0)$ The inverse market demand curve for bean sprouts is given by $P(Y)=100-2Y,$ and the total cost function for any firm in the industry is given by $TC(y)=4y.$

$P=100-2y,TC=4y$

$R=100\frac{-}{{?}_y}$

$R=100y-2y^2,MC=4$

$MR=100-4y$

$($a$)$ The marginal cost for any firm in the industry is equal to $4$ change in price for a one$-$unit increase in output is equal to $-2$

a$)$

$100-4y=4y$ when $y=21,p=-2$

$p=20,p=100-2(21),58$

$p=60,\mathrm{.}42=58$

$($b$)$ If the bean$-$sprout industry were perfectly competitive, the industry output would be $48,$ and the industry price would be $q,4$

$($:${}_1=c\}$

$MC=P$

$4=100-2y$

$y,=48$

$($c$)$ Suppose that two Cournot firms operated in the market. The reaction function for Firm $1$ would be $y_1=24-\frac{y_2}{2}($Reminder: Unlike the example in your textbook, the marginal cost is not zero here.$)$ The reaction function of Firm $2$ would be $y_2=24-\frac{y_0}{2}$ If the firms were operating at the Cournot equilibrium point, industry output would be $,$ each firm would produce $q,,$ and the market price would be $q,$

$($d$)$ For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the graph below.$($e$)$ If the two firms decided to collude, industry output would be $$ and the market price would equal $$

$($f$)$ Suppose both of the colluding firms are producing equal amounts of output. If one of the colluding firms assumes that the other firm would not react to a change in industry output, what would happen to a firm's own profits if it increased its output by one unit? $$

$$

$($g$)$ Suppose one firm acts as a Stackleberg leader and the other firm behaves as a follower. The maximization problem for the leader can be writte $-$

Solving this problem results in the leader producing an output of

$$ and the follower producing $$ This implies an industry output of $$ and price of $$