Problem $7$: Collusive Monopsony $(40$ points$).$ Suppose there are two teams in the

NBA $($team $1$ and team $2).$ Each team has a monopoly in their product market with a

demand curve given by:

P $($q$)=2702$q

Each team$$s production function is given by:

q$()=$

The aggregate supply of labor is given by:

w$($L$)=30+2$L

where L $=1+2$ is the total number of players in the market.

$1.(15$ points in this part$)$ First, assume the teams compete by simultaneously choosing

the number of players.

a$)$ Find team $1$s best response function. $(6$ points$)$

b$)$ Find the number of players $()$ hired by each team $(3$ points$).$ Find the wage level

w $(3$ points$).$

c$)$ Find each team$$s profits n $(3$ points$).$

$2.(15$ points in this part$)$ Next, assume the teams can collude to form a monopsony.

a$)(8$ points$)$ Find the number of players hired in the market $($L$).$ Find the wage

level w$.$

b$)(3$ points$)$ Find the number of players hired by each team $().$ Find each team$$s

profits $($c$).$

c$)(4$ points$)$ Imagine that team $1$ deviates from the collusive agreement while team

$2$ keeps choosing the collusive amount of labor. Given team $2$s choice of labor,

how many players should team $1$ hire to maximize profits? And what is the

corresponding level of profit $($d$)?$

$3.(10$ points in this part$)$ Now, consider the infinitely repeated version of this game.

a$)$ Fill in the blanks to complete the grim trigger strategy. You don$$t need to provide

explanations for your answers. $(6$ points; each blank carries $1$ point$)$

$$In the first period, choose $=.$ In all future periods, choose $=$

unless any team has chosen any other amount in any previous period, in which

case choose $=.$

$3$

$$If both teams follow grim trigger, both earn $=$ in every period t$.$

If team $2$ follows grim trigger but team $1$ deviates in t $=0,$ then team $1$ earns

$=$ in t $=0$ and $=$ in t $=1,2,3,...$

b$)$ What is the lowest level of for which collusion is sustainable? Think about what

we$$ve learned from the grim$-$trigger strategy. Make sure you round up your result

to $2$ decimal places. $(4$ points$)$