Problem $1$: Collusive Monopsony. Assume that there are two teams that produce

baseball games. For simplicity, call them team $1$ and team $2.$ Each team is a monopoly in

their product market with demand curve:

P $($q$)=1202$q

The production function for each team is given by:

q$()=$

where $$ is the quantity of labor hired by the team. The aggregate supply of labor is:

w$($L$)=6+3$L

where L $=1+2$ is the total amount of labor hired by the two teams.

$1.$ Assume that the two teams compete against one another by simultaneously choosing

a quantity of labor to hire.

a$)$ Write out the profit function for team $1.$

b$)$ Find each team$$s best response function.

c$)$ What is the equilibrium amount of labor chosen by each team $()?$

d$)$ What is the equilibrium wage $($w$)?$

e$)$ What is the profit for each team $($n$)?$

$2.$ Now, assume that the two teams collude as a $($monopsony$)$ league.

a$)$ Find the aggregate product demand curve for the league. $($Aggregate the two

teams$$ identical product demand curves.$)$

$1$

b$)$ What is the new equilibrium amount of labor in the market $($L$)?$

c$)$ What is the new equilibrium wage $($w$)?$

d$)$ How much labor is hired by each team $()?$

e$)$ What is the profit for each team $($c$)?$

$3.$ Imagine that team $1$ deviates from this agreement while team $2$ chooses the collusive

amount of labor.

a$)$ How much labor should team $1$ hire to maximize profits $(1)?$

b$)$ What is the total amount of labor in the market $($L$)?$

c$)$ What is the wage $($w$)?$

d$)$ What are team $1$s profits from deviating $($d$)?$

e$)$ Find the cutoff value of such that collusion is sustainable as an equilibrium of

the infinitely$-$repeated game for all values values of greater than the cutoff.