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$1$

Fill in the Blank $35$ points

Assume that two firms compete in an industry, both with constant marginal cost and average cost of $$20.$ The market inverse demand curve is estimated as $P=740-Q$ where the market output $Q$ is the sum of all firms' individual outputs, i$.$e$.,Q=q_1+q_2.$

A$.$ Suppose that firm $2\text{'}$s CEO is somewhat hesitant and waits to see how much firm $1$ will produce before deciding on its own output level. That is$,$ firm $1$ is a Stackelberg leader and firm $2$ is a Stackelberg follower. Let $q_L$ denote the leader's output and $q_F$ the follower's output. Compute each firm's output level, the market price, and each firm's profit.

The leader produces $$ units and the follower produce $$ units. The market price is $

The leader's profit is : and the follower's profit is $$

B$.$ Now suppose that the shareholders of the follower firm $($firm $2)$ become discontented with the firm's profits, and replace the CEO with a more aggressive person. This person does not stand idly by while firm $1$ makes its decisions. Instead, the two firms now choose their output simultaneously. However, the new CEO requests to be paid $10\%$ of the profit increase if any. Compute each firm's output level, the market price, and each firm's profit. How much will firm $2$ nav to the new CEO?

Firm $1$ produce $$ units and firm $2$ produces units. The market price is $ $.$ Firm $1\text{'}$s profit is $9$ and Firm $2\text{'}$s profit is $ $.$ The new CEO is paid

C$.$ Now suppose that the CEOs of firms $1$ and $2$ meet one year at the Swan Ball and have an opportunity to chat about the competitive conditions in their industry. They decide that because they will interact indefinitely in the market they should not behave so aggressively toward one another; instead, they should cooperate and agree that each of them should produce one$-$half of the monopoly output. The next morning, each CEO gets up and contemplates whether he or she should fulfill the agreement. Let $r$ be the interest rate. Compute the present discounted value of the profit obtained by cooperating and the present discounted value of the profit of the cheater while the other firm sticks with the agreement $($given that the firms earn Cournot profit thereafter if any firm cheats$).$

The present discounted value of the profit obtained by cooperating over the indefinite future is

$$

$$

$$ of the cheater while the other firm sticks with the agreement is $72900+\frac{57600}{r}$

$$

The present discounted value of the profit

D$.$ For what values of $r$ is the agreement self$-$sustaininghnthat is$,$ no firm ever cheats from the collusive agreement$)?$ If the interest rate $r$ is than $$ then the agreement is self$-$sustaining $($round up to two decimal places$).$

$1$

Fill in the Blank $35$ points

Assume that two firms compete in an industry, both with constant marginal cost and average cost of $$20.$ The market inverse demand curve is estimated as $P=740-Q$ where the market output $Q$ is the sum of all firms' individual outputs, i$.$e$.,Q=q_1+q_2.$

A$.$ Suppose that firm $2\text{'}$s CEO is somewhat hesitant and waits to see how much firm $1$ will produce before deciding on its own output level. That is$,$ firm $1$ is a Stackelberg leader and firm $2$ is a Stackelberg follower. Let $q_L$ denote the leader's output and $q_F$ the follower's output. Compute each firm's output level, the market price, and each firm's profit.

The leader produces $$ units and the follower produce: $$ units. The market price is