
To know:Whether $200 to be invested or not.

Explanation of Solution
There are two firms: TT and ST
Following is the cost function of TT:
Following is the cost function of ST:
Following is the inverse demand function:
There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:
This implies:
Reaction function of TT firm is given as:
There exists cournot oligopoly between two firms which sells homogeneous product. Profit maximizing condition is as follows:
This implies:
In cournot oligopoly, equilibrium is attained when reaction function of both firms are solved simultaneously.
This implies:
Solving both the equations,
Thus, equilibrium output of TT is 26 and of ST is26
The equilibrium market price is given by:
Profit is calculated by subtracting total revenue and total cost. For TT firm,
Profit is calculated by subtracting total revenue and total cost. For ST firm,
Now, Stackelberg duopoly is followed in which cost functions are same but TT firm is leader and ST is follower.
Under stackelberg duopoly model, profit maximizing condition is as follows:
This implies:
The leader firm TT in Stackelberg duopoly takes into account the reaction function of the follower firm when it selects QTT.
The profit of the leader firm is given by:
The leader firm chooses QTT that maximizes the given profit function.
Hence, QTT that maximizes the profit function of the leader firm is:
Hence, the equilibrium output level for the leader firm is 39.
Calculation of equilibrium output:
Firm St has 19.5 units of output.
Calculation of equilibrium price:
Calculation of profit of TT firm is as follows:
Calculation of profit of ST firm is as follows:
Thus, the equilibrium profit of the leader firm TT under the conditions of Stackelberg oligopoly is $1521, which is higher by $169, compared to the equilibrium profit of $1352 of the firm TT under the condition of Cournot duopoly.
The unrecoverable fixed investment is $200, greater than $169.
That means, the firm TT should not invest $200 as the cost of establishing the first mover advantage exceeds the benefits.
Introduction:
Duopoly is a form of oligopoly market in which there are two firms selling goods in a competitive market where consumer’s choice does not affect them.
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Chapter 9 Solutions
MANAGERIAL ECON.+BUS.STRATEGY (LOOSE)
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