Two firms, A and B, have complete control of the supply of mineral water andboth have zero costs....

Question

Two firms, A and B, have complete control of the supply of mineral water and
oth have zero costs. Their best reply functions (BRP) are given by:
qA= 10-.5qB ………. (1)
qB= 10-.5qA ………… (2)
a) Find the Cournot solution for the market price and output of mineral water and illustrate with
a simple graph.
Answer:
The intersection of two reaction functions determines Cournot solution. To derive it numerically,
we substitute equation (1) in (2) i.e.
qB = 10-0.5*(10-.5qB) or
qB = 10 – 5 + 0.25qB or
0.75qB = 5 or
qB = 5/0.75 = 6.67
And qA = 10-0.5*6.67 =6.67
So cournot output: qA = qB = 6.67
With MR = 200–20Q, the demand curve: P = 200 – 10Q, where Q = qA+qB
Here Q = 6.67+6.67 = 13.33
So cournot price (P) = 200-10*13.333= $66.67
Cournot profit of each firm (πN) = Price*output produced by each firm under Cournot case =
66.67*6.67 = $444.689
) The marginal revenue function facing a monopolist is given by:
MR = 200–20Q
Demonstrate that firms A and B have an incentive to cooperate and maximize
joint profits.
Answer:
When firm A and B cooperate, they would maximize their joint...

David · Accepted Answer

Two firms, A and B, have complete control of the supply of mineral water and  
both have zero costs. Their best reply functions (BRP) are given by: 
qA= 10-.5qB   ………. (1) 
qB= 10-.5qA  ………… (2) 
a) Find the Cournot solution for the market price and output of mineral water and illustrate with 
a simple graph.  
Answer: 
The intersection of two reaction functions determines Cournot solution. To derive it numerically, 
we substitute equation (1) in (2) i.e. 
qB = 10-0.5*(10-.5qB) or 
qB = 10 – 5 + 0.25qB or 
0.75qB = 5 or 
qB = 5/0.75 = 6.67 
And qA = 10-0.5*6.67 =6.67 
So cournot output: qA = qB = 6.67 
With MR = 200–20Q, the demand curve: P = 200 – 10Q, where Q = qA+qB 
Here Q = 6.67+6.67 = 13.33 
So cournot price (P) = 200-10*13.333= $66.67 
Cournot profit of each firm (πN) = Price*output produced by each firm under Cournot case = 
66.67*6.67 = $444.689
b) The marginal revenue function facing a monopolist is given by:  
MR = 200–20Q 
Demonstrate that firms A and B have an incentive to cooperate and maximize  
joint profits. 
Answer: 
When firm A and B cooperate,

Two firms, A and B, have complete control of the supply of mineral water andboth have zero costs. Their best reply functions (BRP) are given by:qA= 10-.5qB qB= 10-.5qA a) Find the Cournot solution for...

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