Question

To examine the​ trade-off between market efficiency and market power from a​ merger, consider a market with two firms that sell identical products. Firm 1 has a constant marginal cost of ​$​, and Firm 2 has a constant marginal cost of ​$2. The market demand is

Qp= 105-p.

Note that

dπ1/∂q1= [105-1(q1+q2)]- 1q1-1=0

dπ2/∂q2= [105-1(q1+q2)]- 1q1-2=0

The​ Cournot-Nash equilibrium occurs where q1 = 15.00 and q= 12.00. ​ Market output is 69. Futhermore , the equilibrium occurs at a price of $______--

Answer 1

Answer:

$q_1 = 35$  units

$q_2 = 34$ units

Market output  =  69

The equilibrium occurs at Price = $36

Step-by-step explanation:

Given that:

$\dfrac{\partial \pi_1}{\partial q_1 } = [ 105 -1 (q_1 + q_2) ] - 1q_1 -1 = 0$

$= 105 -q_1 -q_2 - q_1 -1 = 0$

$= 105 -2q_1 - q_2 -1 = 0$

$= 2q_1 +q_2 = 104 --- (1)$

$\dfrac{\partial \pi_2}{\partial q_2} = [ 105 -1 (q_1 + q_2) ] - 1q_2 -2 = 0$

$= 105 -q_1 - q_2- q_2 -2 = 0$

$= 105 -q_1 - 2q_2 -2 = 0$

$= q_1 + 2q_2 = 103 --- (2)$

By Solving (1) and (2):

Using elimination method: Multiply

 $2q_1 +q_2 = 104$   ---- (1)

 $q_1 +2q_2 = 103$   ---- (2)

(multiply equation (2) by 2 )

$2q_1 +q_2 = 104$

$2q_1 +4q_2 = 206$

                               

     $-3q_2 = -102$    

                             

$q_2 = \dfrac{-102}{-3}$

$q_2 = 34$ units

From (1):

$2q_1 +q_2 = 104$  

$2q_1 + 34 = 104$

$2q_1 = 104 - 34$

$2q_1 = 70$

$q_1 = \dfrac{70}{2}$

$q_1 = 35$  units

Market output  = (34 + 35 ) units

Market output  =  69

The equilibrium occurs at Price = 105 - 69

The equilibrium occurs at Price = $36