Question

business economics

4. By using following basic assumptions on Dynamic Bertrand model of vertical separation, find NE, output of each firms, profit of each firms (in collusion and deviation), and choose the strategy of one(to collude or deviate) to find CS, and SW. Assumptions : 1. model : Dynamic Bertrand with vertical separation 2. Demand curve: P-160-20 3. MC=20 4.Q-q1+42 5. interest rate r-10%

Answer 1

P=160-2Q

Q=q1+q2

MC-20

P=160-2(q1+q2)

P=160-2q1-2q2

TR1=P*Q

TR1=(160-2q1-2q2)q1

TR1=160q1- 2q12-2q1.q2

2 2q12

MR1=∂(160q1- 2q12-2q1.q2)/q1

2 2q12

=160-4q1-2q2….MR1

Π1=TR-TC

=160q1- 2q12-2q1.q2-20q1

2 2q12

∂ Π1/∂q1=160-4q1-2q2-20

Q1=35-.5q2………………….1(best response functions)

TR2=P*Q

TR2=(160-2q1-2q2)q2

TR2=160q2-2q1.q2- 2q22

2q22

Π2=TR2-TC2

=160q2-2q1.q2- 2q22-20q2

2q22

∂ Π2/∂q2=160-2q1-4q2-20

4q2=140-2q1

Q2=35-.5q1……2 (best response functions)

Nash equilibrium is always intersection of BRF

Q1=35-.5q2 Q2=35-.5q1

Putting the value of one in another

Q1=35-.5(35-.5q1)

Q1=35-15.5-.25q1

1.25q1=19.5

Q1=15.6-------1

Q2=35-.5(15.6)

Q2=27.2

P=160-2(q1+q2)

P=160-2(15.6+27.2)

P=74.4

Q=42.8

Firm 1 Π1=TR1-TC1

=1160.64-312

Firm 1 Π1=848.64

Firm 1 Π2=TR2-TC2

Firm 2 Π2=1479.68