Question

Two firms, a and b, compete in a market to sell homogeneous products with inverse demand function P = 400 – 2Q where Q = Q_a + Q_b. Firm a has the cost function C_a = 100 + 15Q_a and firm b has the cost function C_b = 100 + 15Q_b. Use this information to compare the output levels, price and profits in settings characterized by the following markets:

1. Cournot
2. Stackelberg
3. Bertrand
4. Collusion

Answer 1

Answer:

Given that,

Two firms, a and b, compete in a market to sell homogeneous products with inverse demand function P = 400 – 2Q where Q = Q_a + Q_b. Firm a has the cost function C_a = 100 + 15Q_a and firm b has the cost function C_b = 100 + 15Q_b. Use this information to compare the output levels, price and profits in settings characterized by the following markets:

1. Cournot
2. Stackelberg
3. Bertrand
4. Collusion

P = 400 – 2Q , Q = Q_a + Q_{b , MC=15.}

(1) Cournot:

Symmetric equation,

So, 6q=385

q=385/6=64.167

Q=2q=385/3=128.33

p=400-2(128.33)=143.33

(p-MC)q-100

=(143.33-15)(64.167)-100

Answer=8134.76

(2) Stackelberg:

Max ,, st

Let a is leader ,b is follower

=(385-2q_a)/4

So , =(400-15-2q_a-2q_b)q_a

=(385-2q_a-2(385-2q_a)/4)q_a

=(385-2q_a-385/2+q_a)q_a

=(385/2-q_a)q_a=385/2q_a-q_a^2

385/4=96.25

48.125

144.375,

400-2

=111.25

=(111.25-15)96.25=9264.0625

=(111.25-15)(48.125)=4632.03125

(3) Bertrand:

At  

=(400-15)/2=192.5

0.

(4) Collusion:

MR=MC, 400-4Q=15

385=4Q

=96.25, 207.5

(207.5)(96.25)

=18528.125

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