Let market demand be given by Q 200 P Each firms cost func

Let market demand be given by Q = 200 - P. Each firm\'s cost function is C(q_i) = 20q_i, where I = 1, 2. Using the Cournot model (with quantity competition), find each firm\'s output price and profit. Suppose that the duopolists collude or merge to become one firm (monopoly) and the cost function does not charge. find their joint profit-maximizing (monopoly) price, output, and profit. Compute and compare consumers\' surplus and deadweight losses of both cases. What do you conclude from this exercise and to what extent is your conclusion general (i.e., not specific to the functional forms of the demand and cost functions, and the number of firms)? Discuss generally the benefits and costs of monopoly.

Solution

1. Q=200-P

or, P=200-Q=20-(q1+q2)

C(qi)=20qi

Profit z1= Pq1-20q1=200q1-q1^2-q1q2-20q1

FOC: dz1/dq1=0

or, 200-2q1-q2=20

or, 2q1+q2=180 ...........(1)

We know, for Cournot\'s equilibrium we get:

q1=q2=1/3 ..............(2)

So 3q1=180

or, q1=60=q2

So z=200x60-60^2-60x60-20x60=12000-8400=3600

P=200-60=140