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 ​$1​, and Firm 2 has a constant marginal cost of ​$2. The market demand is Qequals15minusp. The​ Cournot-Nash equilibrium occurs where q 1 equals nothing and q 2 equals nothing. ​ (Enter numeric responses using real numbers rounded to two decimal​ places.)

Answer 1

q1=5

q2=4

Step-by-step explanation:

In a Cournot model with a demand of the form
`P=a-bQ` and firms with constant marginal costs we can easily find that the equilibrium quantities are given by

`q_1=(a-2c_1+c_2)/(3)`

`q_2=(a-2c_2+c_1)/(3)`

where
`q_1` is the quantity produced by firm 1 and
`c_1` are its marginal costs. The same for firm 2.

So replacing with the data given in the problem we have that

`q_1=(15-2*1+2)/(3)=(15)/(3)=5`

`q_2=(15-2*2+1)/(3)=(12)/(3)=4`