Answer to Question #147522 in Engineering for Tricia

Question

Consider a market served by 2 firms. Demand for their product is estimated to be P=100-Q, with Q=q1 + q2. Assume that production costs are symmetric and given by C=10q.

(i) Assume that firm 1 was given the opportunity to commit its output level before firm 2 chooses its quantity. Show that firm 1 has indeed incentive to become a market leader by setting its quantity first.

(ii) Is there an incentive for the two firms to merge? Explain your answer clearly.

Answer 1

The market price will be;P=100-q1+q2

Firm 1 has a constant marginal cost C=10q

Firm 1’s profit maximization problem: max π1 =(q1,q2) =[100 − (q1 + q2) q1-10Q

First order conditions: ∂π1/∂π2=100- ( q1+q2) +q1(-1)-10=0 

90-2q1-q2=0

2q1=90-q2

q1=90-q2/2

Therefore, firm 1's reaction to the market in response to q2 will be;

q1=R(q2)=90-q2/2=45-0.5q2

If firm 1 is the leader, we use stakleberg equilibrium to find total revenue of firm 1;

TR1=(100-2q2-2q1)q1

substitute q2 in place of firm 2's reaction function q2=45-0.5q1.

TR=[100-2(45-0.5q1)-2q1]q1=(10-q1)q1=10-2q1

since marginal revenue =marginal cost

10-2q1=10q

10=10q+2q

10=12q

q=10/12