Question

1. Consider a market with inverse demand P (Q) = 100 - Q and 5 firms with cost function C(q) = 40q.
(a) Find the Cournot equilibrium outputs, price and profit.
(b) If 4 firms merge with no efficiency gain, do they increase or decrease their profits? By how much?

(c) Is the result in (b) expected?
(d) What are the effects of this merger on price and social welfare?

Answer 1

a)

P = 100 - Q

TC = 40Q

MC = 40

Equilibrium Condition in competitive market

P = MC

100 -Q = 40

Q = 60

Cournot Equilibrium output

= (N/N+1)*Competitive output

= (5/6)*60

= 50

P = 100 - 50

= 60

Each firm production = 10 units

Profit = TR - TC

= 50*60 - 40*50

= 1 000

Each Profit = 200

b)

Cournot output when four firms merge:

= (2/3)*60)

= 2*20

= 40

P = 100 -40

= 60

Profit = 40*60 - 40*40

= 2400 - 1600

= 800

Each firm profit = 400

Merged firm profit may not be profitable but single firm profit increases.

c)

it was expected that profit of firm will rise.

d)

Price has increased and quantity produced decreased, so there is fall in social welfare of people or deadweight loss rises when few firms are there in market or number of firm decreases.