Question

Two firms are considering entering a new market where currently no other firm exist. It is predicted that there will be enough demand so that both these firms can make positive economic profits. There is no fixed cost and two firms are identical. Discuss how a simultaneous entry game will be different from a sequential entry game for these two firms. Also discuss, how the output decision and market share will be different in these two scenarios.

Answer 1

CASE 1: Simultaneous entry game-

Since the firms are identical and they are entering into the same market that means the demand equation and cost equation would be the same. Now let say the demand equation is:

P= 100-Q, where Q= q(1) + q(2)

and the cost function for both the firms are:

40q(1) and 40q(2) (since they are identical firms)

Firms would take the output of other firms as given and would maximize their own profit.

Revenue for firm 1 is [100-q(1)-q(2)]*q(1), that means marginal revenue would be 100-2q(1)-q(2).

Now marginal cost would be 40 and by applying MR=MC we get q(1) = 30-q(2)/2. Now similarly for firm 2 as well we get q(2)= 30-q(1)/2.

Substituting q(2) into the above equation we get q(1)= 20 units and q(2) = 20 units. That means they both produce equal amounts of goods and the market share would be divided equally between them.

CASE 2: Sequential Game-

Let's say firm 1 moves first, then firm 1 would take the profit-maximizing output decision of firm 2 in its own profit equation and firm 2 would have no choice but to take the output of firm 1 as given.

From above we know that if a firm takes the other's firm output as given that implies-

q(2) = 30- q(1)/2

Now for firm 1 Revenue would be [100 - q(1) - 30 + q(1)/2]*q(1), and MR would give us 70-q(1).

MC is 40 that implies MR=MC gives us q(1)= 30 and q(2)= 15. Therefore the firm enjoys first-mover advantage and would acquire double the market share as compared to firm 2.