Before entry the incumbent firm earns a monopoly profit of 1

Before entry, the incumbent firm earns a monopoly profit of $10 million. If entry occurs, the incumbent and new entrant will earn the duopoly (two firm) profit of $3 million. Suppose the incumbent can convince the government to require all firms to install pollution-control devices at their factories. Should the incumbent urge the government to require the devices? Why on why not?

Solution

Let suppose that the pollution control devices cost $c, it leads to reduce the monopoly profit by $c as now the incumbent will get a profit of $10 - $c in case of no entry and in case of entry the duopoly profit will become $3 -$c , $3-$c for both.

Let one case where $c is less than $3 and one case in which $c is greater than $c.

When $c < $3 let say $c = $2

The profits will be as follows:

with entry the profit will be ($1, $1) as both have to bear a cost of $2 so ($3-$2, $3-$2)

with entry the profit will ($3, $3) so in this case when entry occurs the incumbent should not urge the government to require the device.

It means when $c is less than $3 incumbent will not u]convince the government to require all firms to install pollution control devices because it reduce both profits by $2 and entry will occur because there is still the profit of $1.

When $c > $3 let say $c = $4

in this case the profit will be as follows:

if pollution control device will require then the profit of monopoly will be $10 - $4 = $6 (without entry)

the profits of incumbent and new entrant will be (-$1, -$1) in case of entry.

but due to loss of $1 if the rival firm enter will discourage the entry. And new entrant will not enter.

So here in this case when $c > $3 the incumbent should urge the government to require the device in order to discourage the new entry, (in case of new entry).