farmer and a fisher live next to a river. The farmer uses fertilizer on his field that pollutes the river. The fisher lives downstream of the farmer and catches the fish that live in the river. The fertilizer reduces the fish stocks and therefore also the profits of the fisher.

The marginal profits from fertilizer use for the farmer are given byM

P

=

a

b

Q

MP=abQ

whereQ

Q

is the amount of fertilizer anda

a

andb

b

are parameters. The marginal damages to the fish stock are given byM

E

=

c

+

d

Q

ME=c+dQ

.

What is the minimum amount the fisher would have to pay to the farmer in order for the farmer to reduce fertilizer use to the social optimum?

Please use the following parameter values:a

=

10

a=10

;b

=

1

b=1

;c

=

2

c=2

;d

=

1

d=