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Question 7 10 pts There is an island that has two lakes X and Y . These lakes can be used for fishing. There are 30 fishermen. Each fisherman can fish either on lake \( X \) or on lake \( Y \). The amount of fish a fisherman takes home will be equal to the average of the total amount of fish caught in the lake where the fisherman is active. Let \( l_{x} \) be the number of fishermen fishing on lake X , and \( l_{y} \) is the number of fishermen fishing on lake Y . On lake X , the total number of fish caught is given by: \( F_{\mathrm{x}}= \) \( 20 l_{\mathrm{x}}-0.5 l_{\mathrm{x}}^{2} \) (that is \( l_{\mathrm{x}} \) squared) On lake Y , the total number of fish caught is given by: \( F_{\mathrm{y}}=14 l_{\mathrm{y}} \) a) In which lake do we observe a congestion externality? b) What will be the total amount of fish caught in the two lakes, i.e. \( F_{\mathrm{T}}=F_{\mathrm{x}}+F_{\mathrm{y}} \) ? (Hint: in equilibrium an individual fisherman must be indifferent across lakes) c) What would be the socially optimal amount of amount of fish caught in the two lakes, \( F_{\mathrm{T}}=F_{\mathrm{x}}+F_{\mathrm{y}} \) ? d) Suppose a fishing license is introduced in order to force a move from the competitively chosen \( F_{\mathrm{T}} \), to the socially optimal \( F_{\mathrm{T}} \). How high should the cost of this license be? Upload Choose a file

          Question 7
10 pts

There is an island that has two lakes X and Y . These lakes can be used for fishing. There are 30 fishermen. Each fisherman can fish either on lake \( X \) or on lake \( Y \). The amount of fish a fisherman takes home will be equal to the average of the total amount of fish caught in the lake where the fisherman is active.

Let \( l_{x} \) be the number of fishermen fishing on lake X , and \( l_{y} \) is the number of fishermen fishing on lake Y .

On lake X , the total number of fish caught is given by: \( F_{\mathrm{x}}= \) \( 20 l_{\mathrm{x}}-0.5 l_{\mathrm{x}}^{2} \) (that is \( l_{\mathrm{x}} \) squared)

On lake Y , the total number of fish caught is given by: \( F_{\mathrm{y}}=14 l_{\mathrm{y}} \)
a) In which lake do we observe a congestion externality?
b) What will be the total amount of fish caught in the two lakes, i.e.
\( F_{\mathrm{T}}=F_{\mathrm{x}}+F_{\mathrm{y}} \) ? (Hint: in equilibrium an individual fisherman must be indifferent across lakes)
c) What would be the socially optimal amount of amount of fish caught in the two lakes, \( F_{\mathrm{T}}=F_{\mathrm{x}}+F_{\mathrm{y}} \) ?
d) Suppose a fishing license is introduced in order to force a move from the competitively chosen \( F_{\mathrm{T}} \), to the socially optimal \( F_{\mathrm{T}} \). How high should the cost of this license be?
Upload
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Question 7
10 pts

There is an island that has two lakes X and Y . These lakes can be used for fishing. There are 30 fishermen. Each fisherman can fish either on lake X or on lake Y. The amount of fish a fisherman takes home will be equal to the average of the total amount of fish caught in the lake where the fisherman is active.

Let lx be the number of fishermen fishing on lake X , and ly is the number of fishermen fishing on lake Y .

On lake X , the total number of fish caught is given by: Fx= 20 lx-0.5 lx^2 (that is lx squared)

On lake Y , the total number of fish caught is given by: Fy=14 ly
a) In which lake do we observe a congestion externality?
b) What will be the total amount of fish caught in the two lakes, i.e.
FT=Fx+Fy ? (Hint: in equilibrium an individual fisherman must be indifferent across lakes)
c) What would be the socially optimal amount of amount of fish caught in the two lakes, FT=Fx+Fy ?
d) Suppose a fishing license is introduced in order to force a move from the competitively chosen FT, to the socially optimal FT. How high should the cost of this license be?
Upload
Choose a file

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