Economics 3B03 – Assignment 4 (Winter 2014)

Economics 3B03

–

Assignment

4 (Winter 2014)

Answer all questions.

A heard of mam

m

oths has size s

t

and net natural growth g

t

, where

1.

Find the steady state size of the herd.

2.

Suppose that a tribe of cavemen led by the mighty Alley Oop discovers the herd. Alley Oop is a

powerful leade

r who can unilaterally determine the amount of mammoth hunting done by the

tribe. Being a graduate of MIT (Mesolithic Institue of Technology), Alley Oop always maximizes

current profits. The catch y

t

associated with a hunt of size h

t

is

Y

t

= .02g

t

h

t

A

nd

the cost of hunt is

Find the stady state size of herd under Alley Oop

’

s leadership.

3.

Alley Oop lives and happily, but at the age of 28, his reflexes slow

ed by old age, Alley Oop is

impaled on the tusk of an angry

mammoth

.

The leaderless tribe falls into anarchy, with each

tribeman deciding whether or not he will hunt. Find the steady size of the herd under this

regime.

Economics 3B03 – Assignment 4 (Winter 2014)

Answer all questions.

A heard of mammoths has size st and net natural growth gt, where

1. Find the steady state size of the herd.

2. Suppose that a tribe of cavemen led by the mighty Alley Oop discovers the herd. Alley Oop is a

powerful leader who can unilaterally determine the amount of mammoth hunting done by the

tribe. Being a graduate of MIT (Mesolithic Institue of Technology), Alley Oop always maximizes

current profits. The catch yt associated with a hunt of size ht is

Yt = .02gtht

And the cost of hunt is

Find the stady state size of herd under Alley Oop’s leadership.

3. Alley Oop lives and happily, but at the age of 28, his reflexes slowed by old age, Alley Oop is

impaled on the tusk of an angry mammoth. The leaderless tribe falls into anarchy, with each

tribeman deciding whether or not he will hunt. Find the steady size of the herd under this

regime.