A heard of mammoths has size st and net natural growth

Economics 3B03 – Assignment 4 (Winter 2014)

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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 ytassociated with a hunt of size htis

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.