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Suppose that entrepreneurs do not know for certain how much profits they will get. In particular, assume that anyone that decides to be an entrepreneur will earn 1000 with probability p and 10 with probability 1 - p. Instead, individuals that decide to be workers will earn w with certainty.
Suppose that all individuals are identical and risk-averse. They devote all income to consumption and their instant utility function is u(c) = ln(c).
(a) Which is the expected utility of an individual that decides to become an entrepreneur? Which is the utility of a worker?
(b) Which probability p is necessary to have w = 50 in equilibrium?
(c) Is it true that in equilibrium E(Π) > w? Why is that?
(d) Suppose that in this economy, 100 individuals became entrepreneurs and 100 individuals became workers. Compare the distribution of income of entrepreneurs and workers at the end of the period. Com- ment on the results.
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