Homework 1
(Due September, 22nd)
Question 1
(50
points):
Suppose a firm’s business activities generate a random income of $x. This firm finances
its activities by selling two types of claims (or financial securities). An investor who buys
the first type of security earns:
min (x,F)
An investor who buys the second gets a payoff of:
max(xF,0)
Here x is random. By this I mean that sometimes is large and sometimes small. F, on the
other hand, is fixed and equal to $500.
a)
Draw a graph of the payoff that an investor gets for each claim. Put the random
income x on the horizontal axis and the payoff on the vertical axis.
b)
In light of the discussion of bonds versus stocks, how would you label the first
security? How about the second security? Interpret F and x.
c)
Suppose x can be either $7000 with probability 0.5 or $600 with probability 0.5.
Calculate the expected payoffs of both securities (Note: don’t worry about
computing present values, just calculated the expected payoff in “future” prices).
Question 2
(50
points):
Let’s begin with a refresher about indifference curves and utility functions. This should
be material learned in previous classes and there should be no new material in these first
paragraphs. Suppose a consumer values two goods, A and B, and ranks combinations of
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 Spring '11
 silous
 Econometrics, Utility, Financial Markets

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