Econ 101A — Problem Set 5
Due in class on Th 23 April. No late Problem Sets accepted, sorry!
This Problem set tests the knowledge that you accumulated mainly in lectures 19 to 22. The problem
set is focused on monopoly, oligopoly, and game theory. General rules for problem sets: show your work,
write down the steps that you use to get a solution (no credit for right solutions without explanation), write
legibly. If you cannot solve a problem fully, write down a partial solution. We give partial credit for partial
solutions that are correct. Do not forget to write your name on the problem set!
Problem 1. Monopoly, Oligopoly, and Perfect Competition
(46 points) In this problem you are
asked to compare the outcomes of monopoly, oligopoly, and perfect competition in one market. We are going
to assume very simple functional forms in order to simplify the algebra. We assume that the
fi
rm has a very
simple cost function:
c
(
y
) =
cy,
with
c >
0
.
The marginal cost of production therefore is constant. As for
the market demand, we assume that it takes the simple linear form
p
(
Y
) =
a
−
bY,
with
a > c >
0
and
b >
0
,
where
Y
is the total production on the industry.
1. Consider
fi
rst the case of
perfect competition
. Derive the marginal and average cost curves. How
does the supply curve look like for each
fi
rm? What about in the industry? (aggregate the individual
supply curve over

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