Practice+Final+1_Solution

Quarterincand

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Unformatted text preview: 
 Final
Exam
 
 
 
 
 QUESTION
1.
Cournot
Competition
[35
points]



 
 Nickel
is
a
commodity
whose
market
is
dominated
by
two
players
Quarter
Inc.
and
Dime
 Inc.
The
two
companies
must
decide
simultaneously
(without
knowledge
of
each
other’s
 decision)
how
much
nickel
to
produce
and
supply
to
the
market.
Once
both
firms
select
 their
output
quantity,
the
market
price
adjusts
to
clear
the
market.
So,
each
firm
really
 acts
as
a
“quantity
taker,
price
maker”:
it
chooses
its
quantity
based
on
a
conjecture
 about
the
quantity
it
expects
its
competitor
to
choose,
taking
into
account
how
its
own
 quantity
decision
affects
the
market
price.

 
 The
market
price
for
nickel
is
determined
as
follows:
if
the
total
quantity
(in
tons)
 extracted
by
the
firms
is
Q,
then
the
market
price
per
ton
is
given
by
the
relationship:

 
 .
 
 For
instance,
if
Quarter
Inc.
decides
to
extract
20
tons
and
Dime
Inc.
decides
to
extract
 30
tons,
the
market
price
would
be
$65
per
ton
(
=
90
–
½(20+30)
).
Quarter
Inc.
and
 Dime
Inc.
must
each
individually
and
simultaneously
decide
between
supplying
only
 three
quantities:
50
tons,
60
tons
or
80
tons.

The
marginal
cost
of
extracting
and
 supplying
nickel
is
zero
for
both
firms.

You
should
assume
as
usual
that
Quarter
Inc.
and
 Dime
Inc.
are
both
rational
firms
seeking
to
maximize
their
own
profits.
 
 Below
is
a
chart
of
the
market
prices
and
profits
for
different
choices
that
Quarter
and
 Dime
can
make;
some
of
the
cells
have
been
filled...
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