Econ. 359: Industrial Organization
Spring 2008
Answers to Problem Set Number 5
This problem set is about "excess demand" -- the residual demand
left over after other suppliers have put their quantity onto the market --
and about the marginal revenue from excess demand.
1. The Cali cartel has a marginal cost of $200 per kilo: $100 for the
cocaine plus $100 for protection. Their demand curve -- excess demand --
has a price of $2,000 per kilo with zero sales, with the price declining
by $100 per kilo for each million kilos sold. They would produce and sell
where marginal revenue equals marginal cost. Marginal revenue drops to 300
at 9 million kilos, but down to 100 at 10 million. So the highest profit
is at a production of 9 million. The price would be $1100 per kilo. Total
revenue is $9.9 billion, and total variable cost is $1.8 billion. Subtracting
an additional $400 million in fixed cost leaves initial profits of $7.7
billion.
2. If the Cali cartel is supplying 9 million kilos, excess demand available
for the new entrant has a price of $1100 per kilo with zero sales, dropping
by $100 per kilo for each million kilos they sold. With a marginal costs
at only $150 per kilo, the Medellin cartel's marginal revenue drops below
their marginal cost at just over 5 million kilos. At sales of 5 million,
the price falls to $600 per kilo. Earnings initially equal about $1.85 billion,
after subtracting $400 million in fixed costs. Cali's only has variable costs
this period, but profits nevertheless fall to $3.6 billion this period due
to lower prices.
3. a. In order to keep Medellin out by making them unable to cover fixed
costs by entering, Cali would have to get the price down to $500 per kilo.
That would require a production of 15 million kilos, yielding profits of
$4.1 billion.
b. Profits for the two cartels are given by the following equations, where
the subscript C refers to Cali and M refers to Medellin:
ProfitsC = pqC - 200qC -
400
ProfitsM = pqM - 150qM -
400
The price is given by the equation: p = 2,000 - 100(qC+qM). Substituting
the equation for price into the two profit equations and construct a table
like the one on page 157. If you round off to the nearest million kilos,
you can see from several more iteration of questions 1 and 2 that equilibrium
is reached where Cali and Medellin would both produce 6. At a total quantity
of 12, the price is $800, Cali's revenues are $4,800 and profits are $3.6
billion. This is lower than the $4.1 Cali would earn by flooding the market
to keep Medellin out. Note: You would get slightly different answers if
you rounded quantity off to the nearest 100,000 instead of million kilos.
You can solve for question 3 algebraically by setting MR=MC for each cartel.
The two equations are:
2,000 - 200qC- 100qM = 200
2,000 - 100qC- 200qM = 150
This solves to qM = 6.33 and qC= 5.83, which is why both produce 6 when we
round off to the nearest million.