Problem Set 7
Attila Ambrus, Economics 1051
Spring 2011
Due date: April 5
1. A hold-up problem. [this question introduces you to an important kind
of problem in sequential strategic settings] Suppose that Amtrak is
...
Problem Set 7
Attila Ambrus, Economics 1051
Spring 2011
Due date: April 5
1. A hold-up problem. [this question introduces you to an important kind
of problem in sequential strategic settings] Suppose that Amtrak is choosing
whether or not to build a new high-speed railroad on the East coast. Building
the railroad will involve an initial up-front sunk cost k. To keep the accounting
simple assume that the railway, if built, will run for exactly one year, and that it
will generate (new) revenues of 130,000,000. Operating the railroad for that year
would cost $10,000,00 in fuel, plus some labor costs. The labor costs depend on
the wage. The railroad would need to employ 1000 workers all of whom would
be unionized. The current going wage for union rail labor on the East coast is
$50,000. That is, without the new railroad, these workers would earn $50,000.
a) Very briefly define what is meant by sunk cost, and what is meant by the
‘sunk cost fallacy’. [Go look it up if you do not know]
b) Assuming that the labor can be hired at this going wage, for what values
of k should Amtrak build the new railroad? (Assume that Amtrak aims to
maximize profits without discounting)
c) Suppose that, if the railroad is built, after it is built the rail union can
make a ‘take it or leave it’ wage demand w to Amtrak to apply just for labor on
the new line. The railroad’s only choice is to accept to pay the wage demand
w, or close the new line down. What demand will the union make? Given this,
if you were Amtrak, for what values of k would you build the new line? Why is
your answer different from that in part b?
d) What wage demands and wage offers will be presented to the arbitrator
after the railroad is built? Given this, if you were Amtrak, for what values of k
would you build the new line? Why is your answer different from that in parts
b and c?
2. An inspection game. This example combines mixed strategies in
two-player, zero-sum games with the use of Zermelo’s algorithm.
An environmental protection agency knows that a firm is determined to
discharge a pollutant into a river on one of 3 days. The agency will learn
immediately when the river is polluted because of the telephone complaints it
will receive from local residents. However, to obtain a conviction, the agency has
to catch the firm red-handed. This means that it must try and guess in advance
the day on which the firm will pollute the river so as to have an inspector on
the spot. Unfortunately, the agency’s resources are so overstretched that it can
only afford to dispatch an inspector to the side on one of the 3 days, and the
firm knows this.
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