Suppose that the firm’s expected profit without test information is $75,000. There exists
a perfectly reliable test that produces a positive result with a probability of 0.75 and a
negative result otherwise. In light of a positive result, the firm’s expected profit is
$120,000; after a negative result, its expected profit is $40,000. Find the expected value
of information.
A small nation is considering upgrading its air force to incorporate new technology. It
faces two main choices. The first is to acquire a fleet of the latest fighter aircraft, with
the newest electronics and weapons. The cost of the acquisition (assuming that the U.S.
President and Congress agree to the sale) is $45 million per plane, including a stock of
spare parts that should last five years. The second choice is to buy an electronic upgrade
for existing aircraft, with a complete overhaul of the airframes. The cost of such an
upgrade is $8 million per plane, with about a 10% loss of fleet because of damage
beyond repair and ‘cannibalization’ to obtain the highest number of flyable planes. The
upgrading of existing planes results in aircraft with about 90% of the capability of the
new aircraft.
Top pilots in the small country’s air force are concerned that they may not be flying the
best aircraft, and could face a disadvantage in combat against newer planes flown by a
potential enemy. However, they acknowledge that if a numerical superiority against the
enemy can be obtained, an overall victory is still likely. Their theory is that three of the
upgraded planes should be able to win against one of the newer planes flown by an
enemy (although the pilots expect higher losses in combat). How would an economic
consultant advise the defense ministry of the small country in deciding how best to
spend its available budget for air defense? What objective(s) are important for this
decision? What are the pros and cons of the available options?