**It is the year 2099. The economy is heavily dependent on a rare mineral,
unobtainium, which can only be found among the Asteroids. The market for
unobtainium is one of perfect competition, since a very large number of
miners are searching among the Asteroid belt in small spacecraft and the
market absorbs all their output at the going price of §19 (Nineteen
hyperbucks) per shipload. It costs each miner §1 (one hyperbuck) to
visit a candidate Asteroid, and 15% of the trips succeed in finding the
mineral, with a net gain of §18; the rest return empty-handed, with
a net loss of §1. The Asteroid belt is huge, and unobtainium will
surely become technologically obsolete before the total supply is noticeably
depleted.**

**Since one hyperbuck is a lot of money, our hero, Roger Bucks, is
risk averse. He would be just willing to exchange 3 hyperbucks cash for
a lottery in which he had a 50% chance of winning 18 hyperbucks and a 50%
chance of losing 2 hyperbucks. The exponential model of Roger's utility
function is U(X) = 1.09574(1-e ^{-.1218756X}),
but we will use a simpler model: U(X) = ,
CME(u) = 20u^{2} - 2.**

**Roger can reduce his uncertainty about the next Asteroid on his list
to visit by sending a robot probe to it, at a cost of §0.30. If the
asteroid has unobtainium there is a 75% chance the probe will correctly
report "positive," while if there is no unobtainium, the probability that
the probe will erroneously report "positive" is 30%.**

**Whether he sends a probe or not, he also has the option of buying
an insurance policy from Lloyd's of Luna. The premium is §9.10; if
he returns empty-handed, the insurance company refunds his premium and
covers his §1 expenses; otherwise they keep the §9.10, reducing
his net to §8.90.**