There is a 0.25 probability that the temperature will drop below freezing, and Best Orange Company has to decide on whether or not to fire up its smudge pots to protect its $9500 crop investment. It will cost the company $2000 to employ the smudge pots. If there is a freeze the crop would realize a revenue of $23,000 at market, as opposed to a revenue of $17,000 if there is no freeze (a matter of supply and demand). The crop will not survive a freeze without the smudge pots. Should the pots be used?
This is a great question. To determine whether the company should fire up the pots, you need to compare the expected profit (revenue - cost) of the 2 scenarios.
Scenario 1 is fire up the pots. If we fire up the pots,
our expected revenue is .2(23,000)+ .8(17,000) =
4,600+13,600 = 18,200.
But there is the cost of firing up the pots along w the. Original investment cost so the profit would be 18,200-(2000+9,500) =6,700
the profit if we don't fire up the pots is
we only get a profit if it doesn't freeze. So the expected revenue is
the cost is just the cost of investment 9,500
so expected profit = 13,600-9,500=4,100
since the expected profit of firing up the pots is greater than not, they should fire up the pots!