Summary 575- On behalf of your company, you are preparing a price bid to supply a
fixed quantity of a good to a potential buyer. You are aware that a
number of competitors also are eager to obtain the contract. The buyer
will select the lowest bid. Your cost is $100,000. If yours is the winning
bid, your profit is the difference between your bid and your cost. If not,
your profit is zero. You are considering three possible bids:
Bid $110,000; the probability of winning is .9.
Bid $130,000; the probability of winning is .5.
Bid $160,000; the probability of winning is .2.
a. Assuming your company’s aim is to maximize its expected profit,
which bid should you submit?
b. In part (a), your cost is $100,000 for certain. Now suppose it is
uncertain: either $80,000 or $120,000, with each cost equally likely.
Will this fact change your bidding behavior in part (a)? Explain briefly.
c. Suppose it is possible to gain information about the cost so that you
will know exactly what the cost will be ($80,000 or $120,000) before
submitting a bid. Use a decision tree to find the value of this
information. - A firm is looking for the best (i.e., lowest) price from one of two sellers.
It can approach each seller only once (and at no cost). Seller X’s price is
distributed uniformly between $30 and $40. Seller Y’s price is distributed
uniformly between $32 and $38. Which seller should the firm approach
first, and what is the maximum price it should accept? - A firm anticipates an R&D program requiring as many as three stages. A
successful program (sooner or later) will earn the firm a commercial
profit of $20 million. The investment costs for the respective stages are
$5 million, $3 million, and $4 million, and the conditional probabilities
of success are .2, .3, and .1, respectively. What is the firm’s optimal
investment policy? What is its expected profit? - Suppose you will be shown three prizes in order. You know absolutely
nothing about how valuable the prizes might be; only after viewing all
three can you determine which one you like best. You are shown the
prizes in order and are allowed to select one. However, there is no going
back. You must select a prize immediately after seeing it, before seeing
any subsequent prize.
a. Your sole objective is to obtain the best of the three prizes. (Second
best does not count.) A random selection provides a one-third chance
of getting the best prize. Find a strategy that provides a greater chance.
b. What if there are a large number of prizes (say, 10, 50, or 100)?
Describe in general terms the kind of strategy that would maximize
your chances of obtaining the bestprize. (Do not try to compute an
exact answer.)
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