A steel manufacturer (SM) and BHP are negotiating the price of iron ore. First, SM proposes a price p. Following this offer, BHP can accept or reject. If BHP accepts, SM gets 300 – p and BHP gets p. If BHP rejects the offer, SM gets 0 and BHP 100. What is the outcome of the negotiations?Group of answer choicesSM offers a price of 99 and BHP acceptsSM offers a price of 101 and BHP rejectsSM offers a price of 300 and BHP rejectsSM offers a price of 100 and BHP acceptsSM offers a price of 300 and BHP accepts
Question
A steel manufacturer (SM) and BHP are negotiating the price of iron ore. First, SM proposes a price p. Following this offer, BHP can accept or reject. If BHP accepts, SM gets 300 – p and BHP gets p. If BHP rejects the offer, SM gets 0 and BHP 100. What is the outcome of the negotiations?Group of answer choicesSM offers a price of 99 and BHP acceptsSM offers a price of 101 and BHP rejectsSM offers a price of 300 and BHP rejectsSM offers a price of 100 and BHP acceptsSM offers a price of 300 and BHP accepts
Solution
SM offers a price of 100 and BHP accepts.
Here's why:
Step 1: SM wants to maximize its profit, which is 300 - p. The lower the price p, the higher the profit for SM.
Step 2: BHP wants to maximize its profit too, which is p. The higher the price p, the higher the profit for BHP.
Step 3: If SM offers a price lower than 100, BHP will reject because BHP can get 100 even if it rejects the offer.
Step 4: If SM offers a price higher than 100, it's not in SM's best interest because SM can increase its profit by offering a lower price.
Step 5: Therefore, the optimal strategy for SM is to offer a price of 100. BHP will accept this offer because it's not worse off by accepting the offer (it gets 100 whether it accepts or rejects).
So, the outcome of the negotiations is that SM offers a price of 100 and BHP accepts.
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