(a) An optimist should choose the highway parcel for its $50,000 potential profit in light opposition. The coast parcel has a lower potential profit of $170,000 and a higher potential loss of $20,000 in heavy opposition.
(b) A pessimist should choose the coast parcel for its lower potential loss of $20,000 in heavy opposition. The highway parcel has a higher potential loss of $30,000.
(c) With a 0.9 probability of heavy opposition, the best strategy is the coast parcel with an expected profit of $101,000.
(A) Highway: $ 33000
(B) Coast: $43,000
(d) The expected profit for each parcel:
(A) Highway: $43,000
(B) Coast: $101,000
Thus, the best strategy is the coast parcel.
(a) The developer should choose the highway parcel if he is an optimist. This is because the highway parcel offers a higher potential profit of $50,000 if there is light opposition from environmental groups. The coast parcel, on the other hand, only offers a potential profit of $170,000 in the best-case scenario, and it also has a higher potential loss of $20,000 if there is heavy opposition.
(b) The developer should choose the coast parcel if he is a pessimist. This is because the coast parcel offers a lower potential loss of $20,000 if there is heavy opposition from environmental groups. The highway parcel, on the other hand, has a higher potential loss of $30,000 in the worst-case scenario.
(c) If the probability of heavy opposition is 0.9, then the developer's best strategy is to buy the coast parcel. This is because the expected profit of the coast parcel is higher than the expected profit of the highway parcel.
To calculate the expected profit of each parcel, we multiply the potential profit in each scenario by the probability of that scenario occurring. For the highway parcel, this gives us the following:
Expected profit of highway parcel = ($50,000 * 0.1) + ($20,000 * 0.9)
= $33,000
For the coast parcel, this gives us the following:
Expected profit of coast parcel = ($170,000 * 0.1) + ($20,000 * 0.9)
= $43,000
Therefore, the developer's expected profit is higher if he buys the coast parcel.
(d). The expected profit for each parcel is calculated as follows:
A. Highway parcel:
* Expected profit if light opposition: $50,000
* Expected profit if heavy opposition: $20,000
* Overall expected profit: ($50,000 * 0.7) + ($20,000 * 0.3) = $43,000
B. Coast parcel:
* Expected profit if light opposition: $170,000
* Expected profit if heavy opposition: -$20,000
* Overall expected profit: ($170,000 * 0.7) + (-$20,000 * 0.3) = $101,000
Therefore, the developer's best strategy is to buy the coast parcel with an expected profit of $101,000.