Question

Mobon Oil company owns a lease that entitles it to explore for oil on a parcel of offshore land in California. Since the lease is about to expire Mobon must now decide whether to drill for oil at the site or to sell the lease to exxil oil company, which has just offered Mobon $50,000. Mobon estimates it would cost $100,000 to drill at the site. If the well were dry, all this cost would be lost. If the well were successful, its value to Mobon would depend on the extent of the oil discovered. For simplicity, Mobon assumes there are only two types of successful wells: minor and major success. Mobon estimates that a minor success would result in revenues of $200,000 in excess of the drilling cost, whereas a major success would result in revenue of $500,000 in excess of the drilling cost. Mobon has assessed the following probabilities: If the well is dry then the probability is 0.7, if it is a minor success the probability is 0.2, and if it is a major success the probability is 0.1.

A) construct an appropriate payoff matrix, B) Using the maximax criterion, identify the optimal decision C) Using the maximin criterion, identify the optimal decision D) Using the minimax criterion, identify the optimal decision E) Using the EMV criterion, identify the optimal decision F)Using the expected regret criterion identify the optimal decision and verify that same as e G)Grow a decision tree, prune the tree using EMV criterion and verify same optimal decision as e

Answer 1

Part (A)

Pay-off matrix

Decision Options	State of Nature
	Dry well	Drill Minor Success	Drill Major Success
Sell Lease	50000
Drill for Oil	- 100000	200000	500000

Part (B) Maximax

Maximum pay-off under the second option is 500000 which is more than the pay-off under the first otion. So, optimal decision is: Drill for Oil ANSWER

Part (C) Maximin

Minimum pay-off under the second option is - 100000 which is less than the pay-off under the first otion. So, optimal decision is: Sell Lease ANSWER

Part (D) Minimax

Maximum pay-off under the second option is 500000 which is more than the pay-off under the first otion. So, optimal decision is: Sell Lease ANSWER

Part (E) EMV

EMV(Expected Monetary Value) = ?(pay-off)(probability of pay-off) – sum over all possible values of pay-off.

Since under the first option, there is only one pay-off possible, EMV = that pay-off = 50000

Under the second option, EMV =(- 100000 x 0.7) + (200000 x 0.2) + (500000 x 0.1) = 20000

Since 50000 > 20000, optimal decision is: Sell Lease ANSWER

DONE