Question

The Mineco company owns a rare-earth element ore. If the land has ore and Mineco digs a mine they will make $1,000,000 profit. If the land does not have ore and Mineco digs Alternatively, the land could be sold for $400,000. A geologist has estimated that there is a 65% chance that the land contains ore. piece of land that may have a significant amount of recoverable ww. a mine they will lose $500,000 (5 points) Fill in the payoff table for this decision problem. There should be an entry in every box in the table below. a. State of Nature Alternative Prior Probability b. (5 points) Under the maximin decision criterion what should Mineco do? (5 points) Under the maximum likelihood criterion what should Mineco do? C. d. (10 points) Under Bayes' decision rule, what should Mineco do? (10 points) If Mineco is using Bayes decision rule,, what is the Expected Value of Perfect Information for this problem? e.

Answer 1

a.

Below is the payoff table for this decision problem

		State of Nature
		Land has ore	Land does not have ore
Alternative	Mineco digs a mine	$1,000,000	-$500,000
	Mineco sell the land	$400,000	$400,000
	Prior Probability	65%	35%

b.

In Maximin, we pick the maximum of the minimums of payoffs of decision alternatives

Looking at the payoff table, minimum payoff value for Alternative 1 "Mineco digs a mine' is -$500,000.

Now if we compare value for two alternative - $500,000 and $400,000. The maximum value is $400,000.

Hence, under the maximum criteria Mineco should sell the land.

c.

Maximum likelihood criterion focuses on the most likelystate of nature.

First identify the state of nature with largest probability and then choose the decision alternative that has the largest payoff for this state of nature.

Looking at payoff table, highest probability is for state of natured with 'land has ore' i.e. $1,000,000.

In the net step, we compare payoff of alternatives - $1,000,000 Vs. $400,000 and select the largest payoff (i.e. $1,000,000)

Hence, with maximum likelihood criterion Mineco should dig a mine.

d.

Using Bayes' decision rule, calculate weighted average of its payoff by multiplying each payoff by the prior probabilities and summing these products. This is expected payoffs (EP).

In the next step, choose the decision alternative with largest expected payoff.

For Alternative 1 (Mineco digs a mine)- EP = ($1,000,000)*65% + (-$500,000)* 35% = $475,000

For Alternative 2 (Mineco sell the land) - EP = $400,000

EP is higher for Alternative 1 (Mineco digs a mine).

Hence, Mineco should dig a mine as per Bayes decision rule.

e.

Expected value of perfect information = EP (with perfect information) - EP (without perfect information)

where EP (with perfect information) = Expected payoff if decision could be made after learning the true state of nature

EP (without perfect information) = Expected payoff from applying Bayes decision rule

Payoff Table		State of Nature
		Land has ore	Land does not have ore
Alternative	Mineco digs a mine	$1,000,000	-$500,000
	Mineco sell the land	$400,000	$400,000
Maximum Payoff (Higher among each alternative for each state of nature)		$1,000,000	$400,000
Prior Probability		65%	35%
EP (with perfect information)		($1,000,000 * 0.65) + ($400,000 *0.35) = $790,000

If you liked my answer, please give like/ thumbs up. Thank you.