A group of medical professionals is considering the construction of a private clinic. If the...

Question:

A group of medical professionals is considering the construction of a private clinic. If the medical demand is high (i.e., there is a favorable market for the clinic), the physicians could realize a net profit of $100,000. If the market is not favorable, they could lose $40,000. Of course, they don?t have to proceed at all, in which case there is no cost. In the absence of any market data, the best the physicians can guess is that there is a 50?50 chance the clinic will be successful. Construct a decision tree by fill-in the blanks below in reference to the following chart. The decision choice at Decision 1 is and that at Decision 2 is_ Event 1 is_ and Event 2 is_ . The probability for Prob1 is_ and that for Prob2 is . Payoff 1 is_ and Payoff 2 is . EMV 1 is_ and EMV 2 is . Prob 1 Event 1 Payoff 1 EMV 1 Decision 1 0 Prob 2 Event 2 Payoff 2 Max EMV EMV 2 Decision 2 0

Expected Monetary Value

The expected monetary value is the amount of money expected to be received from a particular decision. For example- if an individual is deciding to open a business given the costs and probabilities, then we can find the EMV of opening the business and not opening the business.

Answer and Explanation: 1

Given information

A group of medical professionals is considering the construction of a private clinic. If the medical demand is high, the physicians could realize a net profit of $100000. If the market is not favorable, they could lose $40,000. In the absence of any market data, the best the physicians can guess is that there is a 50/50 chance the clinic will be successful.

The decision choice at Decision 1 will be to construct the clinic and at decision 2 will be to not construct the clinic. At decision 2, the choice will be that the market is favorable or not favorable. The probability that the clinic is constructed and the market is favorable will be 0.5 and the probability that the clinic is constructed and the market is not favorable will be 0.5.

The decision tree will be given as,

The expected monetary value at Y will be,

{eq}\begin{align*} EMV\left( Y \right) &= \left( {100000 \times 0.5} \right) + \left( {0.5 \times - 40000} \right)\\ &= \$ 30000 \end{align*} {/eq}

So the expected monetary value at Y is $30000.

The expected monetary value at X will be,

{eq}\begin{align*} EMV\left( X \right) &= construct + not\,construct\\ &= \$ 30000 + 0\\ &= \$ 30000 \end{align*} {/eq}

So the expected monetary value at X will be $30000.


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What Is a Decision Tree? - Examples, Advantages & Role in Management

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Chapter 2 / Lesson 12
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Clearly identifying all possible solutions for a given decision is an important part of successful management. In this lesson, you will learn how to use a decision tree to identify and select possible courses of action.


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