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Decision Analysis 3 To accompany Quantitative Analysis for Management, Twelfth Edition, by Render, Stair, Hanna and Hale Power Point slides created by Jeff Heyl Copyright ©2015 Pearson Education, Inc.

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After completing this chapter, students will be able to: LEARNING OBJECTIVES Copyright ©2015 Pearson Education, Inc.3 – 2 1.List the steps of the decision-making process. 2.Describe the types of decision-making environments. 3.Make decisions under uncertainty. 4.Use probability values to make decisions under risk. 5.Develop accurate and useful decision trees. 6.Understand the importance and use of utility theory in decision making.

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Copyright ©2015 Pearson Education, Inc.3 – Introduction 3.2 The Six Steps in Decision Making 3.3 Types of Decision-Making Environments 3.4 Decision Making Under Uncertainty 3.5 Decision Making Under Risk 3.6A Minimization Example 3.8 Decision Trees 3.10 Utility Theory CHAPTER OUTLINE

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Introduction What is involved in making a good decision? Decision theory is an analytic and systematic approach to the study of decision making A good decision is one that is based on logic, considers all available data and possible alternatives, and applies a quantitative approach Copyright ©2015 Pearson Education, Inc.3 – 4

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The Six Steps in Decision Making 1.Clearly define the problem at hand 2.List the possible alternatives 3.Identify the possible outcomes or states of nature 4.List the payoff (typically profit) of each combination of alternatives and outcomes 5.Select one of the mathematical decision theory models 6.Apply the model and make your decision Copyright ©2015 Pearson Education, Inc.3 – 5

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Thompson Lumber Company Step 1 – Define the problem Consider expanding by manufacturing and marketing a new product – backyard storage sheds Step 2 – List alternatives Construct a large new plant Construct a small new plant Do not develop the new product line Step 3 –Identify possible outcomes, states of nature The market could be favorable or unfavorable Copyright ©2015 Pearson Education, Inc. 3 – 6

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Thompson Lumber Company Step 4 – List the payoffs Identify conditional values for the profits for large plant, small plant, and no development for the two possible market conditions Step 5 – Select the decision model Depends on the environment and amount of risk and uncertainty Step 6 – Apply the model to the data Copyright ©2015 Pearson Education, Inc. 3 – 7

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Thompson Lumber Company STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) Construct a large plant200,000–180,000 Construct a small plant100,000–20,000 Do nothing00 TABLE 3.1 – Conditional Values Copyright ©2015 Pearson Education, Inc. 3 – 8

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Types of Decision-Making Environments Decision making under certainty –The decision maker knows with certainty the consequences of every alternative or decision choice Decision making under uncertainty –The decision maker does not know the probabilities of the various outcomes Decision making under risk –The decision maker knows the probabilities of the various outcomes Copyright ©2015 Pearson Education, Inc.3 – 9

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Decision Making Under Uncertainty Criteria for making decisions under uncertainty Copyright ©2015 Pearson Education, Inc.3 – 10 1.Maximax (optimistic) 2.Maximin (pessimistic) (Wald) 3.Criterion of realism (Hurwicz) 4.Equally likely (Laplace) 5.Minimax regret (Savage)

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Optimistic Used to find the alternative that maximizes the maximum payoff – maximax criterion –Locate the maximum payoff for each alternative –Select the alternative with the maximum number Copyright ©2015 Pearson Education, Inc.3 – 11 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) MAXIMUM IN A ROW ($) Construct a large plant200,000–180,000200,000 Construct a small plant100,000–20,000100,000 Do nothing000 TABLE 3.2 – Thompson’s Maximax Decision Maximax

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Pessimistic Used to find the alternative that maximizes the minimum payoff – maximin criterion –Locate the minimum payoff for each alternative –Select the alternative with the maximum number Copyright ©2015 Pearson Education, Inc.3 – 12 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) MINIMUM IN A ROW ($) Construct a large plant200,000–180,000 Construct a small plant100,000–20,000 Do nothing000 TABLE 3.3 – Thompson’s Maximin Decision Maximin

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Criterion of Realism (Hurwicz) Often called weighted average –Compromise between optimism and pessimism –Select a coefficient of realism , with 0 ≤ ≤ 1 = 1 is perfectly optimistic = 0 is perfectly pessimistic –Compute the weighted averages for each alternative –Select the alternative with the highest value Copyright ©2015 Pearson Education, Inc.3 – 13 Weighted average = (best in row) + (1 – )(worst in row)

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Criterion of Realism (Hurwicz) For the large plant alternative using = 0.8 (0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000 For the small plant alternative using = 0.8 (0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000 Copyright ©2015 Pearson Education, Inc.3 – 14 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) CRITERION OF REALISM ( = 0.8) $ Construct a large plant200,000–180,000124,000 Construct a small plant100,000–20,00076,000 Do nothing000 TABLE 3.4 – Thompson’s Criterion of Realism Decision Realism

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Equally Likely (Laplace) Considers all the payoffs for each alternative –Find the average payoff for each alternative –Select the alternative with the highest average Copyright ©2015 Pearson Education, Inc.3 – 15 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) ROW AVERAGE ($) Construct a large plant200,000–180,00010,000 Construct a small plant100,000–20,00040,000 Do nothing000 TABLE 3.5 – Thompson’s Equally Likely Decision Equally likely

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Minimax Regret Based on opportunity loss or regret –The difference between the optimal profit and actual payoff for a decision 1.Create an opportunity loss table by determining the opportunity loss from not choosing the best alternative 2.Calculate opportunity loss by subtracting each payoff in the column from the best payoff in the column 3.Find the maximum opportunity loss for each alternative and pick the alternative with the minimum number 3 – 16 Copyright ©2015 Pearson Education, Inc.

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Minimax Regret 3 – 17 STATE OF NATURE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) 200,000 – 200,0000 – (–180,000) 200,000 – 100,0000 – (–20,000) 200,000 – 00 – 0 TABLE 3.6 – Determining Opportunity Losses for Thompson Lumber Copyright ©2015 Pearson Education, Inc.

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Minimax Regret 3 – 18 TABLE 3.7 – Opportunity Loss Table for Thompson Lumber STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) Construct a large plant0180,000 Construct a small plant100,00020,000 Do nothing200,0000 Copyright ©2015 Pearson Education, Inc.

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Minimax Regret 3 – 19 TABLE 3.8 – Thompson’s Minimax Decision Using Opportunity Loss STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) MAXIMUM IN A ROW ($) Construct a large plant 0180,000 Construct a small plant 100,00020,000100,000 Do nothing200,0000 Minimax Copyright ©2015 Pearson Education, Inc.

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Decision Making Under Risk When there are several possible states of nature and the probabilities associated with each possible state are known –Most popular method – choose the alternative with the highest expected monetary value (EMV) 3 – 20 Copyright ©2015 Pearson Education, Inc. where X i =payoff for the alternative in state of nature i P (X i ) =probability of achieving payoff X i (i.e., probability of state of nature i ) ∑ =summation symbol

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Decision Making Under Risk Expanding the equation 3 – 21 EMV (alternative i ) =(payoff of first state of nature) x (probability of first state of nature) + (payoff of second state of nature) x (probability of second state of nature) + … + (payoff of last state of nature) x (probability of last state of nature) Copyright ©2015 Pearson Education, Inc.

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EMV for Thompson Lumber Each market outcome has a probability of occurrence of 0.50 Which alternative would give the highest EMV? 3 – 22 EMV (large plant)= ($200,000)(0.5) + (–$180,000)(0.5) = $10,000 EMV (small plant)= ($100,000)(0.5) + (–$20,000)(0.5) = $40,000 EMV (do nothing)= ($0)(0.5) + ($0)(0.5) = $0 Copyright ©2015 Pearson Education, Inc.

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EMV for Thompson Lumber STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) EMV ($) Construct a large plant200,000–180,00010,000 Construct a small plant100,000–20,00040,000 Do nothing000 Probabilities0.50 TABLE 3.9 – Decision Table with Probabilities and EMVs Best EMV Copyright ©2015 Pearson Education, Inc. 3 – 23

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Expected Value of Perfect Information (EVPI) EVPI places an upper bound on what you should pay for additional information EVwPI is the long run average return if we have perfect information before a decision is made Copyright ©2015 Pearson Education, Inc.3 – 24 EVwPI = ∑(best payoff in state of nature i ) (probability of state of nature i )

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Expected Value of Perfect Information (EVPI) Expanded EVwPI becomes Copyright ©2015 Pearson Education, Inc.3 – 25 EVwPI = (best payoff for first state of nature) x (probability of first state of nature) + (best payoff for second state of nature) x (probability of second state of nature) + … + (best payoff for last state of nature) x (probability of last state of nature) And EVPI = EVwPI – Best EMV

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Expected Value of Perfect Information (EVPI) Scientific Marketing, Inc. offers analysis that will provide certainty about market conditions (favorable) Additional information will cost $65,000 Should Thompson Lumber purchase the information? Copyright ©2015 Pearson Education, Inc.3 – 26

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Expected Value of Perfect Information (EVPI) Copyright ©2015 Pearson Education, Inc.3 – 27 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($)EMV ($) Construct a large plant200, ,00010,000 Construct a small plant100,000-20,00040,000 Do nothing000 With perfect information 200, ,000 Probabilities0.5 TABLE 3.10 – Decision Table with Perfect Information EVwPI

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Expected Value of Perfect Information (EVPI) The maximum EMV without additional information is $40,000 –Therefore Copyright ©2015 Pearson Education, Inc.3 – 28 EVPI= EVwPI – Maximum EMV = $100,000 - $40,000 = $60,000 So the maximum Thompson should pay for the additional information is $60,000

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The maximum EMV without additional information is $40,000 –Therefore Expected Value of Perfect Information (EVPI) Copyright ©2015 Pearson Education, Inc.3 – 29 EVPI= EVwPI – Maximum EMV = $100,000 - $40,000 = $60,000 So the maximum Thompson should pay for the additional information is $60,000 Thompson should not pay $65,000 for this information

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Expected Opportunity Loss Expected opportunity loss (EOL) is the cost of not picking the best solution –Construct an opportunity loss table –For each alternative, multiply the opportunity loss by the probability of that loss for each possible outcome and add these together –Minimum EOL will always result in the same decision as maximum EMV –Minimum EOL will always equal EVPI Copyright ©2015 Pearson Education, Inc.3 – 30

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Expected Opportunity Loss Copyright ©2015 Pearson Education, Inc.3 – 31 STATE OF NATURE ALTERNATIVE FAVORABLE MARKET ($) UNFAVORABLE MARKET ($)EOL Construct a large plant0180,00090,000 Construct a small plant100,00020,00060,000 Do nothing200, ,000 Probabilities0.5 TABLE 3.11 – EOL Table for Thompson Lumber Best EOL EOL (large plant)= (0.50)($0) + (0.50)($180,000) = $90,000 EOL (small plant)= (0.50)($100,000) + (0.50)($20,000) = $60,000 EOL (do nothing)= (0.50)($200,000) + (0.50)($0) = $100,000

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Sensitivity Analysis EMV(large plant)= $200,000 P – $180,000)(1 – P ) = $200,000 P – $180,000 + $180,000 P = $380,000 P – $180,000 EMV(small plant)= $100,000 P – $20,000)(1 – P ) = $100,000 P – $20,000 + $20,000 P = $120,000 P – $20,000 EMV(do nothing)= $0 P + 0(1 – P ) = $0 Copyright ©2015 Pearson Education, Inc.3 – 32

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Sensitivity Analysis Copyright ©2015 Pearson Education, Inc.3 – 33 $300,000 $200,000 $100,000 0 –$100,000 –$200,000 EMV Values EMV (large plant) EMV (small plant) EMV (do nothing) Point 1 Point Values of P FIGURE 3.1

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Sensitivity Analysis Point 1: EMV(do nothing) = EMV(small plant) Copyright ©2015 Pearson Education, Inc.3 – 34 Point 2: EMV(small plant) = EMV(large plant)

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Sensitivity Analysis Copyright ©2015 Pearson Education, Inc.3 – 35 BEST ALTERNATIVE RANGE OF P VALUES Do nothingLess than Construct a small plant0.167 – Construct a large plantGreater than $300,000 $200,000 $100,000 0 –$100,000 –$200,000 EMV Values EMV (large plant) EMV (small plant) EMV (do nothing) Point 1 Point Values of P FIGURE 3.1

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A Minimization Example Three year lease for a copy machine –Which machine should be selected? Copyright ©2015 Pearson Education, Inc.3 – 36 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000 COPIES PER MONTH Machine A 9501,0501,150 Machine B 8501,1001,350 Machine C 7001,0001,300 TABLE 3.12 – Payoff Table

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Three year lease for a copy machine –Which machine should be selected? A Minimization Example Copyright ©2015 Pearson Education, Inc.3 – 37 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000 COPIES PER MONTH BEST PAYOFF (MINIMUM) WORST PAYOFF (MAXIMUM) Machine A 9501,0501, ,150 Machine B 8501,1001, ,350 Machine C 7001,0001, ,300 TABLE 3.13 – Best and Worst Payoffs

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A Minimization Example Using Hurwicz criteria with 70% coefficient Copyright ©2015 Pearson Education, Inc.3 – 38 Weighted average = 0.7(best payoff) + (1 – 0.7)(worst payoff) For each machine Machine A: 0.7(950) + 0.3(1,150) = 1,010 Machine B: 0.7(850) + 0.3(1,350) = 1,000 Machine C: 0.7(700) + 0.3(1,300) = 880

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A Minimization Example For equally likely criteria Copyright ©2015 Pearson Education, Inc.3 – 39 For each machine Machine A: ( , ,150)/3 = 1,050 Machine B: ( , ,350)/3 = 1,100 Machine C: ( , ,300)/3 = 1,000

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A Minimization Example For EMV criteria Copyright ©2015 Pearson Education, Inc.3 – 40 USAGEPROBABILITY 10, , ,

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For EMV criteria A Minimization Example Copyright ©2015 Pearson Education, Inc.3 – 41 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000 COPIES PER MONTH EMV Machine A 9501,0501,1501,040 Machine B 8501,1001,3501,075 Machine C 7001,0001, With perfect information 7001,0001, Probability TABLE 3.14 – Expected Monetary Values and Expected Value with Perfect Information

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For EVPI A Minimization Example For EVPI Copyright ©2015 Pearson Education, Inc.3 – 42 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000 COPIES PER MONTH EMV Machine A 9501,0501,1501,040 Machine B 8501,1001,3501,075 Machine C 7001,0001, With perfect information 7001,0001, Probability TABLE 3.15 – Expected Monetary Values and Expected Value with Perfect Information EVwPI= $925 Best EMV without perfect information= $970 EVPI = 970 – 925= $45

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Opportunity loss criteria A Minimization Example Copyright ©2015 Pearson Education, Inc.3 – 43 10,000 COPIES PER MONTH 20,000 COPIES PER MONTH 30,000 COPIES PER MONTHMAXIMUMEOL Machine A Machine B Machine C Probability TABLE 3.15 – Opportunity Loss Table

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Decision Trees Any problem that can be presented in a decision table can be graphically represented in a decision tree –Most beneficial when a sequence of decisions must be made –All decision trees contain decision points/nodes and state-of-nature points/nodes –At decision nodes one of several alternatives may be chosen –At state-of-nature nodes one state of nature will occur Copyright ©2015 Pearson Education, Inc.3 – 44

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Five Steps of Decision Tree Analysis 1.Define the problem 2.Structure or draw the decision tree 3.Assign probabilities to the states of nature 4.Estimate payoffs for each possible combination of alternatives and states of nature 5.Solve the problem by computing expected monetary values (EMVs) for each state of nature node Copyright ©2015 Pearson Education, Inc.3 – 45

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Structure of Decision Trees Trees start from left to right Trees represent decisions and outcomes in sequential order Squares represent decision nodes Circles represent states of nature nodes Lines or branches connect the decisions nodes and the states of nature Copyright ©2015 Pearson Education, Inc.3 – 46

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Thompson ’ s Decision Tree Copyright ©2015 Pearson Education, Inc.3 – 47 Favorable Market Unfavorable Market Favorable Market Unfavorable Market Do Nothing Construct Large Plant 1 Construct Small Plant 2 FIGURE 3.2 A Decision Node A State-of-Nature Node

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Thompson ’ s Decision Tree Copyright ©2015 Pearson Education, Inc.3 – 48 Favorable Market Unfavorable Market Favorable Market Unfavorable Market Do Nothing Construct Large Plant 1 Construct Small Plant 2 Alternative with best EMV is selected FIGURE 3.3 EMV for Node 1 = $10,000 = (0.5)($200,000) + (0.5)(–$180,000) EMV for Node 2 = $40,000 = (0.5)($100,000) + (0.5)(–$20,000) Payoffs $200,000 –$180,000 $100,000 –$20,000 $0 (0.5)

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Thompson ’ s Complex Decision Tree Copyright ©2015 Pearson Education, Inc.3 – 49 First Decision Point Second Decision Point Favorable Market (0.78) Unfavorable Market (0.22) Favorable Market (0.78) Unfavorable Market (0.22) Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.50) Unfavorable Market (0.50) Favorable Market (0.50) Unfavorable Market (0.50) Large Plant Small Plant No Plant 6 7 Conduct Market Survey Do Not Conduct Survey Large Plant Small Plant No Plant 2 3 Large Plant Small Plant No Plant Results Favorable Results Negative Survey (0.45) Survey (0.55) Payoffs –$190,000 $190,000 $90,000 –$30,000 –$10,000 –$180,000 $200,000 $100,000 –$20,000 $0 –$190,000 $190,000 $90,000 –$30,000 –$10,000 FIGURE 3.4

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Thompson ’ s Complex Decision Tree 1.Given favorable survey results Copyright ©2015 Pearson Education, Inc.3 – 50 EMV(node 2)= EMV(large plant | positive survey) = (0.78)($190,000) + (0.22)(– $190,000) = $106,400 EMV(node 3)= EMV(small plant | positive survey) = (0.78)($90,000) + (0.22)(– $30,000) = $63,600 EMV for no plant= – $10,000

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Thompson ’ s Complex Decision Tree 2.Given negative survey results Copyright ©2015 Pearson Education, Inc.3 – 51 EMV(node 4)= EMV(large plant | negative survey) = (0.27)($190,000) + (0.73)(– $190,000) = – $87,400 EMV(node 5)= EMV(small plant | negative survey) = (0.27)($90,000) + (0.73)(– $30,000) = $2,400 EMV for no plant= – $10,000

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Thompson ’ s Complex Decision Tree 3.Expected value of the market survey Copyright ©2015 Pearson Education, Inc.3 – 52 EMV(node 1)= EMV(conduct survey) = (0.45)($106,400) + (0.55)($2,400) = $47,880 + $1,320 = $49,200 4.Expected value no market survey EMV(node 6)= EMV(large plant) = (0.50)($200,000) + (0.50)(– $180,000) = $10,000 EMV(node 7)= EMV(small plant) = (0.50)($100,000) + (0.50)(– $20,000) = $40,000 EMV for no plant= $0 The best choice is to seek marketing information

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Thompson ’ s Complex Decision Tree Copyright ©2015 Pearson Education, Inc.3 – 53 FIGURE 3.5 First Decision Point Second Decision Point Favorable Market (0.78) Unfavorable Market (0.22) Favorable Market (0.78) Unfavorable Market (0.22) Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.50) Unfavorable Market (0.50) Favorable Market (0.50) Unfavorable Market (0.50) Large Plant Small Plant No Plant 6 7 Conduct Market Survey Do Not Conduct Survey Large Plant Small Plant No Plant 2 3 Large Plant Small Plant No Plant Results Favorable Results Negative Survey (0.45) Survey (0.55) Payoffs –$190,000 $190,000 $90,000 –$30,000 –$10,000 –$180,000 $200,000 $100,000 –$20,000 $0 –$190,000 $190,000 $90,000 –$30,000 –$10,000 $40,000 $2,400 $106,400 $49,200 $106,400 $63,600 –$87,400 $2,400 $10,000 $40,000

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Expected Value of Sample Information Thompson wants to know the actual value of doing the survey Copyright ©2015 Pearson Education, Inc.3 – 54 =(EV with SI + cost) – (EV without SI) EVSI = ($49,200 + $10,000) – $40,000 = $19,200 EVSI = – Expected value with sample information Expected value of best decision without sample information

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Efficiency of Sample Information Possibly many types of sample information available Different sources can be evaluated Copyright ©2015 Pearson Education, Inc.3 – 55 For Thompson Market survey is only 32% as efficient as perfect information

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Sensitivity Analysis How sensitive are the decisions to changes in the probabilities? How sensitive is our decision to the probability of a favorable survey result? If the probability of a favorable result ( p =.45) where to change, would we make the same decision? How much could it change before we would make a different decision? Copyright ©2015 Pearson Education, Inc.3 – 56

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Sensitivity Analysis p = probability of a favorable survey result (1 – p ) = probability of a negative survey result EMV(node 1) =($106,400) p +($2,400)(1 – p ) =$104,000 p + $2,400 Copyright ©2015 Pearson Education, Inc.3 – 57 We are indifferent when the EMV of node 1 is the same as the EMV of not conducting the survey $104,000 p + $2,400= $40,000 $104,000 p = $37,600 p = $37,600/$104,000 = 0.36 If p < 0.36, do not conduct the survey If p > 0.36, conduct the survey

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Utility Theory Monetary value is not always a true indicator of the overall value of the result of a decision The overall value of a decision is called utility Economists assume that rational people make decisions to maximize their utility Copyright ©2015 Pearson Education, Inc.3 – 58

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Heads (0.5) Tails (0.5) $5,000,000 $0 Utility Theory Copyright ©2015 Pearson Education, Inc.3 – 59 Accept Offer Reject Offer $2,000,000 EMV = $2,500,000 FIGURE 3.6 – Decision Tree for the Lottery Ticket

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Utility Theory Utility assessment assigns the worst outcome a utility of 0 and the best outcome a utility of 1 A standard gamble is used to determine utility values When you are indifferent, your utility values are equal Copyright ©2015 Pearson Education, Inc.3 – 60

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Utility Theory Copyright ©2015 Pearson Education, Inc.3 – 61 Best Outcome Utility = 1 Worst Outcome Utility = 0 Other Outcome Utility = ? (p)(p) (1 – p ) Alternative 1 Alternative 2 FIGURE 3.7 – Standard Gamble for Utility Assessment

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Utility Theory Expected utility of alternative 2 = Expected utility of alternative 1 Utility of other outcome = ( p )(utility of best outcome, which is 1) + (1 – p )(utility of the worst outcome, which is 0) Utility of other outcome = ( p )(1) + (1 – p )(0) = p Copyright ©2015 Pearson Education, Inc.3 – 62

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Investment Example Construct a utility curve revealing preference for money between $0 and $10,000 A utility curve plots the utility value versus the monetary value –An investment in a bank will result in $5,000 –An investment in real estate will result in $0 or $10,000 –Unless there is an 80% chance of getting $10,000 from the real estate deal, prefer to have her money in the bank –If p = 0.80, Jane is indifferent between the bank or the real estate investment Copyright ©2015 Pearson Education, Inc.3 – 63

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Investment Example Copyright ©2015 Pearson Education, Inc.3 – 64 Figure 3.8 – Utility of $5,000 p = 0.80 (1 – p ) = 0.20 Invest in Real Estate Invest in Bank $10,000 U($10,000) = 1.0 $0 U($0.00) = 0.0 $5,000 U($5,000) = p = 0.80 Utility for $5,000 = U($5,000)= p U($10,000) + (1 – p )U($0) = (0.8)(1) + (0.2)(0) = 0.8

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Use the three different dollar amounts and assess utilities Investment Example Copyright ©2015 Pearson Education, Inc.3 – 65 Assess other utility values Utility for $7,000 = 0.90 Utility for $3,000 = 0.50

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Utility Curve 3 – 66 U ($7,000) = 0.90 U ($5,000) = 0.80 U ($3,000) = 0.50 U ($0) = 0 FIGURE 3.9 – Utility Curve 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – ||||||||||| $0$1,000$3,000$5,000$7,000$10,000 Monetary Value Utility U ($10,000) = 1.0 Copyright ©2015 Pearson Education, Inc.

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Utility Curve Typical of a risk avoider –Less utility from greater risk –Avoids situations where high losses might occur –As monetary value increases, utility curve increases at a slower rate A risk seeker gets more utility from greater risk –As monetary value increases, the utility curve increases at a faster rate Risk indifferent gives a linear utility curve 3 – 67 Copyright ©2015 Pearson Education, Inc.

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Preferences for Risk 3 – 68 FIGURE 3.10 Monetary Outcome Utility Risk Avoider Risk Indifference Risk Seeker Copyright ©2015 Pearson Education, Inc.

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Utility as a Decision-Making Criteria Once a utility curve has been developed it can be used in making decisions Replaces monetary outcomes with utility values Expected utility is computed instead of the EMV 3 – 69 Copyright ©2015 Pearson Education, Inc.

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Utility as a Decision-Making Criteria Mark Simkin loves to gamble –A game tossing thumbtacks in the air –If the thumbtack lands point up, Mark wins $10,000 –If the thumbtack lands point down, Mark loses $10,000 –Mark believes that there is a 45% chance the thumbtack will land point up Should Mark play the game (alternative 1)? 3 – 70 Copyright ©2015 Pearson Education, Inc.

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Utility as a Decision-Making Criteria 3 – 71 FIGURE 3.11 – Decision Facing Mark Simkin Tack Lands Point Up (0.45) Alternative 1 Mark Plays the Game Alternative 2 $10,000 –$10,000 $0 Tack Lands Point Down (0.55) Mark Does Not Play the Game Copyright ©2015 Pearson Education, Inc.

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Utility as a Decision-Making Criteria Step 1– Define Mark’s utilities 3 – 72 U(–$10,000) = 0.05 U($0) = 0.15 U($10,000) = 0.30 Copyright ©2015 Pearson Education, Inc. FIGURE – 0.75 – 0.50 – 0.30 – 0.25 – 0.15 – 0.05 – 0 – ||||| –$20,000–$10,000$0$10,000$20,000 Monetary Outcome Utility

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Utility as a Decision-Making Criteria Step 2 –Replace monetary values with utility values 3 – 73 E(alternative 1: play the game)= (0.45)(0.30) + (0.55)(0.05) = = E(alternative 2: don’t play the game)= 0.15 Copyright ©2015 Pearson Education, Inc.

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Utility as a Decision-Making Criteria 3 – 74 FIGURE 3.13 – Using Expected Utilities Tack Lands Point Up (0.45) Alternative 1 Mark Plays the Game Alternative Tack Lands Point Down (0.55) Don’t Play Utility E = Copyright ©2015 Pearson Education, Inc.

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