Managerial Economics

1. Managerial Economics Lecture: Decision making under uncertainty Date: 07.07.14

2. Decisions and Decision Making • Decision = choice made from available alternatives • Decision Making = Process of identifying problems and opportunities and resolving them

3. Managerial Decision Making • Decision making is not easy • It must be done amidst of • ever-changing factors • unclear information • conflicting points of view

4. Categories of Decisions • Programmed Decisions • Situations occurred often enough to enable decision rules to be developed and applied in the future • Made in response to recurring organizational problems • Non-programmed Decisions – in response to unique, poorly defined and largely unstructured, and have important consequences to the organization

5. Decisions and Decision Making • Many decisions that managers deal with every day involve at least some degree of uncertainty and require non-programmed decision making • May be difficult to make • Made amid changing factors • Information may be unclear • May have to deal with conflicting points of view

6. Certainty, Risk, Uncertainty, Ambiguity • Certainty • all the information the decision maker needs is fully available • Risk • decision has clear-cut goals • good information is available • future outcomes associated with each alternative are subject to chance

7. Certainty, Risk, Uncertainty, Ambiguity • Uncertainty • managers know which goals they wish to achieve • information about alternatives and future events is incomplete • managers may have to come up with creative approaches to alternatives • Ambiguity • by far the most difficult decision situation • goals to be achieved or the problem to be solved is unclear • alternatives are difficult to define • information about outcomes is unavailable

8. Economic risk Refers to the chance of loss because all possible outcomes and their probabilities are known • Business Risk The chance of loss associated with a managerial decision • Uncertainty When future outcomes can not be predicted with absolute accuracy but possibilities and probabilities are not known

9. Probability Chance of occurrence • Probability Distribution A list of possible events and probabilities • Payoff matrix Table that shows outcomes associated with each possible state of nature

10. Payoff matrix • A firm will choose only one from two alternative projects • Each calling for an outlay of $10,000 • Profits earned from the two projects are related to the general level of economic activity during the coming year

11. Payoff Matrix • State of the economy Profits Project A Project B Recession $4000 $ 0 Normal 5000 5000 Boom 6000 12000

12. Probability Distribution • A sales manager observes that there is a 70 % chance that a given customer will place a specific order versus a 30% chance that she will not EventProbability of Occurrence Receive order 0.7=70% Do not receive order 0.3=30% Total 1.0=100%

13. Decision Making: The Process of making a conscious choice between 2 or more alternatives producing most desirable consequences (benefits) relative to unwanted consequences (costs). If Planning is truly Deciding in advance what to do, how to do it, when to do it and who is to do it, then Decision Making is an essential part of Planning

14. Categories of Decision Making Decision Making Under Certainty: Linear Programming Decision Making Under Risk: expected value, decision trees, queuing theory, and simulation Decision Making Under Uncertainty: Game Theory

15. State of Nature / Probability N1 N2 ……… Nj ……… Nn Alternative P1 P2 ………Pj ……… Pn A1 O11 O12 ……… O1j ……… O1n A2 O21 O22 ……… O2j ………O2n Outcome …. …. … ………… ……… Ai Oi1 Oi2 ……… Oij ………Oin …. …. … ………… ……… Am Om1 Om2 ……… Omj …… Omn Sum of n values of pjmust be 1 Payoff (Benefit) Table - Decision Matrix

16. A1, A2,…. Am Decision alternatives N1 , N2 ,Nj ……… Nn Decision alternatives, state of nature P1 P2 ………Pj ……… Pn Probability of occurrence Om1 Om2 ……… Omj …… Omn Outcomes

17. Decision Making Under Certainty Implies that we are certain of the future state of nature (or assume we are). Linear programming is a tool for the decision making under certainty. This means:- the probability of pj of future Nj is 1 and all other futures have zero probability

18. Decision Making Under Risk This means:- Each Nj has a known (or assumed) probability of pj and there may not be one state that results best outcome.

19. Decision Making Under Uncertainty This means:- Probabilities pj of future states are unknown.

20. Decision Making Under Risk There exist a number of possible future states of Nature Nj. Each Njhas a known (or assumed) probability pjof occurring. There may not be one future state that results in the best outcome for all alternatives Ai. Examples of future states and their probabilities • Alternative weather (N1=rain, N2=good weather) will affect the • probability of alternative construction schedule; the probabilities P1 of • rain and p2 of good weather can be estimated from historical data 2. Alternative economic futures (boom and bust) determine the relative Profitability of high risk investment strategy.

21. n  j=1 (pjOij) Ei= Decision Making Under Risk Expected Values (Ei) : given the future states of nature and their probabilities, the solution in decision making under risk is the alternatives Ai that provides the highest expected value Ei, which is defined as the sum of the products of each outcome Oij times the probability pj that the associated state of nature Nj occurs Choose the Alternative Ai giving the highest expected value

22. Decision Making Under Risk Example of Decision Making Under Risk Not Fire in your house Fire in your house State of Nature Alternatives Probabilities P1 =0.999 P2=0.001 n  j=1 Insure house $-200 $-200 (pjOij) Do not Insure house 0 $-100,000 Ei= Calculate Expected Values (Ei) Would you insure your house or not? E1=$-200 E1=0.999*(-200)+0.001*(-200) E2=$-100 E2=0.999*0+0.001*(-100,000)

23. Example: Consider that you own rights to a plot of land under which there may or may not be oil. You are considering three alternatives: Doing nothing (don’t drill), drilling your own expense of 500000$ (Drill alone), and farming out, the opportunity to someone who will drill the well and give you part of the profit if the well is successful. Drilling your own a small Well will make 300000$ profit and a Big well 9300000$. Farm out alternative with Dry hole will not cost at all, but a small Well Will make 125000$ and a Big Well will make 1250000$ profit. Constitute the Payoff table and calculate the expected value of each alternative solve the problem.

24. Decision Making Under Risk Well Drilling Example-Decision Making Under Risk State of Nature / Probability Alternative N1:Dry Hole N2 :Small Well N3:Big Well Expected Value P1=0.6 P2=0.3 P3=0.1 $0 A1:Don’t Drill$0 $0 $0 A2:Drill Alone$-500,000 $300,000 $9,300,000 $720,000 $162,000 A3:Farm Out$0 $125,000 $1,250,000 E1=0.6*0+0.3*0+ 0.1*0 E2=0.6*(-500,000)+0.3*(300,000)+ 0.1*(9,300,000) E3=0.6*0+0.3*(125,000)+ 0.1*(1,250,000) $720,000 A2 is the solution if you are willing to risk $500,000 Calculate Expected Values (Ei)

25. Decision Tree • The visual mapping of a sequential decision making process • A convenient way to represent decisions, chance events and possible outcomes in choices under risk and uncertainty • The diagram can incorporate all the specific objectives of the decision maker have been established • The structure of the tree emphasizes the ingredients , choices, outcomes and probabilities • The more precise the tree become, the more precise the more precise one’s thinking becomes about the problem

26. Decision Making Under Risk Calculate Expected Values (Ei) Decision Trees Decision node Ai Chance node Nj Outcome (Oij) Probability (Pj) Expected Value Ei x = No Fire: (-200) x (0.999) (-199.8) = + = $-200 Insure (-200) x (0.001) (-0.2) = Fire: (0) x (0.999) (0) No Fire: = Don’t Insure + =$-100 (-100,000) x (0.001) (-100) Fire: = Mathematical solution is identical, visual representation is different

27. Simulation • First step Construction of a mathematical model of the managerial decision-making that we want to simulate

28. Simulation • An aerospace engineer constructs a miniature model plane and wind tunnel to test the strength and resistance of the model plane to change in wind speed and direction • This modeling mimics the essential features of the essential features of the real-world situation

29. Simulation • The firm might construct a model for the strategy of expanding the output • The between the output of the commodity and its price, output, selling costs, revenues and taxes • Calculate the firm’s profit • Varying the value of each variable substituted into the model the firm can get an estimate of the effect of the change in the variable on the output of the model or profit of the firm

30. Simulation • This refers to sensitivity analysis • To fully simulate the strategy to expand output, the firm needs the probability distribution of the concerned variables(output, commodity prices, input prices, depriciation……) • Randomly selected values of each variable of the model are then fed into the computer program to generate the present value of the firm’s profit is recorded

31. Simulation • The probability distribution of the firm’s profits so generated can then be used to calculate the expected profit of the firm and the standard deviation of the distribution of the profit (As a measure of risk) • Using this information the firm determine the optimal strategy to adopt

32. Simulation • Problem -Full scale simulation is expensive -Only for the large projects when decision king is too complex to analyze with decision tree But very powerful as consider all the interactions among all the variables

33. Decision Making Under Uncertainty We do not know the probabilities pj of future states of nature Nj Where more than one possible outcome to a decision Probability of each possible outcome is not known Decision making is necessarily subjective

34. Decision Making Under Uncertainty • Two specific decision rule -Maximin criterion -Minimax regret criterion

35. Decision Making Under Uncertainty • Maximincriterion postulates that the decision maker should determine the worst possible outcome of each strategy and then pick the strategy that provides the best of the worst possible outcomes

36. Decision Making Under Uncertainty • The firm could follow the strategy of introducing a new product -Would provide a return of $20000 if succeeded -lead to a loss of $10000 if failed -Not to invest in the venture have zero profit or loss

37. Decision Making Under Uncertainty • Pay off matrix State of nature Strategy success failure maximin Invest $20000 -$10000 -$10000 Do not invest 0 0 0*

38. Decision Making Under Uncertainty • Manger picks the strategy that provides the best (Maximum) of the worst(minimum) possible outcomes(maximin) • This is the decision of not investing as that has the maximum of the minimum payoffs • Pessimistic approach • Appropriate when the firm is strongly risk avert

39. Decision Making Under Uncertainty • Minimax regret criterion postulates that decision maker should select the strategy that minimizes the maximum regret or opportunity cost of the wrong decision whatever the state of nature that actually occurs • Regret is measured by the difference between the payoff of a given strategy and payoff of the best strategy under the same state of nature

40. Decision Making Under Uncertainty • If the best option is chosen no regret • If not the option that will incur the minimum regret

41. Decision Making Under Uncertainty • Pay off matrix State of nature Regret matrix Maximum regret Strategy success failure success failure Invest $20000 -$10000 0 10000 $10000* Do not invest 0 0 $20000 0 $20000

42. Decision Making Under Risk State of Nature / Probability Alternative N1:Dry Hole N2 :Small Well N3:Big Well A1:Don’t Drill$0 $0 $0 A2:Drill Alone$-500,000 $300,000 $9,300,000 A3:Farm Out$0 $125,000 $1,250,000 Decision Making Under Uncertainty

43. Decision Making Under Uncertainty $1,450,000* $3,033,333* $458,333 $250,000 Maximize [(best outcome)+(1-)(worst outcome)] [0.2(9,300,000)+(1-0.2)(-500,000)] E2=-500,000+300,000+9,300,000 3 [0.2(1,250,000)+(1-0.2)(0)] E3=0+125,000+1,250,000 3 Decision Making Under Uncertainty: Example Coefficient of optimism (Maximax) (Maximin) Hurwicz Equally Alternative Maximum Minimum (=0.2) Likely Optimist Pessimist A2:Drill Alone$9,300,000 * $-500,000 A3:Farm Out$1,250,000 $0*

44. Decision Making Under Risk State of Nature / Probability Alternative N1:Dry Hole N2 :Small Well N3:Big Well A1:Don’t Drill$0 $0 $0 A2:Drill Alone$-500,000 $300,000 $9,300,000 A3:Farm Out$0 $125,000 $1,250,000 State of Nature / Probability Alternative N1:Dry Hole N2 :Small Well N3:Big Well Maximum Regret We do not know probabilities $9,300,000 A1:Don’t Drill$0 $300,000 $9,300,000 A2:Drill Alone$500,000 0 0 $500,000 $8,050,000 A3:Farm Out$0 $175,000 $8,050,000 Decision Making Under Uncertainty: Maximum Regret

45. A2 is the solution. We choose the minimum among maximum regrets. Decision Making Under Uncertainty: Maximum Regret State of Nature / Probability Alternative N1:Dry Hole N2 :Small Well N3:Big Well Maximum Regret We do not know probabilities $9,300,000 A1:Don’t Drill$0 $300,000 $9,300,000 A2:Drill Alone$500,000 0 0 $500,000 $8,050,000 A3:Farm Out$0 $175,000 $8,050,000