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Readings Readings Baye 6th edition or 7th edition, Chapter 3 BA 445 Lesson A.4 Uncertainty 1 Overview Overview BA 445 Lesson A.4 Uncertainty 2 Overview Expected Value distinguishes good decisions from good luck. Gambling with positive expected value virtually guarantees long-run success. — So, make good decisions and patiently wait for success. Confidence Intervals can test whether business success resulted from good decisions, and whether failure resulted from bad decisions. — So, test successes and failures to evaluate decisions. Regression Analysis can test whether demand is more likely linear or log-linear, and can estimate which coefficient values are more likely. Those estimates then affect predictions and decisions. BA 445 Lesson A.4 Uncertainty 3 Ad-In and Downloads Add-Ins Before class, be sure Analysis ToolPack is added in to Excel. • Click Excel options • Click Add-Ins • You should see Analysis ToolPack listed Spreadsheet Downloads Before class, download the following Excel spreadsheets http://faculty.pepperdine.edu/jburke2/ba445/PowerP1/SimGamble.xlsx http://faculty.pepperdine.edu/jburke2/ba445/PowerP1/MultiRegression.xlsx BA 445 Lesson A.4 Uncertainty 4 Expected Value Expected Value BA 445 Lesson A.4 Uncertainty 5 Expected Value Overview Expected Value distinguishes good decisions from good luck. Gambling with positive expected value virtually guaranteeing long-run success. — So, make good decisions and patiently wait for success. BA 445 Lesson A.4 Uncertainty 6 Expected Value Gambling • Gambling is risking money or anything of value with the goal of winning additional money or value. • Most business decisions (what to produce, what to charge, who to hire, what to pay, …) involve gambling. For example, you produce today but the price you can charge customers can change in the future, so your profit is risky. • Most consumption decisions also involve gambling. For example, buying fire insurance on your house is gambling. If your house burns, you win; if it does not burn, you loose. Flanders from the Simpsons does not have fire insurance on his house because “it’s too much like gambling”. BA 445 Lesson A.4 Uncertainty 7 Expected Value Gamblers verses Entertainment Seekers and Thrill Seekers Good poker players in Las Vegas may be good gamblers (seeking money). Good gamblers avoid other good gamblers, and seek bad players. Bad players can be bad gamblers (bad players that think they can win against good players) or can be thrill seekers or entertainment seekers. A bad poker player that looses then says “at least I had fun” is an entertainment seeker. Keanu Reeves is a well-known thrill seeker. He survived a near-fatal motorcycle crash in 1988 and still bears the scars of another accident in 1996. BA 445 Lesson A.4 Uncertainty 8 Expected Value Risk Aversion • Whether you should gamble may at first seem to depend on whether you are a risk taker or a risk avoider. (But we will see it often does not.) • A risk taker allows possible gains to offset possible loses from a gamble. • A risk avoider focuses on avoiding loss. • For example, propping open fire doors (say, on the third floor of CCB) gains time but could lead to loss of life. Risk takers would prop open the doors but risk avoiders would not. BA 445 Lesson A.4 Uncertainty 9 Expected Value Repeated Risk • Gambling risk depends on whether one gambles just once, or many times. • Gambling your life savings on one hand of blackjack generates significant risk. • Gambling your life savings divided into thousands of good gambles generates little risk, like playing thousands of hands of blackjack if you have an advantage from counting cards. BA 445 Lesson A.4 Uncertainty 10 Expected Value Expected Value • How do you identify a good gamble? • Expected value (EV) is the sum of probabilities times payoffs. • Positive expected value identifies a good gamble. We will see that most people should take good gambles. • Negative expected value identifies a bad gamble. We will see that most people should avoid bad gambles. BA 445 Lesson A.4 Uncertainty 11 Expected Value Example • Is roulette a good gamble? • Any player placing $1 on a number (which is one number out of 38 possible, counting 0 and 00) can earn $35 profit, so expects EV = (1/38)(35) + (37/38)(-1) = -$2/38 <0 BA 445 Lesson A.4 Uncertainty 12 Expected Value Example • Is poker a good gamble? • Since the casino (the house) takes a payment (rake), the sum total of the EV of each player is negative, so at least one player expects EV < 0 (the sucker) • If you can’t spot the sucker in the first half hour at the table, then you are the sucker. BA 445 Lesson A.4 Uncertainty 13 Expected Value Example • Is rolling through a stop sign a good gamble? • Rolling through a stop sign gains valuable time if you are not caught and looses both time and money if you are caught and ticketed. So, EV = Prob.(not caught)(Gain) + Prob.(caught)(Loss) can be either positive or negative. • In Prof. Burke’s experience, it is positive at Pepperdine. BA 445 Lesson A.4 Uncertainty 14 Expected Value Example • Is rolling through a car gate a good gamble? • Rolling through a car gate gains valuable time if you are not crushed by the gate that has not yet opened and looses both time and money if you are crushed. So, EV = Prob.(not caught)(Gain) + Prob.(caught)(Loss) can be either positive or negative. • In Prof. Burke’s experience, it is positive exiting the parking lot Pepperdine’s CCB building. BA 445 Lesson A.4 Uncertainty 15 Expected Value Example • Should you gamble $1 of value if there is a 55% chance of winning $1 and a 45% chance of loosing $1? • If you are young, this is a practical question because over your lifetime you will face a series of such gambles (gambling your money in blackjack, gambling your time looking for something you lost in your yard, gambling your gas looking for a better parking spot,…). BA 445 Lesson A.4 Uncertainty 16 Expected Value Simulation • Should you gamble $1 of value if there is a 55% chance of winning and a 45% chance of loosing? • If you gamble only once, there is a 45% chance you will loose. • If you gamble 1000 times, then all of the simulations in the Excel file SimGamble.xls should report a win because the expected value = .55(+$1) + .45(-$1) = $.10 is positive. Conclusion • Avoid bad gambles (Vegas, the lottery, purchase protection plans, …) • Accepting good gambles (arriving at the airport 50 minutes early rather than 1 hour early, looking for better parking,...) virtually guarantees long-run gains. • Exception: You may choose a few bad gambles (unsubsidized health insurance) if you cannot afford to lose. BA 445 Lesson A.4 Uncertainty 17 Expected Value Good decisions • Accepting good gambles is good decision making. • Focus on making good decisions, and do not be distracted by the outcome. You are virtually guaranteed long-run success. Playing the lottery is a bad decision (it has negative expected value). • Playing just one time might produce a good outcome. • Playing frequently virtually guarantees long-run loss. Investing in the stock market can be a good decision (it can have positive expected value). • Investing just one time might produce a bad outcome. • Investing frequently virtually guarantees long-run success. BA 445 Lesson A.4 Uncertainty 18 Confidence Intervals Confidence Intervals BA 445 Lesson A.4 Uncertainty 19 Confidence Intervals Overview Confidence Intervals can test whether business success resulted from good decisions, and whether failure resulted from bad decisions. — So, test success and failures to evaluate decisions. BA 445 Lesson A.4 Uncertainty 20 Confidence Intervals Testing your decisions • Have you been making good or bad decisions? • The Excel file MultiRegression.xls lists the net results of 100 gambles, and tests whether those results were coming from good gambles (with positive expected value). • The test is based on the regression equation p=a+e p is your profit from a gamble, e is the uncertain, unpredictable, uncontrollable random outcome (like the draw of a card) with zero expectation a is the regression constant • Expected profit p equals coefficient “a” (since expected e = 0) • a > 0 means your gambles have positive expectation • a < 0 means your gambles have negative expectation BA 445 Lesson A.4 Uncertainty 21 Confidence Intervals Gamble Test Summary Output p=a+e The results estimate a = -.853 The 95% confidence interval for a is -1.966 to .258 Since the interval contains both positive and negative numbers, there is not enough data to determine whether or not those gambling results were coming from good gambles. BA 445 Lesson A.4 Uncertainty 22 Regression Analysis Regression Analysis BA 445 Lesson A.4 Uncertainty 23 Regression Analysis Overview Regression Analysis can test whether demand is more likely linear or log-linear, and can estimate which coefficient values are more likely. Those estimates then affect predictions and decisions. BA 445 Lesson A.4 Uncertainty 24 Regression Analysis Regression Analysis • In addition to constants, regression analysis can estimate coefficients of variables (correlation coefficients) • One use is for estimating or measuring demand functions. • Important statistics: Confidence Intervals and t-statistics. • Measures the significance of estimates R-square or Coefficient of Determination, and F-statistic. • Determines whether the model is better than no model. • Determines whether one model is better than another model. BA 445 Lesson A.4 Uncertainty 25 Regression Analysis Question: Passage of the 1983 Dairy Product Stabilization act lead to a tax on milk producers. The tax was used to advertise milk. However, the tax was later ruled unconstitutional, and so milk advertising decreased. To assess the likely impact on milk consumption, consider the following data on the weekly consumption of milk (in millions of gallons), weekly price per gallon, and weekly expenditures on milk advertising (in hundreds of dollars). http://faculty.pepperdine.edu/jburke2/ba445/PowerP1/MultiRegression.xlsx BA 445 Lesson A.4 Uncertainty 26 Regression Analysis Use Data Analysis in Excel to perform two regressions: • Linear Q = a + b P + c A + e • Log Linear ln(Q) = a + b ln(P) + c ln(A) + e Determine which model better fits the data. Suppose that the weekly price of milk is $3.10 per gallon, and weekly advertising falls 25 percent to $100 (in hundreds). Using the better model, estimate the weekly quantity of milk consumed after the court’s ruling. BA 445 Lesson A.4 Uncertainty 27 Regression Analysis Answer: The competing equations are: Linear Q = a + b P + c A + e Log Linear ln(Q) = a + b ln(P) + c ln(A) + e BA 445 Lesson A.4 Uncertainty 28 Regression Analysis Linear Regression Summary Output Q=a+bP+cA+e R2 = 0.5472 and Adj.R2 = 0.5379, where greater coefficients of determination indicate the data better fits the linear regression line F = 58.6092, where the greater that F-statistic, the better the data fits the linear regression line BA 445 Lesson A.4 Uncertainty 29 Regression Analysis Log-Linear Regression Summary Output ln(Q) = a + b ln(P) + c ln(A) + e R2 = 0.4014 and Adj.R2 = 0.3891, where greater coefficients of determination indicate the data better fits the linear regression line F = 32.5221, where the greater that F-statistic, the better the data fits the linear regression line BA 445 Lesson A.4 Uncertainty 30 Regression Analysis Conclusion: The linear model better fits the data, with higher values of all three statistics: R2, Adj.R2, and F. Under the linear model, at P = $3.10 and A = $100, estimated milk consumption is 2.029 million gallons per week : Q = 6.52 – 1.61(3.10) + .005(100) = 2.029. BA 445 Lesson A.4 Uncertainty 31 Review Questions Review Questions You should try to answer some of the review questions (see the online syllabus) before the next class. You will not turn in your answers, but students may request to discuss their answers to begin the next class. Your upcoming Exam 1 and cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams. BA 445 Lesson A.4 Uncertainty 32 BA 445 Managerial Economics End of Lesson A.4 BA 445 Lesson A.4 Uncertainty 33