Problem 3: (Application of the prospect theory probability weighting function): A famous implication of prospect theory is a preference for positively skewed prospects and an aversion to negatively skewed prospects. For example, Tversky and Kahneman (1992) found that people frequently preferred:
1) Gaining $95 with certainty over a 95% chance of gaining $100 and a 5% chance of gaining $0.
2) Losing $5 with certainty over a 5% chance of losing $100 and a 95% chance of losing $0.
3) A 5% chance of gaining $100 and a 95% chance of gaining $0 over gaining $5 with certainty
4) A 95% chance of losing $100 and a 5% chance of losing $0 over losing $95 with certainty.
These prospects can be represented as (?, ?; 0,1 − ?) where ? = 100 or ? = −100 and either ? = 0.05 or ? = 0.95. Using the probability weight w(?) = (1 − ?)? + ??, with 0 ≤ ? ≤ 1, and 0 ≤ ? ≤ 1 for the best outcome of a lottery, and the weight ?(?) = (1 − ?)(1 − ?) + ?? for the worst outcome of a lottery, and setting ? = 0.80, ? = 0.10, show that prospect theory predicts all four choices simultaneously. Use the weight ?(?) = 1 for a lottery that offers a single outcome with probability ? = 1. Assume a simple linear value function of the form ?(?) = ?.
Now, we have
1) V(95) = 95w(p) = 95(1) = 95; V(100,0.95; 0,0.05) = 100(0.02+0.8(0.95)) = 78.
Thus, 95 > 78 or Gaining $95 with certainty is preferred over a 95% chance of gaining $100 and a 5% chance of gaining $0.
2) V(-5) = -5; V(-100,0.05;0,0.95) = -100(0.02+0.8(0.05)) = -6.
Thus, -5 > -6 or Losing $5 with certainty is preferred over a 5% chance of losing $100 and a 95% chance of losing $0.
3) V(5) = 5; V(100,0.05;0,0.95) = 100(0.02+0.8(0.05)) = 6.
Thus 6 > 5 or A 5% chance of gaining $100 and a 95% chance of gaining $0 is preferred over gaining $5 with certainty.
4) V(-95) = -95; V(-100,0.95;0,0.05) = -100(0.02+0.8(0.95)) = -78.
Thus -78 > -95 or A 95% chance of losing $100 and a 5% chance of losing $0 is preferred over losing $95 with certainty.
Problem 3: (Application of the prospect theory probability weighting function): A famous implication of prospect theory...
Problem 4: (Prospect theory explanation for the Common Ratio Effect): A famous experimental violation of EU is the finding by Kahneman and Tversky that most people preferred $3000 with certainty over an 80% chance of $4000, but preferred a 20% chance of $4000 over a 25% chance of $3000. Using the probability weight w(?) = (1 − ?)? + ?? for the probability of the best outcome of a lottery and the weight w(?) = (1 − ?)(1 − ?)...
1. Why might some prefer a prix fixe (fixed price) dinner costing about the same as an à la carte one (where you pay individually for each item)? (Assume the food is identical.) 2. Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has a 40% chance of wealth of $100,000 and...
1) Random variable x has a uniform distribution defined by the probability density function below. Determine the probability that x has a value of at least 220. f(x) = 1/100 for values of x between 200 and 300, and 0 everywhere else A) 0.65 B) 0.80 C) 0.75 D) 0.60 2) The method of sampling that ensures that every subgroup of interest in a particular study is represented in the sample is called: A) systematic random sampling B)...
Can someone do 28, 32, 40, and 44
198 CHAPTER 3 Probability c. Use the results of parts a and b to find ed value of Cash 4 admission to college); the Law School Admissions Test, or LSAT; and the Graduate Record Exam, GRE (used for admission to graduate school). 32. New York's "Pick 10" is a 10/80 lottery Sometimes, these maltiple-choice tests discourage guessing by subtracting points for wrong answers In particular, a correct answer will be worth +1...
The following ANOVA model is for a multiple regression model
with two independent variables:
Degrees
of
Sum
of
Mean
Source
Freedom
Squares
Squares
F
Regression
2
60
Error
18
120
Total
20
180
Determine the Regression Mean Square (MSR):
Determine the Mean Square Error (MSE):
Compute the overall Fstat test statistic.
Is the Fstat significant at the 0.05 level?
A linear regression was run on auto sales relative to consumer
income. The Regression Sum of Squares (SSR) was 360 and...
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Budgetary Policy and Economic Growth Errol D'Souza The share of capital expenditures in government expenditures has been slipping and the tax reforms have not yet improved the income...