The Independence Axiom of expected utility states that the preference relation is such that: L a...
The Independence Axiom of expected utility states that the preference relation is such that: L a L b ⇐⇒ αLa + (1 − α)L c αLb + (1 − α)L c . Note that ⇐⇒ means “is equivalent to.” What does is mean in the language of economics and finance?
Homework Answers
The given sign shows a two way, equal relationship between the LHS and RHS.
In Economics language, it means there exists a causal relationship between the two. The LHS causes and leads to RHS and the RHS causes and lead to LHS.
In finance language, it means the two equations are equal And give same results.
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The Independence Axiom of expected utility states that the
preference relation is such that: L a...
12. The observed frequencies and calculated expected frequencles in parenthesis) of 200 students on their preference...
12. The observed frequencies and calculated expected frequencles in parenthesis) of 200 students on their preference for a university health plan is shown Plan A 40(36) 20(24) Plan B 50(54) 40(36) No Preference 0(30) 20(20) Female Male Expected frequencies are in parenthesis. You are to do test of independence with the null hypothesis, Ho: The plans A, B, and no preference are independence of gender (male and female). a) Find the degree of freedom. 2 b) Find the critical value...
Question 1 In a chi -square test of independence , the null hypothesis states that-----------. a....
Question 1 In a chi -square test of independence , the null hypothesis states that-----------. a. the two variables of interest are related in the population. b. the column frequencies equal the row frequencies c. the sum of the and the column frequencies equal the total frequency d. the two variables of interest are unrelated in the population Question 2 A survey asked people whether they identified as a morning person, night person, or had no preference. a. 270 replied...
7. The Axiom of Distribution of Probabilities Across Alternatives (aka Frame Invariance) prevents what pathology of...
7. The Axiom of Distribution of Probabilities Across Alternatives (aka Frame Invariance) prevents what pathology of decision making? A. Inability to make choices under risk B. Neglecting base rates C. Manipulation by framing effects D. Obsession with infinitely improbable alternatives E. Becoming a "money pump" The following applies to questions 8-9 below. Consider the following sequential game (note Player 1's payoffs are in the upper right cells): 5 3 0 -5 9. What dominant strategies, if any, does Player 2...
1. Assume a consumer has as preference relation represented by u(c1, 2) for g E (0,...
1. Assume a consumer has as preference relation represented by u(c1, 2) for g E (0, 1) and oo > n > 2, with x E C = Ri. Answer thefollow (x1+x2)" ing: a. Show the preference relation that this utility function induces "upper b. Show the preference relation these preferences represent are strictly C. Give another utility function that generates exactly the same behavior as level sets that are convexif U(x) is Convex for any xeX monotonic. this one....
2. Assume a consumer has as preference relation represented by u(x1, x2) = axi + bx2...
2. Assume a consumer has as preference relation represented by u(x1, x2) = axi + bx2 with x E C = R4, and a, b > 0. Answer the following: a. Show the preference relation this consumer is convex and strictly monotonic show preferences are not strictly convex for this consumer. b. Graph the indifference curves for this consumer. Now, solve for an explicit expression for the indiffence curve (i.e., x (x1; ū) i constructed in class for an indifference...
1. Suppose that I give you the following utility function There are two potential outcomes. With ...
1. Suppose that I give you the following utility function There are two potential outcomes. With probability 1/2 there is good news and Yo-9. If there is bad news then YB = 3. a) What is the expected value of Y? b) What is the expected utility of the consumer with the utility function above? c) Is expected utility greater than, equal to or less than the expected value? Does this mean that the consumer is risk averse, risk neutral...
Joe's wealth is $100 and he maximizes his expected utility. Joe’s utility as a function of...
Joe's wealth is $100 and he maximizes his expected utility. Joe’s utility as a function of his wealth is U(W) = W1/2. Joe might oversleep his economics exam. He figures there is only a 1 in 10 5 chance that he will, but if he does, it will cost him $100 in fees to the University to take an exam later. Joe's neighbor, Mary, never oversleeps. She offers to wake Joe one hour before the test, but he must pay...
Problem 3. Carol's risk preference is represented by the following expected utility formula: T, CI π...
Problem 3. Carol's risk preference is represented by the following expected utility formula: T, CI π , C2 1. Suppose Carol is indifferent between the following two options: the first option A returns $100 with probabilityand $49 with probability and the second option B returns $X for sure. Determine X. Is X smaller than the expected return of A? 2. Suppose Carol's wealth is 100. Suppose she will loose all her wealth with probability 0.01. If she wants to insure...
ating o as g 4. Suppose that the representative consumer's preference change, in that his or...
ating o as g 4. Suppose that the representative consumer's preference change, in that his or her rate of substitution of leisure for consumption increases for any quantities of consumpon and leisure a. Explain what this change in preferences means in more intuitive language b. What effects does this have on the equilibrium real wage, hours worked, outp consumption? c. Do you think that preference shifts like this might explain why economies experience ot, with reference to the recessions (periods...
3. A taxpayer has utility function U(x, L) = x ^1/2 − L where L is...
3. A taxpayer has utility function U(x, L) = x ^1/2 − L where L is hours of labour supply and x is consumption. The taxpayer earns a wage of $4 per hour worked (which is fixed throughout the analysis). (a) Suppose that the government imposes a proportional (percentage) tax at rate τ on labour income, so that the taxpayer’s budget constraint is x = (1 − τ )4L. Solve for the optimal labour supply (L) and consumption (x) as...
12. The observed frequencies and calculated expected frequencles in parenthesis) of 200 students on their preference for a university health plan is shown Plan A 40(36) 20(24) Plan B 50(54) 40(36) No Preference 0(30) 20(20) Female Male Expected frequencies are in parenthesis. You are to do test of independence with the null hypothesis, Ho: The plans A, B, and no preference are independence of gender (male and female). a) Find the degree of freedom. 2 b) Find the critical value...
7. The Axiom of Distribution of Probabilities Across Alternatives (aka Frame Invariance) prevents what pathology of decision making? A. Inability to make choices under risk B. Neglecting base rates C. Manipulation by framing effects D. Obsession with infinitely improbable alternatives E. Becoming a "money pump" The following applies to questions 8-9 below. Consider the following sequential game (note Player 1's payoffs are in the upper right cells): 5 3 0 -5 9. What dominant strategies, if any, does Player 2...
1. Assume a consumer has as preference relation represented by u(c1, 2) for g E (0, 1) and oo > n > 2, with x E C = Ri. Answer thefollow (x1+x2)" ing: a. Show the preference relation that this utility function induces "upper b. Show the preference relation these preferences represent are strictly C. Give another utility function that generates exactly the same behavior as level sets that are convexif U(x) is Convex for any xeX monotonic. this one....
2. Assume a consumer has as preference relation represented by u(x1, x2) = axi + bx2 with x E C = R4, and a, b > 0. Answer the following: a. Show the preference relation this consumer is convex and strictly monotonic show preferences are not strictly convex for this consumer. b. Graph the indifference curves for this consumer. Now, solve for an explicit expression for the indiffence curve (i.e., x (x1; ū) i constructed in class for an indifference...
1. Suppose that I give you the following utility function There are two potential outcomes. With probability 1/2 there is good news and Yo-9. If there is bad news then YB = 3. a) What is the expected value of Y? b) What is the expected utility of the consumer with the utility function above? c) Is expected utility greater than, equal to or less than the expected value? Does this mean that the consumer is risk averse, risk neutral...
Problem 3. Carol's risk preference is represented by the following expected utility formula: T, CI π , C2 1. Suppose Carol is indifferent between the following two options: the first option A returns $100 with probabilityand $49 with probability and the second option B returns $X for sure. Determine X. Is X smaller than the expected return of A? 2. Suppose Carol's wealth is 100. Suppose she will loose all her wealth with probability 0.01. If she wants to insure...
ating o as g 4. Suppose that the representative consumer's preference change, in that his or her rate of substitution of leisure for consumption increases for any quantities of consumpon and leisure a. Explain what this change in preferences means in more intuitive language b. What effects does this have on the equilibrium real wage, hours worked, outp consumption? c. Do you think that preference shifts like this might explain why economies experience ot, with reference to the recessions (periods...
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