problemset2_2024 (2)

.pdf

School

McGill University *

*We aren’t endorsed by this school

Course

447

Subject

Economics

Date

Feb 20, 2024

Type

pdf

Pages

3

Uploaded by MinisterLorisPerson443

Report
Problem Set 2 Economics of Information and Uncertainty ECON 447, Winter 2024 The solution is due on February 13 . Please upload your solution as a single pdf-file to the corresponding assignment on mycourses before the deadline. Late submissions will not be accepted. You can work in groups, but everyone has to hand in her/his own solution. Copied solutions and ”failed to submit” will receive 0% for this particular problem set. I will post a sample solution shortly after the submission due date. The TA will use the TA office hours on February 15 for a conference to discuss the solution. 1. (taken from Edoardo Gallo, Cambridge, Winter 2018) Suppose an individual has to pay 2 to enter a competition. The prize is 19 and the probability that he wins is 1/3. He is an expected utility maximizer with vNM utility function u where u ( x ) is the utility value that the individual attaches to having wealth level x . His current wealth is 10. Calculate (i) the certainty equivalent and (ii) the risk premium for each of the following cases: (a) u ( x ) = log ( x ), (b) u ( x ) = x 2 , and (c) u ( x ) = x . Will he enter the competition if u ( x ) = log ( x )? 2. A risk-lover. Suppose that there are two states of the world and that each state realizes with probability 1/2. A decision maker receives $ x 1 0 in state 1 and $ x 2 0 in state 2. The decision makers is an expected utility maximizer and he has vNM utility function v ( x ) = x 2 . (a) In the 2-states of the world diagram, draw the indifference curve of the decision maker through the lottery P = ( x 1 , x 2 ) = (8 , 4). (b) Determine CE ( P ) and R ( P ) and show them in the diagram. 1
(c) If the decision maker can choose exactly one lottery of all lotteries ( x 1 , x 2 ) that have expected outcome 6 (i.e. 1 / 2 x 1 + 1 / 2 x 2 = $6), which one does he choose? You can explain your answer referring to the diagram. 3. For each of the following vNM utility functions, determine the Arrow Pratt measure of absolute risk aversion, and whether the risk aversion is increasing, decreasing or constant in x . (a) Quadratic vNM utility function: v ( x ) = x αx 2 , α > 0 (b) Log utility function: v ( x ) = ln( x ) (c) Power utility function: v ( x ) = x 1 σ 1 σ for σ > 0 (d) Exponential utility function: v ( x ) = e α · x for α > 0 4. Degrees of risk aversion. (a) Consider two decision makers who both have expected utility pref- erences over the lotteries over the non-negative real line. Decision maker 1 has vNM utility function v 1 ( x ) = x 1 / 4 + 5 and decision maker 2 has v 2 ( x ) = x 1 / 2 . Is one of the decision makers more risk- averse than the other? How does your response change if instead v 1 ( x ) = x 1 / 4 + 5 x ? (b) (van Zandt, Exercise 5.5) A risk-averse expected utility decision maker has decreasing absolute risk aversion. Her certainty equiv- alent for a lottery that pays 0 and 800 with probabilities 1 / 3 and 2 / 3, respectively, is 500. Which does she prefer, to get 400 and 1200 with probabilities 1 / 3 and 2 / 3, respectively, or to get 900 for sure? Explain. 5. First order stochastic dominance. 2
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help