Practice Questions. a) Using Bayes Rule calculate the probability that the manager is high effort type.

Transcription

1 Practice Questions Assume you are the owner of a company based in USA with a division located in UK. You hired a manager to lead the UK office. You would like to assess the managers effort level. Assume there are two possible types of the manager: either always showing high effort or always showing low effort. Based on the previous interviews, you assign a priori probability of 0.6 for the manager to show high effort (H) and a priori probability of 0.4 of low effort (L). In any quarter, if he shows high effort, there is 2/3 probability that sales will be high and 1/3 probability that the sales will be low. Similary if he shows low effort, there is 1/3 probability that sales will be high and 2/3 probability that the sales will be low. For the first three quarters you observed two high sales quarters and then one low sale quarter. a) Using Bayes Rule calculate the probability that the manager is high effort type. b) Suppose you are using Rabin s mental model, with two urns (one urn for high effort type and one urn for low effort type). The urns are refreshed after every two quarters of data. Suppose further that in your mental model you have 3 balls in each urn with distributions of balls labeled high sales and low sales corresponding to the true probabilities. Given the three quarter observation of (High Sales, High Sales, Low Sales) what probability will you assign to manager being high effot type? c) Repeat part b) if the urns in the mental model are never refreshed.

2 2) One specific model of mental accounting (that we used in the Basketball ticket example in class) considers the utility of purchasing of a good/service as the sum of two terms: u! + v( p) This in effect segregates the joy of consumption from the pain of payment. u! is the positive utility of consumption of the good, v( p): negative utility due to the payment p Assume the following value function for assessing the disutility of payments: v(x) For example if you bought a pizza (with consumption utilility of u! pizza = 10) through paying $25, your utility from transaction will be: u! pizza + v( 25)=10-5 = 5 x Now assume, for dinner you went to a restaurant (dinner costs $50), while waiting for your table, you had a few drinks at the bar (cost of $10). You have two optios: A) Pay for your drinks at the bar and as a result have two payments for the night: one for the drinks at the bar ($10) and one for the meal ($50). B) Put the drinks on your dinner bill, so you have a single payment at the end of the night totaling $60. In either case you will enjoy two consumption utilities u! drinks + u! meal, the difference is whether you will have two or one disutility assocaited with the payments. Which option should you choose to maximize your utility from the night? Explain your reasoning in detail.

3 3) Suppose you manage a team of employees who make parts for the automative industry. You observed that some employees are not putting their best effort and as a result producing less parts per day. You decide to induce better performance in your team members by providing a system of paycuts for workers with poor performance. How might hedonic framing be used to make the system of penalties more effective? Specifically, choose one of the following and explain your reasoning in detail. Impose a paycut of $1000, every six months or Impose a paycut of $2000 at the end of the year. Assume a prospect value function exhibiting diminishing marginal disutility from losses. You may use the graph below if it helps you in your explanation.

4 4) Assume Tyler s utility function is given in the graph below. Consider Gamble A which gives $9 with 2/3 probability and $0 with 1/3 probability u(x) a) What is the expected value of Gamble A? x b) What is the expected utility of Gamble A? c) Does Tyler prefer to play the Gamble A or a sure payment equaling the expected value of Gamble A? Explain. d) What is the certainty equivalent of Gamble A? (i.e. what is the maximum amount that Tyler is willing to pay to play Gamble A).

5 5) Assume Jeri s consumption utility from watching movies on Netflix is given by: u c (x) =10 x 2 +16x where x is the number of the movies watched in a month. Assume Netflix is charging a fixed monhtly fee of p 0 = $10 after which subscribers can watch unlimited number of movies. Assume Jeri s transaction utility is given by: u t (x) = (0.4x 6)p a) How many movies will Jeri watch in a month if her behavior is described by rational choice theory where she maximizes her consumption utility? b) How many movies will Jeri watch if she is maximizing the sum of her consumption utility and transaction utility?

6 6) Assume you asked subjects in your experiment to rank Gamble A vs B and Gamble C vs D Gamble A: You will win $1 million for sure Gamble B: You will win with 5% probability $4 million, with 94% probability $1million and with 1% probability $0. Gamble C: You will win with 6% probability $1 million, with 94% probability $0. Gamble D: You will win with 5% probability $4 million, with 95% probability $0 You found out that majority of the subjects rank Gamble A over Gamble B while ranking Gamble D over Gamble C. a. Show that these rankings are not consistent with Expected Utility Theory b. Show that these rankings are not consistent with the Sure Thing Principle. You might want fill and use the following table in your reasoning. Feel free to draw your own table if you prefer. Gamble A Gamble B Gamble C Gamble D 94 Black Balls 5 Red Balls 1 Yellow Ball