ARE 115A Problem Set 4 SQ24

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Name 1: Student ID 1: Name 2: Student ID 2: Name 3: Student ID 3: ARE/ECN 115A Spring 202 4 Problem Set 4. RISK, RISK TAKING AND INSURANCE Due: Thursday , June 6 th at 11:59 PM Instructions During this problem set, you will apply concepts of risk and risk preferences to explore how risk affects peoples’ choice of economic activities and their income. You will also explore how the presence of insurance – both formal insurance and informal risk sharing arrangements – can change peoples’ choice of activities and welfare. Finally, you will explore how asymmetric information can adversely affect the performance of insurance markets. 1. By writing your name above and submitting the Problem Set, you are agreeing to adhere to the Copyright statement and the Code of Academic conduct as highlighted on the course syllabus. 2. Download this PDF file to your computer and open it using Acrobat Reader (the free version of the software). Trying to fill it in through your Internet browser or with another software may cause some features of this document not to work. 3. For this Problem Set, you are not required to submit an Excel file. 4. You may work individually or in groups of up to 3 members. You can use the Discussion Board page on Canvas to find group members. 5. Your group will turn in a single PDF of the problem set on Gradescope. Identify the members in your group on both this pdf and on Gradescope at the time of submission. That is, when you upload the assignment, you must identify all members of your group; otherwise, only the individual who uploads the assignment will receive credit. You must also write the names and ID numbers of all group members on this pdf. A 5-point penalty will be applied per name that is not indicated on the pdf submission. 6. To answer each question, write your responses in the designated boxes. DO NOT change the size of the boxes. 7. Start your Problem Set early. Late Problem Sets will not be accepted.

Question 1: Risk Preferences A lvaro and Estela live in the village of Los Reyes in the state of Michoacan, Mexico 1 . They each have zero wealth, so their consumption is equal to the income they earn from their economic activity. Each of them must choose one (and only one) of the following three activities: • Activity 1: Full time farming. Strawberry farming is risky because of a combination of weather and pests. Under full time farming, the farmer works 7 days per week on their farm. There is a 67 % probability of having a GOOD harvest and a 33 % chan c e of having a BAD harvest. If the harvest is GOOD, the farmer earns an income of $200. If the harvest is BAD, the farmer earns an income of only $50. • Activity 2: Full time construction work. This activity has no risk. An individual who decides to work full time in construction earns $1 44 with certainty. • Activity 3: Part-time farming. In this third activity, the farmer works during the week as a strawberry farmer and works in construction during the weekend. Since he is not able to work full time on the farm, the probability of having a GOOD harvest and earning $200 drops to 45 %, and the probability of having a BAD harvest and earning only $50 increases to 55 %. The individual also earns $ 25 with certainty as a construction worker (the person earns this $ 25 from construction in addition to his farm income under both a GOOD and BAD harvest). (a) What is the expected value of consumption for each activity? Report your answers in Table 1 below. Table 1 Activity Expected Value of Consumption: E(C) 1: Full time farming 2: Full time construction work 3: Part time farming 1 Mexico has become one of the leading exporters of strawberries in the past 15 years. Michoacan is the most important strawberry producing region in Mexico.

We also know that A lavaro and Estela view risk differently, and that is why they have different utility functions (listed below). A lvaro : Estela : ?(𝐶) = 2 𝐶 ?(𝐶) = √𝐶 (b) Using those utility function s , compute the certainty equivalent (CE), the risk premium (RP) and expected utility (EU) associated with each of the three activities for each individual. Report your answers in Table 2 below. Report precise final results, which means that you should use all decimals of your intermediate results to get your final answer. Round your final answers to TWO decimal places. Table 2 Individual Activity EU CE RP A lvaro 1: Full time farming A lvaro 2: Full time construction work A lvaro 3: Part time farming Estela 1: Full time farming Estela 2: Full time construction work Estela 3: Part time farming

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(c) Which activity will be chosen by each individual? If an individual is indifferent between two activities (say A or B), write "Activity A OR Activity B" Table 3 Individual Choice of Activity A lvaro Estela (d) Which type of risk preferences describe each individual? (Risk Neutral, Risk Averse, or Risk Loving?) Table 4 Individual Risk Preferences A lvaro Estela Question 2: Conventional Insurance Continue to use the same context from question 1, but now consider conventional insurance. Juana is an insurance agent who offers conventional crop insurance contracts only to full time farmers. She is not interested in offering insurance to part time farmers. The contracts are straightforward. At the beginning of the season, farmers pay a premium of $ 41.25 . At the end of the season, Juana pays farmers an indemnity payment of $1 25 if the farmer had a BAD harvest. If the farmer had a GOOD harvest, Juana doesn’t pay the farmer anything. For parts a - d, assume the world is described by symmetric information. In other words, Juana can wri te and enforce a contract that requires the farmer to choose full time farming. (a) What is Juana ’s expected profit from this contract? ( Juana ’s profit is just the premium she collects from the farmer minus the indemnity payment she makes to the farmer).

(b) What is the expected consumption for an individual who chooses full-time farming with Juana ’s insurance contract (Activity 4)? (c) What is the expected utility associated with full-time farming with an insurance contract (Activity 4) for A lvaro and Estela ? Report TWO decimal places. Table 5 (d) Now assume that each individual can choose between the four available activities: Full Time Farming without Insurance (Activity 1 above), Full time construction work (Activity 2 above), Part Time Farming without insurance (Activity 3 above) and Full Time Farming with Juana ’s insurance contract (Activity 4). Which activity will each individual choose? If an individual is indifferent between two activities (say A or B), write "Activity A OR Activity B Table 6 Individual Choice of Activity A lvaro Estela Individual Expected Utility from Activity 4 A lvaro Estela

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