Last Name: _______ __________First Name: ____ ________ Student ID: ________
Last Name: ____________________First Name: ___________________ Student ID: ________________
TA (circle one): OSCAR CRISTINA ARE/ECN 115A JAVIER YAXI
Spring 2017 Problem Set #4: RISK TAKING, INSURANCE MARKETS and IMPACT EVALUATION
(Due in class June 6, 2017) Cristina, Oscar and Javier are maize farmers in the village of Girasol. They each have zero wealth (W=0), 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 with hybrid maize: Hybrid maize has two important characteristics. First, it is labor
intensive. To get the full benefit of hybrid maize, a farmer should work full time (7 days per week) on their farm.
Second, hybrid maize is risky, because it is vulnerable to a combination of weather and pests. If a farmer works full
time, she has a 50% probability of having a GOOD harvest and earning income of $280 and a 50% chance of having a
BAD harvest and earning only $40. Activity 2: Full time farming with traditional maize. Traditional maize varieties are also labor intensive, however
traditional maize is very well adapted to local weather conditions and thus has no risk. If a farmer works full time she
will earns $140 with certainty. Activity 3: Part-time farming with hybrid maize: In this third activity, the farmer plants hybrid maize and works
Monday through Thursday on her farm managing the hybrid maize, and she works Friday through Sunday as a
construction worker in a nearby city. Since she is not able to work full-time on the farm, it is more likely that she
suffers damages from pests or bad weather. Specifically, the probability of having a GOOD maize harvest and
earning $280 drops to 25%, while the probability of having a BAD harvest and earning only $40 increases to 75%.
The individual also earns $40 with certainty as a construction worker (i.e., she earns $40 in addition to her farm
income under both a GOOD and a BAD harvest). 1. What is the expected value of consumption for each activity (3 points)?
Activity 1:
Activity 2:
Activity 3:
2. Cristina, Oscar and Javier view risk differently. This is reflected in the differences in their utility functions, which are
listed below. Using those utility functions, 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 1
below (9 points). Cristina: U ( C )=2C Oscar: U ( C )=40 C−0.05 C2 Javier: 2
U ( C )=0.1C 1 Table 1. Certainty Equivalent, Risk Premium and Expected Utility for 3 Activities
Activity 1
Activity 2 Activity 3 EU Cristina
CE Cristina
RP Cristina
EU Oscar
CE Oscar
RP Oscar
EU Javier
CE Javier
RP Javier
3. Which activity will be chosen by each individual (3 points)?
Cristina chooses:
Oscar chooses:
Javier chooses:
4. Which type of risk preferences describe each individual (3 points)? (Risk Neutral, Risk Averse, or Risk Loving?)
Cristina is:
Oscar is:
Javier is:
5. Assume that the three farmers start with the same level of wealth. In this environment would you expect wealth
inequality to remain the same, increase or decrease over time? Explain your answer (2 points).
The government is interested in supporting higher adoption rates of hybrid maize and asks Yaxi, the CEO of “Take a
Chen-ce on Me” Insurance Company to offer crop insurance to hybrid maize farmers. Yaxi conducts a market analysis and
decides to offer conventional crop insurance contracts to full time hybrid maize farmers (Activity 1). She is not interested
in offering insurance to part-time hybrid maize farmers. The contracts are straightforward. At the beginning of the
season, farmers pay a premium of $120. At the end of the season, Yaxi pays farmers an indemnity payment of $240 if the
farmer had a BAD harvest. If the farmer had a GOOD harvest, Yaxi doesn’t pay the farmer anything. For questions 6-10,
assume that Yaxi has perfect information about the farmer’s activity choice. In other words, if a farmer buys her
insurance, Yaxi is able to enforce a contract that requires the farmer to choose full-time hybrid maize farming.
6. What is the expected value of Yaxi’s profit from an insurance contract? (Yaxi’s profit is just the premium she collects
from the farmer minus the indemnity payment she makes to the farmer) (2 points).
7. What is the expected value of consumption for an individual who chooses full-time hybrid maize farming (Activity 1)
with Yaxi’s insurance contract (3 points)?
8. What is the expected utility associated with full-time hybrid maize farming with an insurance contract for each
individual (3 points)?
9. Now assume that each individual can choose between the four available activities: Activity 1 with Insurance, Activity
1 without Insurance, Activity 2, and Activity 3. Which activity will each individual choose (3 points)? Cristina Oscar Javier
10. In this environment of perfect information based insurance, would you expect wealth inequality to remain the same,
increase or decrease over time? Explain your answer. Compare your answer here to your answer to question 5 (3
points).
2 Now let’s make a more realistic assumption about information. Assume that Yaxi can observe whether a farmer plants
hybrid maize, but she cannot observe how much time the farmer spends working on her fields. This means that a farmer
who plants hybrid maize may purchase the insurance contract and then choose to either farm full time or farm part time.
An individual who plants traditional maize cannot purchase an insurance contract.
11. Which activity will be chosen by each individual now (3 points)? (Activity 1 with Insurance, Activity 1 without
Insurance, Activity 2, Activity 3 with Insurance, or Activity 3 without Insurance)
12. What is Yaxi expected profit? Will she be willing to offer the insurance contract (3 points)? Why or why not? (what
type of problem does Yaxi face)?
Maize holds a special place in the lives of many Mozambicans.
is concerning how low agricultural yields are for maize producers in
prone Manica province where a lot of farmers practice subsistence
address this problem, a project to increase agricultural production and
productivity was designed by a group of UC Davis students. The
consisted of providing a new variety of a drought tolerant maize seed to
sample of farmers located in Manica, which was specifically targeted
drought prone. However, it
the droughtfarming. To
raise
farm
project
a
random
because it is To evaluate the impact of this program, the students want to estimate
impact of the drought tolerant maize variety on agricultural yields
First, they drew a random sample of 1,000 households that received the
tolerant maize seed in Manica to serve as the treated group (D=1). At
time, they drew another random sample of 1,000 households in the
Sofala province who were not part of the program to serve as the
(D=0). Via surveys, the students observed Y for both groups in tons per the
causal
denoted
Y.
drought
the
same
neighboring
control group
hectare. The students used these measures of Y to estimate the Average
Effect of the program by subtracting the average yield of the 1,000
in Sofala from the average yield of the 1,000 households in Manica. Treatment
households 13. At this point, the students reach out to you to ask for your guidance. Help the team understand Selection Bias by:
a. Providing an equation that defines Selection Bias using notation from the Potential Outcome Framework that
we developed in class (4 points).
b. Writing a sentence that defines the two main terms in your equation (4 points).
c. Giving a careful and clear, but brief explanation of when selection bias would exist (i.e., when it would not be
equal to zero) (4 points).
14. Without any further information, do you expect selection bias in the students’ estimate of the Average Treatment
Effect to be zero, negative or positive? Explain your answer (4 points).
For the rest of this question, use the table below. These average yields measured in tons of maize per hectare presume that
you know all the counterfactual values of this outcome variable (e.g., you know E[Y 1 i∨Di=0 ] , which is what the average yield for drought tolerant maize would have been for those who did not adopt drought tolerant maize)
Table 1
3 Di=0 D i=1 E[Y 0 i∨D i ] 5.2 1.4 E[Y 1 i∨Di ] 5.5 2.5 15. Which of the numbers in the table above can be measured by the researchers based on their survey data (2 points)?
16. Based on this table, what is the students’ estimate of the Average Treatment Effect (4 points)?
17. How large is the selection bias (provide a number) (4 points)?
18. What is the true causal impact of the program on Y? (i.e., what is the true Average Treatment Effect?) (4 points) 4

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