Subsidy Policies with Learning from Stochastic Experiences Jing Cai Alain de Janvry Elisabeth ...

43 Pages·2015·1.48 MB·English

Subsidy Policies with Learning from Stochastic Experiences∗
Jing Cai †
Alain de Janvry ‡ Elisabeth Sadoulet§
December 2, 2015
Abstract
Manyproductsthatareprivatelybeneficialtopoorpeoplehaveahighpriceelasticityofdemand
and ultimately zero uptake at market prices. This has justified the provision of extensive subsidies
to induce uptake and learning, expectedly boosting future demand. When the outcome of using the
product is stochastic, learning takes specific forms that condition the optimum subsidy scheme to
achieve a set desired level of uptake. We use data from a two-year field experiment in rural China
to define the optimum subsidy scheme for a new weather insurance product for rice producers.
We estimate both the reduced form channels of causation of subsidies on uptake, and a structural
model of learning from stochastic experiences that we use for policy simulation. Results show that
the optimum current subsidy depends on past subsidies and payout levels, implying that subsidies
should vary locally year-to-year and may need continuous state intervention.
Keywords: Subsidy, Insurance, Take-up, Stochastic Learning
JEL Classification Numbers: D12, D83, H20, G22, O12, Q12
∗We thank Michael Anderson, Frederico Finan, David Levine, Ethan Ligon, Jeremy Magruder, Craig
Mcintosh, and Edward Miguel for their helpful comments and suggestions. We also thank participants at
numerousseminarsandconferencesfortheirhelpfulcomments. WearegratefultotheofficialsofthePeople’s
InsuranceCompanyofChinafortheirclosecollaborationatallstagesoftheproject. Financialsupportfrom
the International Initiative for Impact Evaluation (3ie) and the ILO’s Microinsurance Innovation Facility is
greatly appreciated. All errors are our own.
†Corresponding author: Department of Economics, University of Michigan, 611 Tappan Street, 365A
Lorch Hall, Ann Arbor, MI 48109-1220 (e-mail: [email protected])
‡Department of Agricultural and Resource Economics, University of California, Berkeley, CA 94720 (e-
mail: [email protected])
§Department of Agricultural and Resource Economics, University of California, Berkeley, CA 94720 (e-
mail: [email protected])
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1 Introduction
To subsidize or not to subsidize is one of the most controversial issues in development policy,
and what is done can be highly consequential. In general, governments and donors have been
reticent to subsidize for fear of inducing perverse behavior that will reproduce and possibly
increase the need for future subsidies. Undesirable behavioral responses include increased
preference for leisure (Maestas et al. (2013)), entitlement effects, and crowding out effects
(Cutler and Gruber (1996)). At the same time, because of learning and economies of scale,
there are particular development objectives that could not be achieved without subsidies. A
recurrentthemehasthusbeenhowtodesign’smart’subsidiesthatcanfulfilltheirimmediate
purpose of enhancing uptake while offering an exit option when demand objectives have
been met and not distorting market incentives. This has applied prominently to issues
ranging from the adoption of privately or socially beneficial technological and institutional
innovations, the promotion of export-oriented industrialization, and achieving national food
security objectives. Subsidies have been extensively applied to the adoption of privately
beneficial products and services under-used by the poor such as vaccination, insecticide-
treated bednets, and water filters (Cohen and Dupas (2010)).
Use of subsidies has also been common to promote the adoption of financial products to
reduce exposure to uninsured weather risks. These risks are known to be a major source
of welfare losses for farmers and of distorted behaviors in resource allocation (Rosenzweig
and Binswanger (1993), Dercon and Christiaensen (2011)). To confront this situation, many
governments have introduced comprehensive financial strategies for disaster response that
include prominently the transfer of risk through index-based insurance products (Cummins
and Mahul (2009)). Index insurance has been selected over standard insurance because it
avoids the problems of adverse selection and moral hazard and sharply reduces transaction
costs in implementation (Chantarat et al. (2013)). Because such financial products are
typically hard for farmers to understand and have had a notably low spontaneous take-up,
governments have been willing to subsidize them.1 But subsidies can be enormously costly,
and governments and donors have been seeking to design subsidy schemes that can achieve
a desired coverage at a minimum cost and could eventually be phased out once experience
with the product has established its value.
Subsidies can induce immediate take-up if demand for the insurance product is price
elastic. Randomized control trials in Ghana (Karlan et al. (2014)) and India (Mobarak and
1ForexampleinMexico,CADENAprovidesindex-baseddroughtinsurancetosome2millionsmallholder
farmers at a cost fully assumed by the state and federal governments. In India, the Weather Based Crop
Insurance Scheme covers 9.3 million farmers with an index-based scheme. Insurance purchase is compulsory
for farmers that borrow from financial institutions. For food crops, cost to farmers is less than 2% of
the commercial premium (Clarke et al. (2012)). In Mongolia, an index-based insurance program covers
catastrophic losses of animals at full government cost (Mahul and Skees (2007)). In general, index-based
weather insurance has not reached scale and sustainability without extensive subsidies.
2
Rosenzweig (2014)) show that subsidies can raise uptake from 10-20% of farmers at market
price to 60-70% with a 75% subsidy. If take-up can in turn induce learning, future subsidies
can expectedly be reduced and potentially eliminated. However, learning about the value of
an insurance product is a stochastic process. Holding the insurance product has no learning
value per se. Learning the benefits of insurance only occurs when an insured shock triggers a
payout to oneself (direct learning) or to someone in your own social network (social learning,
see Foster and Rosenzweig (1995), and Conley and Udry (2010)). In studying the dynamics
of demand for index insurance, Karlan et al. (2014) find that Ghanean farmers demand for
insurance in subsequent years is strongly influenced by having directly received a payout or
having observed payouts paid to farmers in their own social networks. This dynamic learning
process is quite complex. It typically involves a recency bias, with overweighting of recent
climatic events. There is also a discouragement effect, with declining demand over time
when insurance premiums have been paid and no payouts were made as the weather was
good. In India, Cole et al. (2014) find that observing payouts in the village is as convincing
in inducing demand in the subsequent season as receiving a payout oneself. There is erosion
of this effect over time, with declining demand as no shocks occur. They find that erosion is
less when payouts were to one self than when they were to others.
In this paper, we study the impact of subsidies and stochastic payouts on demand for a
new weather insurance product for rice farmers in China. Following the framework of Sutton
and Barto (1998), we construct a model of learning from stochastic experiences in which
individuals update their valuation of the insurance product based on their past valuation of
the product and their prediction error relative to the recent realization. The model includes
three channels through which learning operates: (1) A direct learning effect from own payout
experience, with an expected positive effect if there has been an insured shock and a payout
has been received, and a negative effect if a premium has been paid and either no shock
occurred or a shock occurred without a corresponding payout, creating in the latter case a
discouragement effect. (2) A social learning effect from network payout experiences, which
follows the same process of positive and negative effects in relation to stochastic payouts.
The extent of network learning depends on the scope of take-up in one’s own social network.
And (3), a habit forming effect, with past use of the product influencing current demand.
These direct and social learning effects from stochastic experiences are in turn affected by
the provision of subsidies in three particular ways. (1) A scope effect whereby subsidies
enhance uptake and hence the opportunity to witness payouts. (2) An attention effect given
to information generated by payout experiences, which increases with the price paid for the
insurance, and is hence undermined by subsidies. And (3), a price anchoring effect, with
past prices affecting current willingness to pay for the product, and hence past subsidies
potentially discouraging current demand (Ariely et al. (2003)).
Using this theoretical framework, we designed a two-year randomized field experiment
that included 134 villages with around 3,500 households in rural China. In the first year,
we randomized subsidy policies at the village level - offering either partial subsidy of 70%
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of the actuarially fair price or full subsidy. In the second year, we randomly assigned eight
prices with subsidies ranging from 30% to 90% at the household level, with everything else
remaining the same in the contract.
Inareducedformestimation,weshowthatsecondyeardemandamonghouseholdshaving
received full subsidy the first year is higher but not differentially price elastic compared to
households with partial subsidy. We then identify the channels of causation described above
between subsidy policies and subsequent demand.
We find that receiving payouts has a positive effect on second year demand, and make
demand less price elastic. The positive effect of the payout is stronger when the households
had to pay for the insurance rather than receiving it for free, giving evidence of an atten-
tion effect. Symmetrically, the reduction in demand when there was no payout is stronger
when households had to pay for the insurance, showing evidence of a discouragement effect.
Observing friends receiving payouts improves second year take-up for households who were
not insured the first year, but there’s no such effect for households who had purchased the
insurance in the first year, regardless of whether they received payout by themselves or not.
For those that receive the insurance for free we see a mild effect of friends’ payout experience
if they did not receive a payout themselves. To explain why the learning effect is smaller
under the full subsidy policy, we show that people paid less attention to the payout informa-
tion if they received the insurance for free. Restricting the sample to households who were
willing to purchase the insurance at a 70% subsidy in the first year and are facing higher
subsidies in the second year, we estimate whether people with partial subsidy policy in the
first year were more likely to buy insurance in the second year, and do not find any price
anchoring effect. Finally, to study the habit formation effect, we estimate the impact of
first-year take-up on second-year purchase, using the randomized subsidy policy and default
options as instrumental variables for first-year take-up decisions. We find that, holding the
insurance does not influence either the level or the slope of the demand curve in the following
year. This means that simply enlarging the coverage rate is not enough to secure persistence.
Reduced form results help us validate the empirical relevance of the channels at work
in the structural model of learning from stochastic experiences. We estimate the structural
model with the channels through which learning from stochastic events occurs using Max-
imum Likelihood. We then use the estimated structural model for policy simulation. In
line with the Chinese government, the objective of the subsidy policy is to achieve a desired
level of uptake that will shelter public budgets from post-disaster relief operations. Current
subsidies can be reduced all the more the lower the last year price and the higher the last
year payout. Because payouts are random, inducing both positive learning when they occur
and discouragement effects when they do not, subsidies need to be continuously adjusted to
achieve the desired take-up rate at the minimum cost. We provide a simple policy rule that
the government can use to determine the optimum level of subsidy in a particular location
and time to achieve the desired level of uptake.
The use of subsidies to induce learning in repeated purchase goods has been studied for a
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number of products where learning is non-stochastic. For example, Dupas (2014) finds that
for insecticide-treated bednets, a one-time subsidy has a positive effect on take-up one year
later, mainly driven by a large positive learning effect. Fischer et al. (2014) examine the
subsidy policy tradeoff between learning and anchoring effects based on an experiment with
three health products with different scopes for learning. They find that positive learning can
offset the price anchoring effect in long-term adoption. Learning and permanence effects also
applytofertilizerandimprovedseeds. Carteretal.(2014)findthatsubsidiesinMozambique
induce both short-term take-up and long-term persistence in demand, which they attribute
to both direct and social learning. Our results suggest that for products with learning from
stochastic experiences such as weather insurance, subsidies may have to be continuously
adjusted according to past subsidies and payouts, and likely can never be fully eliminated
due to the specific form that this stochastic learning takes.
This analysis also speaks to the observed low adoption rates of weather insurance, despite
its presumed importance.2 Existing research has studied factors influencing take-up such as
liquidity constraint, lack of financial literacy, present bias, and lack of trust in the insurance
provider (Duflo et al. (2011), Gaurav et al. (2011), Giné et al. (2008); Cole et al. (2013);
Cai et al. (2015)). But insurance demand remains low even after some of these barriers were
removed in experimental treatments. The stochastic nature of the insurance benefits may
contribute importantly to understanding this puzzle.
Finally, the paper contributes to the literature on the design by countries of financial
strategies for disaster risk financing and insurance. These strategies typically combine fi-
nancial reserves, contingent credit, index insurance, and post-disaster budget reallocations
and borrowing. The design of such strategies has been explored in actuarial terms for
cost-minimization (Clarke et al. (2015)) and through Probabilistic Catastrophe Risk Models
(CAPRA (2015)) that combine a characterization of exposure and hazard to predict vulnera-
bility. We extend this analysis to the level of behavior. We formalize how to use subsidies to
optimize the insurance component of these financial strategies when learning from stochastic
experiences determines private uptake.
The paper proceeds as follows. In section 2 we explain the background for the insurance
product in China. In section 3, we present the experimental design and the data collected. In
section4, wedevelopastructuralmodelofdynamiclearningthatconceptualizesthedifferent
channels at work. In section 5, we outline the reduced form estimation strategy and present
the aggregate result obtained and its decomposition by channels. Section 6 reports on the
estimation of the structural model and on use of the estimated model for policy simulations.
Section 7 concludes with policy implications.
2For example, Cole et al. (2013) find an adoption rate of only 5%-10% for a similar insurance policy in
two regions of India in 2006. Higher take-up levels with steep price elasticities were however found in two
recent studies in India (Mobarak and Rosenzweig (2012)) and in Ghana (Karlan et al. (2014)).
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2 Background
Rice is the most important food crop in China, with nearly 50% of the country’s farmers
engaged in its production. In order to maintain food security and shield farmers from
negative weather shocks, in 2009 the Chinese government requested the People’s Insurance
Company of China (PICC) to design and offer the first rice production insurance policy
to rural households in 31 pilot counties.3 The program was expanded to 62 counties in
2010 and to 99 in 2011. The experimental sites for this study were randomly selected
rice producing villages 4 included in the 2010 expansion of the insurance program, located in
Jiangxiprovince, oneofChina’smajorriceproducingareas. Inthesevillages, riceproduction
is the main source of income for most farmers. Because the product was new, farmers, and
even government officials at the village or town level, had very limited understanding of
weather insurance products and had never interacted with the insurance company.
The product is an area-index insurance that covers natural disasters, including heavy
rain, flood, windstorm, extremely high or low temperatures, and drought. If any of these
natural disasters occurs and leads to a 30% or more average loss in yield, farmers are eligible
to receive payouts from the insurance company. The amount of the payout increases linearly
with the loss rate in yield, from 60 RMB per mu for a 30% loss to a maximum payout
of 200 RMB per mu for full loss.5 Areas for indexing are typically sub-village level large
fields that include the plots of 5 to 10 farmers. The average loss rate in yield is assessed
by a committee composed of insurance agents and agricultural experts. Since average gross
income from cultivating rice in the experimental sites is around 800 RMB per mu, and
production costs around 400 RMB per mu, the insurance policy covers 25% of gross income
or 50% of production costs. The actuarially fair price for the policy is 12 RMB per mu per
season6. It is however the government policy to offer the insurance at a subsidized price in
order to achieve a desired high take up rate. If a farmer decides to buy the insurance, the
premium is deducted from the rice production subsidy deposited annually in each farmer’s
bank account, with no cash payment needed.7
3Although there was no insurance before 2009, if major natural disasters occurred, the government made
payments to households whose production had been seriously hurt. However, the level of transfers was
usually far from sufficient to help farmers resume normal levels of production the following year.
4These refer to natural villages, whereas "administrative villages" refer to a bureaucratic entities that
typically contain several natural villages.
5For example, consider a farmer who has 5 mu in rice production. If the normal yield per mu is 500kg
and the farmer’s yield decreased to 250kg per mu because of a windstorm, then the loss rate is 50% and he
will receive 200∗50%=100 RMB per mu from the insurance company.
61 RMB = 0.15 USD; 1 mu = 0.165 acre. Farmers produce two or three seasons of rice each year. The
annual gross income per capita in the study region is around 5000 RMB.
7Starting in 2004, the Chinese government provided production subsidies to rice farmers in order to
increase production incentives. Each year, subsidies are deposited directly in the farmers’ accounts at the
Rural Credit Cooperative, China’s main rural bank.
6
Like any area-yield insurance product, there may be concern that it is vulnerable to
moral hazard through collusion among insured farmers. However, the moral hazard problem
should not be large here as the maximum payout (200 RMB) is much lower than the profit
(800 RMB), and the product does require natural disasters to happen in order to trigger
payouts.
3 Experimental Design and Data
3.1 Experimental Design
The experimental sites include 134 randomly selected villages in Jiangxi Province with
around 3500 households. We carried out a two-year randomized experiment in Spring 2010
and 2011.
The experimental design is presented in Figure 1. The main treatments involve random-
izationofthesubsidylevelinbothyears. Inthefirstyear, werandomizedthesubsidypolicies
at the village level. The insurance product was first sold at 3.6RMB/mu, i.e. with a 70%
subsidy on the fair price, to households in order to observe take-up at that price. Households
from 62 randomly selected villages were then surprised two days after the initial sale with an
announcement that the insurance will be offered for free to all of them, regardless of whether
they had agreed to buy it or not at the initial price. These villages are referred to as the
"free sample" while the remaining 72 villages as the "non-free sample". From this design, we
can distinguish "buyers" of insurance that agreed to pay the offer price of 3.6RMB/mu, from
"users" of insurance, which include all buyers from the non-free sample and all households
from the free sample. As reported on Figure 1, take-up at 3.6RMB/mu was similar in the
two samples at around 40-43%, but access to insurance is of course radically different, with
100% take-up when free.
Forthisvillagelevelrandomization,villageswerestratifiedbytotalnumberofhouseholds.
In order to generate exogenous variation in individual insurance take-up decisions, we also
randomized a default option in 80% of the villages. This was done as follows: In each village
half of the households were assigned with a default "BUY" option, while the other half were
assigned with a default "NOT BUY" option. If the default was BUY, the farmer needed to
sign off if he did not want to purchase the insurance; if the default was NOT BUY, then the
farmer had to sign on if he decided to buy the insurance. Both groups otherwise received the
same pitch for the product. The randomized default option will be used in some estimations
as an IV for the first year insurance purchase decisions together with the randomized subsidy
policy. The 2010 summer was marked by a fairly large occurrence of adverse weather events
that triggered insurance payouts, with almost 60% of the insured receiving a payout from
the insurance company.
In the second year, we randomized the subsidy at the household level. The subsidy
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level ranged from 90% to 40% of the fair price, i.e., the price faced by households varied
from 1.2 RMB to 7.2 RMB. Except for the price, everything else remained the same in the
insurance contract as in the first year. In total, eight different prices were offered. Similar
to the design in Dupas (2014), only two or three prices were assigned within each village.8
For example, if one village was assigned with a price set (1.8, 3.6, 5.4), each household in
that village was randomly assigned to one of these three prices. To randomize price sets at
the village level, villages were stratified by size (total number of households) and first year
village-level insurance payout rate. For the price randomization, households were stratified
by rice production area.
In both years, we offered information sessions about the insurance policy to farmers, in
which we explained the contract including the insurance premium, amount of government
subsidy, responsibility of the insurance company, maximum payout, period of coverage, rules
for loss verification, and procedures for making payouts. Households decided on insurance
purchase individually right after the meeting. In the second-year information session, we also
informed farmers of the payouts made during the first year. Specifically, we made public the
list of people in the village who were insured and those who had received a payout during
the first year and announced the village-level average payout level.
3.2 Data and Summary Statistics
The empirical analysis is based on the administrative data of insurance purchase and payout
from the insurance company, and from household surveys conducted after the insurance
information session in each year. Since all rice-producing households were invited to the
information session, and almost 90% of them attended, this provides us with a quasi census
of the population of these 134 villages. In total, 3474 households were surveyed.
Summary statistics of selected variables are presented in Table 1. Panel A shows that
household heads are almost exclusively male and cultivate on average 12 mu (0.80 ha) of rice.
Rice production is the main source of household income, accounting on average for almost
70% of total income. Households are risk takers, with an average risk aversion of 0.2 on a
scale of zero to one (risk averse).9 In Panel B, we summarize payouts issued during the year
following the first insurance offer. With a windstorm hitting some sample villages, 59% of all
insured households received some payout, with an average payout size of around 90 RMB.
The payout rate among insurance takers was not significantly different between free vs. non-
8Pricesetswitheithertwoorthreedifferentpriceswererandomlyassignedatthevillagelevel. Forvillages
assigned with two prices (P ,P ),P <= 3.6 and P > 3.6; for villages with three prices (P ,P ,P ),P <
1 2 1 2 1 2 3 1
3.6,P ∈(3.6,4.5), and P >4.5.
2 3
9Risk attitudes were elicited by asking households to choose between a certain amount with increasing
values of 50, 80, 100, 120, and 150 RMB (riskless option A), and a risky gamble of (200RMB, 0) with
probability (0.5, 0.5) (risky option B). The proportion of riskless options chosen was then used as a measure
of risk aversion, which ranges from 0 to 1.
8
free villages, at 61% and 57%, respectively. For the non-free villages, this corresponds to
24% of all households. All households, regardless of whether they purchased the insurance or
not, could also observe their friends’ experiences10. In the sample of non-free villages, 68% of
households had at least one friend receiving a payout, while in free villages, 81% households
observed at least one of their friends receiving a payout. As a result, since more households
were covered by insurance in villages with free-distribution, most households were able to
enjoythebenefitsofinsurancecoveragebythemselves, orcouldobservetheirfriends’positive
experiences with the product. Lastly, in Panel C, we show the overall take-up rate in both
years. In the first year the take-up rate was 41%. In the second year, insurance demand
was significantly higher - about 53%. On average (over all prices), the insurance take-up
increased by 7.3 percentage points in non-free villages, and by 16.3 percentage points in free
villages.
To check the price randomization, we regress the five main household characteristics
(gender, age, household size, education, and area of rice production) on a quadratic in the
insurance price and a set of village fixed effects:
X = α +α Price +α Price2 +η +(cid:15) (1)
ij 0 1 ij 2 ij j ij
where X represents a characteristic of household i in village j, Price is the post-subsidy
ij ij
price faced by household i in village j, and η a village fixed effect. Table 2 reports the
j
coefficient estimates and standard errors for α (column 1) and α (column 2). All of the
1 2
coefficient estimates are small in magnitude and none of them is statistically significant,
confirming the validity of the second year price randomization.
4 Theoretical Framework
4.1 Set-up
The net utility of buying insurance is posited to be additive in gains and costs. Assume that
there are two states of nature, and let pL be the probability of a negative weather shock, and
pH = 1−pL. The benefit VL of having an insurance in states of weather shock is the utility
gain of receiving a payout at the low realization of income yL, VL = U(yL+payout)−U(yL)),
while the utility gain in absence of shock VH = 0. Without other information, the expected
utility gain of having insurance at the onset of the first year is:
EV = pLVL +pHVH.
1
10We conducted a social network census before the experiment in year one. In that survey we asked
householdheadstolistfiveclosefriends,eitherwithinoroutsidethevillage,withwhomtheymostfrequently
discuss rice production or financial issues. For detailed description of the network data, please refer to Cai
et al. (2015).
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In the context of an insurance, any learning from one period is contingent on the realization
of the state of nature. We assume a simple learning model, the temporal difference rein-
forcement learning (TDRL in Sutton and Barto (1998)), which incorporates recency effects.
In this model, individuals update their valuation based on the realization in the previous
period:
(cid:0) (cid:1)
EV = EV +λ V∗ −EV (2)
t t−1 t−1 t−1
where V∗ is the experienced benefit in year t − 1. This experienced benefit results from
t−1
eitheryourownrealizationV orobservingyournetworkrealizationNetV intheprevious
t−1 t−1
year. It also depends on I , an indicator of whether the individual was insured or not.
t−1
Without specifying further the functional form, V∗ = g(V ,NetV ,I ).
t−1 t−1 t−1 t−1
The term V∗ −EV represents a prediction error. If it is positive the realized value of
t−1 t−1
the insurance was higher than its expected value, and conversely if negative. The valuation
is then incremented upward or downward accordingly. This model has a single parameter
λ that controls the rate at which information from past observations is discounted. With
λ = 1, expected value of insurance is simply last year’s realization; with λ = 0, there is no
updating in expected benefits of insurance. The higher the parameter, the more responsive
individualsaretotherecentrealizations. Themodelthuscaptures“recencybias”. Wefurther
specify λ to be function of the price paid for the insurance: λ = λ(p )
t t−1
The costs of insurance include three terms, the price at which the insurance is offered p ,
t
a gain-loss in utility which we assume to be a linear function of the difference between the
offered price and a reference price, γ(p −p ), and a transactions cost δ . Transactions costs
t rt t
are assumed to depend on past experience, i.e., δ = δ(I ).
t t−1
Adding a preference shock (cid:15) , the overall utility of purchasing insurance for an individual
t
is:
W −(cid:15) ≡ EV +λ (g(V ,NetV ,I )−EV )+βp +γ(p −p )I +δ −(cid:15) (3)
t t t−1 t t−1 t−1 t−1 t−1 t t rt t−1 t t
4.2 Link with the Experiment
In the experiment, we analyze the purchase of insurance in years 1 and 2:
Buy = 1 if (cid:15) < W ≡ EV +βp∗
1 1 1 1 1
= 0 otherwise
Buy = 1 if (cid:15) < W ≡ EV +λ(p )(g(V ,NetV ,I )−EV )+βp +γ(p −p )I +δ(I )
2 2 2 1 1 1 1 1 1 2 2 1 1 1
= 0 otherwise
Note that there are two prices for period 1: The price p∗ is the unique price at which the
1
insurance was first offered to all farmers in order to elicit their demand for insurance. Then,
10