Journal of Natural Disaster Science, Volume 31, Number 2, 2009, pp3-12

Premium subsidy for crop insurance as an incentive device in China:
In which respects might it work wrongly?

Tao YE*,***
Muneta YOKOMATSU**
Norio OKADA***Graduate School of Engineering,**Disaster Prevention Research Institute,
Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan*** State Key Laboratory of Earth Surface Processes and Resource Ecology,
Beijing Normal Univeristy, Beijing 100875, China(Received for 20 Apr., 2010 and in revised from 1 Jun., 2010)
ABSTRACT
Direct subsidy for crop insurance premiums paid by producers is widely adopted bypolicy-makers in many countries. It is generally believed to be a good device for income
transfer to rural producers. In the recently launched crop insurance program in China, it isalso employed as an incentive tool to encourage per-producer output and discourage ruralto-urban migration besides its traditional role. This research develops a dual-economy
model to check three essential hypotheses that may support the Chinese government’s
decision. The model incorporates subsistence constraint in consuming agricultural products,
which essentially changes the yield-revenue relationship of agricultural products. The
analytical results from the model do not support these plausible hypotheses. When rural
producers insure their crops with partial coverage, output at the individual level drops
rather than increases. Meanwhile, the provision of insurance plus premium subsidy crowds
the agriculture sector with too many laborers engaged in agricultural production. In thissense, government subsidy for crop insurance premiums induces efÞciency loss rather thangain. The authors suggest that a comprehensive cost-benefit analysis should be carriedout comparing premium subsidy and other types of risk-reduction and income-transfer
programs, for the better use of government budget.
Keyword: premium subsidy; crop insurance; output decision-making; economic efÞciency

locally or in distant large cities seasonally. The large
labor flow in China started in the mid-1980s after therelaxation of long-standing controls over rural-urban
migration [１,２]. In 2008, the number of rural laborers
migrating to urban areas reached 16.4 million, accounting for 22.6% of the total rural population (population with the status of “rural resident” or nongcun

I. INTRODUCTION
In the face of uncertainty in agricultural production and fluctuation in market price (s), an increasing
number of Chinese farmers are choosing to accessoff-farm income sources to gain higher, more stable
income, by working in the non-farming sectors either
3

T.YE, M.YOKOMATSU, N.OKADA

hukou in the household registration system) [３]. In
2008, the annual average income of the urban household reached slightly more than three times that of therural household [４], which creates a strong incentive
for rural-to-urban migration. Meanwhile, according
to the authors’ survey, many rural farming households
are reducing their rice plantation plans so that morelabor-hours can be allocated to off-farm jobs provided
locally. The impact of the rational choices of farming
households is revealed macroscopically. In 2003, theaggregate output of grain was 431 million tons, a dropof more than 100 million tons from that of 1998 [５ ].
Moreover, the drop mentioned above is in accordancewith strict institutional control of migration under the
hukou system. If the hukou system were removed,
massive migration to cities would be expected tooccur [６].
In the face of this issue, the Chinese government
must deal with a certain trade-off: migration and offfarm income sources can definitely help rural households increase annual income and reduce rural-urban
disparity, but it simultaneously reduces agricultural
productivity and undermines the foodstuff self-sufficiency of the country. In this sense, the Chinese government is carrying out a series of policies to increase
the incomes of rural households on the one hand
and to keep them in their place on the other. These
policy instruments include: 1) giving direct lump-sum
subsidy to rural producers who continue agricultural
production, particularly grain plantation; 2) imposing
penalties on rural households whose crop lands areleft uncultivated; 3) launching an agricultural disasterinsurance program and simultaneously giving direct
subsidy for insurance premiums; 4) giving direct
lump-sum subsidies to producers who purchase farming machinery in order to encourage technical progress; and 5) as an experiment, allowing free transferof land use rights in some regions since 2008.
Amongst all the mechanisms mentioned above,
direct subsidy for crop insurance premiums has
been widely adopted as both an income-transfer andan incentive tool [７]. According to some popular
wisdom [８~10], government subsidy is necessary forthe emergence of a crop insurance market. Output
of agricultural production is likely to rise if producers are provided with insurance, and an abundanceof agricultural products drives prices down and thenpromotes social welfare. Urban consumers, however,would take all these benefits away, since producers’
labor income comes from the sales revenue of crops.
In this sense, the government should carry out further
redistribution policy to compensate producers. If it isagain in the form of premium subsidy, then a virtuous
circle could probably be established.
There are three pieces of essential logic inthis hypothesis: premium subsidy will attract moreresources, including labor, capital, and land, to beengaged in agricultural production so 1) per-farm
output increases; 2) the number of farms is likely togrow; and 3) the abundance of agriculture products
brings about a higher level of social welfare. Thoughpolicy instruments based on this hypothesis have been
widely carried out, it is quite controversial. A study
carried out by Nelson and Loeham [11], with a similar
approach to [９], distinguishes between risk-increasing
factors and risk-decreasing ones. It has been foundthat the provision of crop insurance will induce
producers to increase the use of risk-increasing factors while reducing the use of risk-decreasing ones,
revealing a typical moral-hazard structure. This analytical result has been supported by empirical studies
carried out in the US [12~14]. They have paid attention
mainly to producers’ decision-making regarding specific factors of input rather than the overall output
level, e.g., how many kilograms/bushels of grain
will be produced per acre. In this sense, the three key
statements in the hypothesis have not been verified by
the existing literature.
This paper addresses whether these three essential logics are valid. In the model, we consider ageneral equilibrium economy in which social welfare
is measured by the aggregate of the individual welfare level. First, in such an economy, the total natural
endowment available for production will be controlled. Only when resources are allocated efficiently
can the social optimum be achieved. Second, in theequilibrium, prices are endogenously decided by themarket per se. In particular, subsistence consumptionof agricultural products will be incorporated. It allows
us to grasp whether there is a gain in social welfare
if the price of agricultural products drops rapidly inresponse to a slow increase in supply.
The plan of this paper is as follows. In the next
section, we introduce the basic structure of the model,
including the key assumptions, essential featuresof the ex-post equilibrium, as well as the insurance
4

PREMIUM SUBSIDY FOR CROP INSURANCE AS AN INCENTIVE DEVICE IN CHINA:IN WHICH RESPECTS MIGHT IT WORK WRONGLY?

termined. The assumption of free migration implicitly
leads to an equilibrium of equalized labor income insome sense, which may be questioned because China
has been well known for its rural-to-urban income
gap for years. Nevertheless, if we look at the reasons for the income gap, many of them, e.g., costs oftransportation and obtaining a working permit, areneutral in the decision-making of seasonal migrants,
and will not change the pattern of allocation of labor
and risk-bearing. For more information on the structure of neutrality of urban residents as well as lumpsum transaction costs in migration, please refer to themore complete dual-economy model developed by Ye
et al. [15]. The model is a static one. Coupled with theassumption of free migration, this model is equivalent to a labor allocation problem. At the beginningof each period, each laborer first considers in which
sector they are going to work in the following period.
If they choose the rural sector, they are then “rural
producer,” and have to further choose a planned output level of production, X , which they believe canmaximize their expected welfare state. On the other
hand, if a laborer chooses to work in the urban sector,
they are called “urban worker” and simply follow the
mandatory working time without ex-ante planning.
The production process then starts and the state of theworld is to be determined. There are only two statesof nature assumed for the sake of simplicity, statet = 0 in which no disasters occur and state t = 0 in
which disasters occur and damages are claimed. The
probability of falling under each state is π(0) and π(1) , respectively. In this model, only the rural sector
will be affected by natural disasters and the output
of agricultural products could probably be damaged.
Once a disaster occurs, the yield of all producers inthis small economy is assumed to be damaged by
the disaster simultaneously to the same degree. So
all rural producers will get δ(t)X of an agricultural
product (e.g., grain) in any state t, 0<δ(1) <δ(0) =1 . In order to avoid regressive results, it is strongly
assumed that δ(1) >0 . Otherwise, in state 1, there
will be no harvest in the agricultural sector and further discussion is meaningless. This seemingly strong
assumption is actually innocuous to some extent. It isequivalent to the case where homogeneous producers
under collective risks exchange full-cover mutual insurance. In this sense, their labor incomes will be thesame for any arbitrary collective state of nature [15~17].

system that we are going to discuss. On this basis,
producers’ ex-ante decision-making will be discussed.
We will verify these three logics one by one: 1) Do
producers increase their output level if premiumsubsidy is provided and the effective premium ratedrops? 2) Does the number of laborers engaged in rural production increase correspondingly? And 3) is social welfare promoted because of the subsidy? In the
final part of this paper, discussion will be presented
identifying the gap between the model findings andthe reality, and will provide clues for further study.
II. THE CONTEXT OF THE ECONOMY
A.The dual economy
We consider a simple closed dual economy with
two sectors and two regions, both rural and urban.
There is a population of homogeneous laborers in thiseconomy and initially, all of them stay in rural areas.
As a complete dual economy, it is generally assumed
that there is a part of the population staying in theurban sector. Urban residents, however, as observedin reality, do not have any incentive to move to findwork in rural areas as the rural sector does, either
because of the income gap or because of the special
techniques required in rural production, particularly in
China and some other countries. On the other hand, it
is only rural residents who seasonally or permanently
migrate to urban areas. It is actually the mobility ofrural residents that determines the labor allocation
structure. Since the focus of the model is on the allocation of resources (labor) and risk-bearing, immobile
urban residents make neither contribution nor a difference to the result of the model. We assume that rural
residents who work in the rural sector (“rural producers” in this model) account for a fraction of n andthat the rest, 1−n fraction of rural residents, work in
the urban sector (“urban workers”). Be aware that in
the model when we talk about “urban workers,” thisactually refers to individuals who come from rural
areas while working in the urban sector. Without lossof generality, we normalize the population to 1. The
rural sector produces agricultural products used for
private consumption, while the urban sector produces
urban goods for both private consumption and capitalstock investment.
The labor market between regions/sectors is
open without any friction, so n is endogenously de5

T.YE, M.YOKOMATSU, N.OKADA

Urban workers’ labor income is, consequently, riskfree.
We further assume that there is some insurance
option available for producers, either the package directly offered by insurance companies or that offeredwith government intervention. The package follows
the general form of the yield insurance in FCIP (Federal Crop Insurance Program) in the United States
and cost insurance in China. Indemnity per acre is
calculated by σ . $&0, " ! # !%' σ here denotes the indemnity coefficient, which is the price guarantee if it
is yield insurance or cost reimbursement if it is cost―
insurance. ξ is the trigger yield put in the contract.
〜δ・ξ denotes the realized yield, with ξ representing
the planned per-acre yield and ! ( {! (0), ! (1)} representing the state-contingent discounting factor.
In order to simplify the formulation of the insurance contract so that it can be put into the context ofour model, we made two important assumptions. On
the one hand, it is assumed that land is homogeneousin terms of fertility as well as risk. So given the samelevel of input, the possible outcomes of output fromall land will be the same. On the other hand, we assume that insurers can observe producers’ behavior
perfectly. In real situations, e.g., in the current crop
insurance program in China, it has been observedthat some producers may put less effort into planting
correctly, increasing the risk of poor harvest after the
insurance contract is underwritten. We make this assumption to prevent our discussion from diversifying
to a moral hazards issue. The actual loss induced by adisaster can be simplified to

B. Ex-post equilibrium
After the production process is finished, the expost economy reaches equilibrium through exchange
and trade. The budget constraint for an individual in
the ex-post exchange economy isin which p(t) is the state-contingent relative priceof agricultural products to urban goods. x(t) and y(t)are the state-contingent consumption of agricultural
products and urban goods, respectively. e(t) is thestate-contingent labor income of an individual, whichequals product revenue if the individual works in therural sector or wages paid by a firm if the individual
works in the urban sector. Subscript i = 1,2 is used todenote the rural producer and the urban worker, respectively. Social aggregate budget constraint follows
nx 1 (t ) + (1 " n ) x 2 (t ) = n ! (t ) X(3)ny1 (t ) + (1 " n ) y2 (t ) = (1 " n )e2 " nC (X ) = Y

We assume that technology in the urban sector follows a constant return to scale with respect tolabor. In this static framework, the aggregate urban
goods available for consumption must equal the total wages paid to urban workers (1−n)e2, which iscertain, minus the total costs involved in agricultural
production, nC(X).
Individuals choose their best consumption bundles according to their preference. The ex-post utility
level is measured by a quasi-linear utility functionu (x , y ) = f (x ) + y with"1
+ 1"1 #
"1 1"1 # ,0 < # < 1,,,b xf (x ) = ,,b ln x
, #=1
,.
,
yielding a demand system that is inelastic
with respect to consumption of agricultural products. Compared to the popular Stone-Geary utility
function [18] of the same feature, the demand systemyielded by this quasi-linear utility function has zero
income elasticity of demand and constant price elasticity of demand, which exactly equals parameter − .
With this assumption, the ex-post equilibrium can be
determined as(

max &$0, " ! # !'% = (1 " ! ) .

Provided the assumptions above are correct, it isequivalent for a producer to specify the proportion ofacres (l / L) and the proportion of output ρ it wants
to insure, since per-acre output ξ times land cultivated L is exactly planned output level X, ρ・X ,＝ξ・1.
In this sense, total indemnity can be calculated equivalently by
m = $ #)#X #",(2)

p (t ) x i (t ) + yi (t ) = ei (t ) ,

(1)

)(

)

"1 #

with ) = ! (0) " ! (1) denoting the actual damage ratio induced by a disaster and " = ! L * 1 denoting the ratio of insured acres to total acres cultivated.

p (t ) = b # [n ! (t ) X ],(4)

by assuming interior solutions. This price system
6

PREMIUM SUBSIDY FOR CROP INSURANCE AS AN INCENTIVE DEVICE IN CHINA:IN WHICH RESPECTS MIGHT IT WORK WRONGLY?

sectoral” structure of risk diversification: the flow oflaborers and goods may alter the actual risk-bearing
pattern from what it seems to be. Risk transfer fromrural producers to urban consumers has been carriedout by the goods market, before the financial/insurance market comes into the picture. Consequently,
market allocation of catastrophic risk regarding subsistence goods is so inherent that we should not deal
with it in the same manner in which we deal withrisks in many other sectors/situations.
It is, however, unrealistic for rural producers toprovide domestic disaster insurance to urban consumers since the transaction costs will be significantly
high. In this sense, when we come to the sub-modelwith insurance contracts, it must be provided by someforeign insurer and the model collapses into a partial
one in terms of the insurance market. Insurance canbe provided both to rural producers, against crop
failure (although there is no “income failure”), and tourban consumers, against a drop in purchasing power
and reduced consumption. Both types of insurance
will result in welfare promotion as they cope with different types of risks in the economy. In the preceding
part, however, we focus on the insurance provided
to rural producers because the objective of this study
is to discuss rural producers’ decision-making undersubsidized insurance premiums.

will exactly allocate each individual the per-capita
amount of agricultural products to consume. Ex-postindirect utility follows

(

)

(

)

vi ei (t ), p (t ) = arg max ui x i (t ), yi (t )()= ei (t ) " ' p (t )(5)+,b # p1"# " #b,,
,0 < # <1with.
' (p ) = ,- 1 " #,,"1,,.b (ln b p + 1) , # = 1
Another important feature of the quasi-linear
utility function is that the ex-post utility function isa monotonic transfer of the planned output level, X.
There are some important features of the equilibrium:a) p (0) ! (0) " p (1) ! (1) < 0 .
Rural producers will gain higher product revenue if a disaster happens and destroys a part of theharvest. This feature creates an essential difference
between this model and popular wisdom. In most of
the literature, either analytical research or empiricalestimation, a positive revenue-yield relationship isassumed, although in many cases, there is a negative
price-yield relationship. This feature is determinedby the assumption of subsistence constraint together
with a closed economy. If either of the two assumptions is removed, the model will collapse into one thathas been widely treated. The corresponding change in
the implication of the model, however, does not meanthat the model is not robust. Such a revenue-yield relationship widely exists in the market, particularly the
fresh vegetables and fruits, for which distant shipping
and long-term storage are not possible. As for cereal
products, it is not widely seen because they can on the
one hand be stored for years at acceptable cost andgovernments are always concerned about their prices,
for the sake of food security, on the other hand.

III. EX-ANTE DECISION-MAKING AND EQUILIBRIUM
1) Criteria for ex-ante decision-making
Individuals’ ex-ante decision-making is a twostage process. Provided with all state-contingent outcomes (ex-post welfare states) and their corresponding probability, an individual will choose the sector
that can bring the highest ex-ante expected utility towork in.
As a rational expected utility maximizer, a producer is then to choose planned output level X andinsurance coverage level ρ , taking the market prices
for agricultural products and insurance coverage asparameters:b) Var &$v1 !'% < Var &$v2 !'%This means that the cross-state variance of statecontingent welfare states of the rural producer issmaller than that of the urban worker. In other words,
urban workers bear more risk than rural producers.
This is a result of feature a), the negative revenueyield relationship. If there is a domestic insurance
market working for risk transfer, it must then be rural
producers who provide insurance coverage. It reveals
quite an important structure in this study: althoughrural producers suffer from yield loss (the direct riskbearer), they are actually not the final victims. Thisis the critical point of what we may call the “inter-

max EW1 = / t % (t )W (v1 (e1 (t ) , p (t ))) ,X ,"which is subject toe1 (t ) = p (t ) ! (t ) X " C (X ) + (t " & ) # m
m = $ #)#X #"0 * " *1

7

, for t=0, 1. (6).

T.YE, M.YOKOMATSU, N.OKADA

The expected ex-ante welfare level is measured by von Neumann-Morgenstern (VNM) utility
function W(・) as a function of ex-post indirect util-

1v1 (t ) 1e1 (t )/ % (t ) 1e (t ) 1X

=0,

t

1

ity v1 (e1 (t ), p (t )) . W (#) is introduced to define the riskaverse preference of the producer. Ex-post income

(8)

" =0

which yields optimal planned yield X0.
b) If 0 ＜ρ＜ 1
We call this type of insurance demand “partial
coverage.” The first-order conditions hold thatconsists of three parts, product revenue p (t ) ! (t ) X, production costs −C(X) , and the state-contingent
insurance item (t−v)・m. For ease of description, weallow producers to take out loans at the beginning ofeach period and repay them after yield and revenue
are realized. If a disaster does not happen, the t = 0
and the insurance item is exactly the premium rate
charged to the producer. The last inequality holds
because a producer cannot insure cropland that is not
actually cultivated. The introduction of insurance into
the system changes the state-contingent incomes ofrural producers, the ex-ante expected welfare level,
and consequently the ex-ante equilibrium. It has no
impact on the mechanism of determining the ex-postequilibrium, however.
This maximization problem is quite general but
causes a lot of problems due to our general equilibrium structure. It becomes analytically intractable when
we try to determine the population distribution. As indicated, risk-neutral producers in imperfect financial
markets (e.g., under budget/liquidity/credit constraint)
behave as if they were risk averse [19]. In this sense,
we provide an alternative to the elegant structure as acompromise:(1 " & ) p (0) ! (0) + & p (1) ! (1) " C 0 (X ) = 0 . (9)c) If ρ＝ 1
The first-order conditions for maximization canbe updated to/ % (t ) &$ p (t ) ! (t ) " C 0 (X ) + (t " & ) $) '%! = 0 . (10)t2) Ex-ante equilibria
In the model, the statistics imply
dEW1 dEV1
dEW2 dEV2
,
,
<0,
>0.
dn
dn
dn
dn

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The more individuals are engaged in agricultural
production, the lower the expected utility they will
receive. Sharp price drops can be induced by an abundance of agricultural products, and this correspondingly reduces the labor income of producers. The effect of the first half of the sentence is predicted by theliterature, but the other half is not really mentioned.
The effect of population distribution on individuals’
welfare states is shown in Fig. 1.

max EV1 = / t % (t ) v1 (e1 (t ) , p (t )) ,
X ,"

EW1

which is subject to

EW2(1 (t ) : e1 (t ) = p (t ) ! (t ) X " C (X ) + (t " & ) # m(2 : m = $ # ) # X # "(3 : 0 * " * 1, for t=0, 1, (7)0(4 : C (X ) + &m * Kwith a Greek letter before each constraint as its
corresponding Lagrangian multiplier. First-order conditions for maximization require the last budget constraint to bind at K. In other words, the rural producer
tries to take out a loan of the maximal amount, K. We
have three solutions.
a) If " = 0 and m = 0
This corresponds to the case in which no insurance is provided, or where the producer feels that it is
not optimal to purchase insurance coverage. The firstorder condition for this case isn*1

Figure 1. Determination of equilibrium population
distribution
Recall that the criterion for choosing between
sectors is simply to check which sector can provide
higher expected ex-ante utility. In this sense, thepopulation distribution reaches equilibrium if there isa marginal individual who is perfectly indifferent toworking in either sector, holding that
EW1 = EW2 , or EV1 = EV2 .

8

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PREMIUM SUBSIDY FOR CROP INSURANCE AS AN INCENTIVE DEVICE IN CHINA:IN WHICH RESPECTS MIGHT IT WORK WRONGLY?

With constraint , static population distribution n will be endogenously determined. We specify
α＝ 1/2 and C (X ) = c # X to derive explicit analytical results.
When risk neutrality is assumed, the expected
ex-ante utility level coincides with the expected income level. Since we further assume that the costfunction is linear in X, there is no concave set for
maximization in the benchmark case. In this sense,

&

X0

U0

&0 * % (1)

X pc

U pc
&1

U fc

X fc

X

(13)

X0 = K c .

1

&

0

U

Figure 2. Production behavior of the risk-neutral rural
producer under free migration

Together with constraint (12), it yields the equilibrium ( X 0 , n0 ) .
When rural producers purchase partial coverage, the equilibrium (X pc , n pc ) is determined by (9)together with constraint . When full coverage ispurchased, the equilibrium (X pc , n pc ) is determinedby (10) together with .

We may interpret Fig. 2 in the following way. At
the beginning, there is no insurance market, or insurance is provided at an unacceptable price (generally,
commercial insurance is offered with premium loading so the rate is definitely higher than is fair), andproducers do not use the instrument to manage theirrisk.
The government then announces a premium subsidy program. Once the subsidy rate is high enough toallow insurance behavior to break even, & * & 0 , producers will purchase partial coverage and their output
level decreases from X0. This observation is quite
different from popular wisdom. In the model, yieldand producers’ labor income shows a negative relationship, not a positive one as is generally assumed.
Along with the decrease in individual output level, thesocial aggregate welfare level drops. There is excessive entry into the rural sector, while each producer
produces less than the social optimal level.
Should the effective premium rate continue todrop as the government subsidy rate increases, producers will increase the coverage rate and it will finally bind at ρ＝ 1. The demand curve of producers aswell as their supply curve of grain binds at this point,
1. So does the curve of social aggregate welfare level.
Producers will turn to increase their output level because they saved budget to invest in production fromcheaper insurance coverage. Social aggregate welfare
begins to increase. Nevertheless, this increase is not
because of the improvement in economic efficiency,
but due to the extra resources that have been brought
into this system by the government subsidy. It must
be emphasized here that we did not take the government’s budget for premium subsidy into account.

3) Comparative statics
In the model, we measure economic efficiency
by the social welfare function, which is a plain aggregate of all individual welfare functions:U i = ni EV1 + (1 " ni ) EV2 , for i = 0, pc, fc . (14)The three subscripts in the equation represent
the case with no insurance contract, partial insurance
coverage, and full insurance coverage.
Performing basic comparative statics, we have*dX pc
d & > 0, dX fc* d & < 0 ,dn pc d & < 0, dU pc d & > 0,U pc & =& 0 = U 0 , and0dU fc d & < 0,U fc & =0 > U 0 * .

The sign of dn fc / d& is not certain but it necessarily holds that n fc > n 0 . Production behavior at theindividual producer’s level as well as the social aggregate welfare state against changes in the effective
premium rate is shown in Fig. 2.

9

T.YE, M.YOKOMATSU, N.OKADA&

So we may summarize here that when factor mobility and intersectoral labor allocation is taken into
account, premium subsidy is likely to result in ruralsector overpopulation while each producer produces
less than when no insurance is provided. Premiumsubsidy will probably result in a loss in economic
efficiency rather than a gain. We have the interval1& (M )& (0)&0 * % (1)(& , & ) in which economic efficiency will definitely be0

undermined because of the premium subsidy.

&1

IV. GOVERNMENT BUDGET FOR PREMIUM SUBSIDY

&

(

)

(

)

From Fig. 3, it is straightforward that the budget
for premium subsidy increases dramatically when thesubsidy rate goes up. Whether government expenditure on the premium subsidy mentioned above is costeffective or economically efficient remains a question
for further discussion, since we do not have a context
for comparison among the investment choices of thegovernment.

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V. CONCLUSION AND DISCUSSION
In this research, a simple model is developed toprovide some alternative insights into producers’ behavior under the subsidized insurance program. The
major findings from our model include: 1) premiumsubsidy does not always induce producers to produce
more output; 2) premium subsidy attracts more laborers to engage in agricultural production; and 3)
premium subsidy could induce welfare loss because
it undermines economic efficiency. Finding No. 2 issimilar to popular wisdom but No. 1 and No. 3 diverges from it.
There are several critical structures in the modelthat provide the alternative findings listed above. Our
assumption of a closed economy together with the inelastic demand system that determines the yield-revenue structure opposes common sense. This featureessentially changes the slope of the individual supply
curve when partial coverage is purchased and yields a“V”-shaped curve. Second, in the structure of generalequilibrium, the social optimum will be unique. The
abundance of any product will be at the cost of the(16)

Finally, if the government wants to increase social aggregate welfare by investing substantial budget
in premium subsidy, it has to prepare a budget withthe size of the area of the light-gray square:
F2 = $& M fc (& ) " & !% M fc (& )
&
'

(

)

M fc (& )Figure 3. Required financial resources for premiumsubsidy to reach a critical effect

The kink point between demand for partial coverage and full coverage is 1. So, the critical government budget to reach this point equals the area of thedark-gray square:
F1 = $& M pc (&1 ) " &1 %! M pc (&1 )&'M pc (& )M

In the framework of perfect factor mobility,
what will the necessary budget be for the government
to achieve critical intervention effects? Suppose theinverse supply function of an international insurer is＝ (M) , the upsloping concave curve in Fig. 3, lying between π (1) and 1 for the existence of loading
factors. M ( )＝n ( )・m ( ) is the aggregate demandfor insurance coverage or producers.
As we know from Fig. 2, the break-even pointof the insurance market is 0. Consequently, a budget
with the length of the thick-black-font segment in Fig.
3 will be necessary:
F0 = & M pc (& 0 ) " & 0

% (1)

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10

PREMIUM SUBSIDY FOR CROP INSURANCE AS AN INCENTIVE DEVICE IN CHINA:IN WHICH RESPECTS MIGHT IT WORK WRONGLY?

output of other products—obviously we must have asolution in this trade-off. Excessive entry into farm
production and under-production by operating farmers results only in welfare loss.
Direct subsidy for crop disaster insurance premiums does not necessarily encourage producers to
produce more output. A small amount of subsidy only
leads to a smaller per-capita output level. Premiumsubsidy does lead to a larger population engaged inagricultural production. This result is very similar tothat derived by Innes [20] that there is excessive entry
into farm production and under-production by operating farmers, although in his model, it is the result of
ex-post relief in the absence of ex-ante government
policy.
Let us return to reality with our model findings.
This research is basically theoretical, without any dataor econometric estimation. In this sense, we cannot
provide specific policy implications. Nevertheless,
it is suggested that a government, like the Chinese
government, should have taken the observations of
this research into account before any kind of premiumsubsidy is provided. Premium subsidy requires large
fiscal resources and it distorts the market as well as
individuals’ choice. Besides, there are still several
alternatives for disaster reduction in the agriculture
sector, which may increase producers’ income level
and consequently attract more laborers to engage in
agricultural production. Cost-benefit analysis among
investment in risk-mitigating infrastructures, post-disaster relief, direct income transfer, and premium subsidy should be carried out. Complicated models may
be required to achieve this task, such as input-output
econometric models (I-O), CGE models, sequential
interindustry models (SIM), and dynamic stochastic
general equilibrium models (DSGE) [21].

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Case Study of the IHDP-IRG Core Science Project”
and the DRH (Disaster Reduction Hyperbase)-CASiFiCA (Case Station-Field Campus) project fundedby the Special Coordination Fund for Promoting Science and Technology, Ministry of Education, Culture,
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12