DRAFT
FOP. STAFF USE ONLY
THE RELATIVE MERITS OF ALTERNATIVE APPROACHES TO APPLIED
WELFARE ECONOMICS
Anne Case (Consultant)
and
Lyn Squire
CPD Discussion Paper Number 1985-1
February 1984
cPn Discussion Paper~ report on work in Progress and are circu1ated
t0r Sank staff use to stimulate dis~ussion and comment. The ~il!Ws
tnd interpretations are those of the authors.
Abstract
The Relative Merits of Alternative Approaches to Applied Welfare Ecnoaics
This paper compares alternative methods of analyzing price policy.
The "single-market" approach uses the standard technique of consumer and pro-
ducer surplus. In agriculture, where substitution possibilities may be espe-
cially strong, a single-market approach may leave out important repercusions
in related markets. Accordingly, the single-market approach is compared with
a "11lll ti-market" approach in which an effort is made to inco~porate all those
markets likely to experience significant repercusions following an interven-
tion in any one market.
The comparison takes advantage of a multi-market model prepared for
the analysis of agricultural pricing policy in Korea by Braverman, Hammer, and
Ahn (CPD Discussion Paper No. 1983-2). The comparison reveals that there are
important linkages with other markets. For example, a 10 pe~cent reduction in
the producer price of HYV rice results in an 11 percent decline in the use of
fertiliser according to the multi-market model. The single-market model is
unable to capture this effect. Similarly, because of an induced change in the
price of traditional rice, the 10 percent reduction in the price of HYV rice
results in a 7.5 percent decline in real rural incomes according to the multi-
market model whereas the single-market model reports a decline of only 1.5
percent.
The interactions between markets that prove important in the Korean
case are those between the price of HYY rice and the use of fertiliser and
between the same price and the price of traditional rice. The final section
of the paper, therefore, shows how a simple extension of the standard consumer
surplus/producer surplus method can adequately allow for these considerations.
The paper concludes that a single-market analysis may often yield misleading
or incomplete results but that it may be possible to improve the situation
substantially by relatively simple methods.
TABLE OF CONTENTS
?age ~,umber
I. Introduction---•••••·•••••·•·•·•·••••••••••••·
II. Korean. Agricultural Pricing Policy ••••••••••••
III. The Two Methods
Multi-market Analysis •••••••••••••••••••••••
Single-market Analysis ••••••••••••••••••••••
IV. Comparison of Results
Estimation ••••••••••••••••••••••••••••••••••
Positive Analysis •••••••••••••••••••••••••••
Normative Analysis ••••••••••••••.•••••••••••
V. An Alternative Approach
Testing for Interactions ••••••••••••••••••••
An Augmented Single-Market Approach •••••••••
VI. Conclusion .••.••.••..•......... ..
Appendix A: Compensating Varia
Appendix B: Consumer Surplu~-··
Appendix C: Regression Results.
The Relative ~terits of Alternative
Aopr,,,.ches to :\f>D lled Welfare ~co"o1111£.!_
I. I '.':TRODUCTION
This paper compares the positive and normative results of a ~ultt•
market, agricultural pricing model with those of a single-market approach.
The main advantage of the first approach is its explicit treatment ~f market
interactions and interdependencies that may affect policy conclusions
significantly but which are ignored by the second method. A further advantage
of the particular multi-market model analyzed here results from t':"1e use of
microeconomic demand systems that allow direct calculations of co::.pensating
variation (or a close approximation) as the basis for welfare state111ents. ~e
single-market approach, on the other hand, relies on measures of consW1er
surplus. These advantages of the multi-market approach must, however, be set
against its greater cost both in eonstruction ano probably in
implementation. The issue, therefore, is whether the &lle~ed sup•rior
accuracy of the multi-market. approach is of sufficient ~•lue to offset its
presumed greater cost.
The analysis takes advantage of at1 existing multi-market model for
Korea [Braverman, Hammer, Ahn, 19811. 1i,e model was l!onstructed to explore
alternative methods of reducing the deficit in the central buda•t arisi~g frOtl
the government's agricultural pricin~ policie~. Section tl contains a brief
description of the major feature• of Korean agriculture and Section ttt
outlines the 1tr1Jcture of the multi-market model and deflne, the ~lfat•e
m•~•ure9 for the two alternative approaches. The comparison of ?OSitlve and
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developed and then compared with the full multi-market method in Section V.
s~cc ion VI summarizes che main conc:usions, draws several operational ir:1p aca-
tlons, and ~~ggests directions for fu~ther research.
II. KOREAN AGRICULTURAL PRICING POLICY
In order to achieve self-sufficiency in rice, stabilize grain prices,
and uttain parity between urban and rural incomes, the government of South
Korea has managed public trade in rice and barley for almost thirty years.
The Grain Management Fund (GMF), responsible for all public sales in rice and
barley, purchases a significant portion of the rice and barley produced each
year l./ and then sells t~is grain in the urban sector at prices below the
GMF's own purchase prices, but at prices well above the international prices
of these grains. In ~·ears when the domestic production is insufficient to
meet domestic demand, the GMF is !esponsible for importing the .necer:~ry
grains.
Similarly, all public trade in fertilizer is managed by the Ferti-
lizer Fund (FF). The FF, under contracts prenegotiated with Aomestic pro-
ducers, purchases specified amounts of fertilizer at prices above interna-
ei.onal prices, and then sells this fertilizer to farmers at prices below the
FF procurement price. When domestic demand falls short of the amount that the
FF has guaranteed to purchase, the fertilizer remainin~ is sold by the FF in
cha international market at prices lower even than the far:n ourchase price.
The r.MF and FF procurement and release prices and the international
prices of rice, barley and fertilizer for recent years are shown in Table 1.
I/ tn 1979, the GMF purchased 1.7 milllon metric t~ns of rice, 31 percent ~f
Mtfona1 production, 11nd ton percent oF. marketed 1turplus of bulev.
Table I: Prices of Rice, Barley and Fertilizer
Crop Rice Rice elf Barley Barley elf Fert i Uzer Fer I. t l izer cif
Year Purchase Selling ·Price Purchase Selling · Pr lee Purchase Selllng Price
Price Price of Rice Price Price of Price Price of
Barley Fertilizer
1977 330273 319513 n.a. 190908 187805 148588 n.a. 103356 69212
1978 392277 338338 n.a. 238471 194379 87604 n.a. 104156 81796
1979 486860 432125 223000 267062 195255 90024 129000 106717 82280
(77586)
1980 638318 540086 343000 303472 221735 10161.0 187055 122916 122280
(118750)
n.a.: Prices not available.
Note: For rice and barley, the prices are for polished grain. (;'I
Fertilizer purchase price ls a quantity weighted average of the prices of urea,
potash, phosphate and three complex fertilizers.
Sources: Selling prices of rice and barley: Annual Report oQ the Price Survey, EPB.
Selling price of fertilizer: Report on the Results of Production Cost Survey
of Agricultural Products, HAF.
Purchase price of fertilizer, EPR.
elf price of fertilizer: Anderson (1981), with prices provided by EPR in parenthesis
Jtf price of rice: GMF
elf price of barley: Anderson (1981)
- 4 -
The differences between government purchase and release prices, as well as the
cost of processing and storing the grains and fertilizer, have left both t~e
Q-!F and FF ~ith substantial deficits-in recent years. Tables 2 and 3 show the
mark~d rise in Grain Management and Fertilizer Fund deficits. At present, the
government of Korea wishes to reduce the GMF and FF deficits through changes
in the rural procurement and urban release prices of rice and barley and the
sale price of fertilizer. lf
As expenditure on rice and barley accounts for approximately 30
percent of an average urban household's expenditure on food and 50 percent for
that of an average rural household, the government's pricing of grains has a
·significant effect on households, as consumers, in both sectors. Y Farm
households are affected additionally, as producers, by both government grain
and fertilizer prices. In 1979, the average farm household produced 3700 kg.
of unhulled rice and 990 kg. of unhulled common barley; sales of the two
grains accounted £or 70 percent of the farm's agricultural gross receipts. In
addition, the average farm used over 800 kg. of gove1·nment fertilizer in crop
production, amounting to 11 percent of the farm's agricultural 1.1anagement
expenditures. Thus, any change in the government's pricing of grains and
fertilizer is likely to affect the welfare of l:ousebn"..ds in both sectors, as
consumers, and is likely to have an additional affect on the we .. ~are of rural
households, as producers.
l/ Because the government is under contract with fertilizer producers, it is
assumed that the ~overnment purchase price of fertilizer ma? not be changerl
during the time period of the analysis.
Z/ Information on urban households ls from issues of the Family Income and
Expenditure Survey, Economic Planning Board. Information on farm households
is from issues of the Farm Household Economic Surve:·, ~inistry of Agriculture
and Fisheries (MAF), and from the Production Cost %r·•ey.
-s-
Table 2: Deficit in the grain Management Fund
Year Rice Barley Other Subs:dy Total
Grains fo,'.
Wheat
Flout
1970 4 28 4 28
1971 (51) 45 6
1972 (49) 61 4 .6 22
1973 (9) 88 10 165 254
1974 327 356 19 548 1250
1975 163 220 7 546 936
1976 197 286 5 15 503
1977 219 433 (2:1) 631
1978 1540 145 (94) 1591
1979 1851 285 (49) 2087
1980 1400 1068 (51) 2417
Total 5592 3015 (160) 1280 9727
-
Note: Parenthesis denotes a surplus.
Source: XAF, Food Grain Policy Bureau.
Table 3: Deficit in the Fertilizer Fund
Year 1979 1980 1981
Deficit 483 1257 1677
Cumulated 1715 2972 4649
Deficit
Source: MAF
III. THE TWO METHODS
'.1ul ti-market Analysis
The multi-market approach is developed from a microecononic base
describing consumer and producer behavior. Let the indirect utility function
of a representative household be:
V = V (p, y)
where pis a vector of consumer prices and y is full income and may be
expressed as:
y • A + wT + " (q, r, K)
where A is unearned income, w is the wage rate, T the stock of time available
to the househ~ld, and ff is profit from the household's agricultural
enterprises written as a function of p~oducer prices (q), input prices
including wages (r), and fixed factors (K).
The compensating variation (E) for any given change in selec·,ed
consumer and producer prices may be obtained from:
o o l . l
v(p , y) • v(p , y + E) -1-
where the superscript O
indicates base values and the superscript 1 denotes
final values. Thus, E measures the payment that is required to keep the
individual as well off with the new price regime as he was with the old
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regime. The-forms for the indirect utility function and the profit function
used in the Kor~a model and the implied expression f;)r conpensating variation
are described in Appendix A.
The pr~fit and indirect utility functions allow the derivation of
output supply, input demand and consumer demand. These functions can be
aggregated for all household groups to arrive at market demand and supply
functions. Markets clear according to various institutional arrangement1. In
the specific case of Korea, the prices of high-yielding variety (HYV) rice,
barley, and fertilizer are set by the government, any imbalance between
domestic supply and demand being eliminated by means of international trade.
The price of traditional rice, however, is determined within the model by the
interaction of domestic supply and demand.
The microeconomic foundations of the model and the market-clearing
conditions allow the analyst to examine the consequences of seve~al
interactions. Toes~ arise from:
substitution possibilities in consumption,
substitution possibilities in production,
input - output linkages,
the income effect of a change in profits on consumer demand, and
- price endogeneity.
The effects of these interactions are fully captured in the multi-market
model- Their presence affects predictions concerning the effect of price
changes on production and consumption as well as on compensating variation
through changes in farm profits and through induced changes in consumer
prices.
The calculation of the overall impact of pricing policy on production
and consumption allows an assessment of the implications for government
- s-
revenue. In particular, for the Korea exercise, government revenues can be
~here R is government revenues, Si is the marketed surplus of the i th crop or
sales of domestically produced fertilizer, Mi is the quantity of imports of
the 1 th item, and p: is the c.i.f. price of the i th item. The change in
government revenue (6R) resulting from changes in controlled prices is then
simply the differences in revenue under the old and new price regimes:
-2-
In this calculation, full allowance is made for the general equilibrium
interactions noted above.
To complete the an .• lysis, it is necessary to derive a measure of
efficiency gain. From aquations 1 and 2, the ~hange in welfare
(tM) associated with any change in producer and consumer price is:
where n- th group.
_, is the m1mber of households in the j t:,.W meas•1res the
change in real income to the economy. lJ If t;.W is positi·.re, welfare haR
increased. Equations 1, 2 and 3 comprise the normative componenc of the
analysis. These equations are us2d in the subsequent comparison of the two
lJ See Zabalza (1982).
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approaches. In addition, ~e report the effects of changeq in pricing policy
on production and c0nsumption when full allowance is made for the ~arket
interactions noted above.
Single-market Analysis
We now want to derive a similar set of measurP.s for a single-market
analysis. Starring with ecp.~ati on 1, the true measure of comoensating
variation, Appendix B identifies the assumptions required to arrive at th~
standard, single-market approximation associated with consumer surplus
analysis. This procedure yields tht.? following approxi.mation:
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where !)CS i is the change "in consumer surplus arising from changes in the
price of HYV rice and barley and ~S is the change in producer surplus
i
arising from changes in the prices of the same crops and fertilizer.
In arriving at this !pproximation, several assumptions are
required. The first bea~s solely on the normative analysis. A general
expression of welfare change can be derivP.d that requires only the assumption
of approximate constancy of the marginal utility of income. To implement this
measure, however, it would be necessary to allow for all the market
interactions and interdependencies associated ~ith the multi-market
analysis. To arrive at a single-market analysis, it is necessary to eliminate
these interactions. Such elimination will affect bo:h the notmativ~ and the
positive analyses. In particular, for the single-market analysis, all induced
price changes are ignored and all cross-price effects arising from changes in
controll•~d ;>rices are lgnot·ed (see Appendix B).
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As a ·result of these aPsumption, changes in ccnsumotion and
production predicted ~y the s in_gle-market model will differ fror.i those of the
multi.:..market model. It follows that single-market predictions of changes in
government revenues (see equation 2) and changes in welfare (see equation 3)
will also differ. These differences are explored in Section IV.
IV. COMPARISON OF RESULTS
Estimation
For the multi-market approach an AIDS consumer demand system and
Cobb-Douglas profit functione were estimated from cross-sectional, household
data. For the single-market approach, however, linear demand and supply
curves were estimated from "data" generated by the multi-market model. The
intention here is to duplicate the behavior of an analyst applying the single
market approach. We have, therefore, assumed that the analyst is confronteJ
with a set of historical "observations" on consumption, production, and
prices. These observations are derived from tne multi-market model by setting
government-controlled prtces and reading off the associated levels of
production and consumption. In this way, the historical "data" for the
s'.ngle-marke~ analysis incorporate fully all the interactio"s and market
inde?endencies of the real world as capt~red in the multi-market model. The
single-market analyst is then assumed to run a series of linear regressions
relating consumption or production to own-price only. This procedure
introduces two types of error. First, the true relationship between quantity
and price is unlikely to be linear. And second, the analysis fails to control
for changes in other important va~iables. This way of defining the single-
market approac~ nas the advantage that we avoid issues concernin~ the ability
of the multi-market model to capture reality. The multi-market model is
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assumed to be a faithful reflection of reality so that differences between the
results of this ~odel and those of the single-market analysis ari~e s0lely
from the two so~rces of error noted above. The l~near regression results are
reported in Appendix c.
Positive Analvsis
The overall significance of the difference between the two app,..oachl?s
for estimates of production and consumption can be seen in Table 4. Note that
the single market mo~el captures accurately changes in consumption and
production expected to accompany changes in the rural price of HYV.
Differences occur, however, for estimates of traditional rice production and
fertilizer use. These differences between the models' estimates are due
primarily to three of the interactions present in the multi-market model:
input-output links, substitution in production and price endogeneity •
.
The important input-output linkage is that between output price And
fertilizer use. Change in fertilizer price has only a small impacc on HYV and
barley production (not shown in Table 4), but changes in commodity prices have
significant effect on demand for fertilizer. For example, a 30 percent
reduction in rural HYV price reduces fertilizer use by 31 percent. This
cha.nge in fertilizer use is not monitored by the sin~le market model.
Further, the multi-market model's incorporation of substitution in
production proves to be important. A reduction in the rur~ 1 HYV subsidy
causes farmers to switch out of HYV production and into that of traditional
rice. While the single-market model capturas the reduction in HYV production,
it fails to predict that, simultaneously,_ traditional rice production
increases. F,Jr example, a 30 percent reduction in HYV rice results in a l 5
Table 4
Predictions of Conqumption and Production
Percent Change in ?rice of:
Rural HYV Fertilizer All Prices l/
Percent Effect on: Z/ -10 -30 10 30 10 30
HYV Production -TI:7 ~ - 5 -=cr. 7 -=r.9 -To.1 -5o.7
s~ -15.9 -47.7 0 0 -15.9 -47.7
Traditional Rice Production ~ 4.6 15. 1 0 -0 .1 5.6 18 .8
SM 0 0 0 0 0 0
Use of Fertilizer MM -11.3 -31.4 -9.9 -24.8 -22.S -63.3
SM 0 0 -13 .4 -40.0 -13.4 -40.0
Rural HYV Consumption MM 1.3 10.3 0 -0.1 3 .1 9.6
SM 3.4 10.1 0 0 3.4 10 .1
1/ Prices are moved in the direction required to reduce the deficit. That is
.rural HYV and barley prices are reduced and urban HYV, urban barley and
fertilizer release prices are increased.
y Base values for the analysis (in 1000 metric tons) are: HYV production -
3577.1, traditional rice production - 2110.8; Fertilizer use in barley and
rice production - 882.9; Rural HYV consumption - 722.3.
3/ ~1 - multi-market analysis; SM - single-market analysis.
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percent increase in traditional rice production. This has further effects
~hich are lost in the single-market model. In order for the traditional rice
m~rket to clear, the increase in supply of traditional rice must be matched by
an increase i.t demand, which is brought about by a fall in traditional rice
price. Changes in the price of traditional rice, endogenous in the multi-
market model, then affect rural and urban consUtnption, farm profits and rural
and urban welfare. In the single market model, all of these interactions are
lost.
~formative Analysis
Differences in the two approaches' estimates of change in government
revenue, sector welfare and efficiency can be seen in Tables. Note that the
single market model, in capturing accurately changes in production and con-
sumption of grains given changes in the rural price of HYV, provid~s estimates
of deficit changes which are not quantitatively different from those of the
multi-market model. For example, the single market model estimates that a 30
percent reduction in HYV price will be accompanied by a 100 percent reductior.
in the government deficit, while the multi-market model predicts a 93 percent
reduction in the deficit. The small difference in these estimates arises
because of the input-output linkage present in the multi-market model:
ignoring the reduction in deoand for fertilizer when rural HYV price is
reduced, the single-market model overestimates the deficit reduction. 1J
1J Fertilizer not sold in the rural sector must be exported at a price ~ven
lo~er than rural release price,
Table 5
Predictions of Welfare Gains and Losses
Percent Change in Price of:
Rural 1-{YV Fertilizer All Prices ti
Percent Effect on: 2/ -10 -30 10
.30 10 30
Government Budget Deficit MMY -42.4 -92.6 -4.5 -11.8 -80. 7 -184.7
s~ -46.3 -1on.2 -1.8 -3.5 -81.5 -19().6
Average Rural Welfare MM -2.7 -7.5 -0.1 -0.3 -3.3 -8.8
SM -0.8 -1.5 -0.1 -0.2 -1.2 -2.2
Average Urban Welfare MM 0.2 0.5 0 0 -0.2 -0.3
SM 0 0 0 0 -0.2 -0.7
Efficiency Gain MM 1,356 2,965 144 381 2,591 5,834
(in 100 million won)!:./ SM 1,685 3,242 58 112 2,650 6,163
l/ Prices are moved in the direction required to reduce the deficit. That is
rural HYV and barley priees are reduced and urban HYV, urban barley and
fertilizer release prices are increased.
21 Base values for the analysis are: Government Budget Deficit 324~ hundred
million won; Average Rural Real Disposable Income: 29900 won: Average
Urhan Real Disposable Income: 23900 won.
1/ MM - multi-market analysis; SM - single-market analysis.
!:./ USS m 484 won in 1979.
- lS -
The single-market model does not fare as well in predicting the
change i~ deficit ex?ected to accompany a change i~ fertilizer price. This
occurs for two reasons. First, in overestimating the reduction in demand for
fertilizer whe~ the fertilizer price is increased, the single-market model
underestimates government savings. In addition, an increase in fertilizer
price reduces both barley and HYV production, which results in a smaller rural
subsidy. While the multi-market approach models this interaction and the
consequent government savings, the single-market a?proach ignores both. JJ
Similarly, one of the interactions present in the multi-market model
is partially responsible for differences in the approaches' estimates of
welfare change. The single market model, failing to capture the effects of a
change in HYV price on the traditional rice market, underestimates rural
welfare loss. Reduction in the rural HYV price results in reduction of the
trt:o~.itional rlce price, which causes crop profits and rural welfa·re to fall
farther than they otherwise would have. For the same reason, the single-
market model cannot capture the increase in urban welfare which results from
the decrease in traditional rice price.
The endogeneity of the traditional rice price is the first of two
reasons why the models' welfare measures differ. The second is due to the
difference between the approximations of welfare change employed by the
models. Sl)ecifically, the multi-market model's welfare estimate al)!)roximates
compensating variation, and therefore approximates the area beneath a Hicks:an
compensated demand curve. The single-market models' welfare estimate is that
1/ While a 10 percent increase in fertilizer price reduces HYV production b~•
only 1 percent (25 thousand metric tons), this results in substantial govern-
ment savings. On each ton of HYV rice imported rather than purchased do~esti-
cally, the government saves 152000 won.
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of change in consumer surplus, or the area beneath a Marshallian demand
curve. 13elow i:1itial equilibrium price, the Ricksian der.tand curve lies i!lside
the '.larshallian demand curve for a normal good. This re.suits in a single
market model overestimation of welfare ~ai!l when rice and barley prices
fall. This error, which only affects the triangle, is more than outweighed by
the failure to allow for the price endogeneity of traditional rice.
The differences in the approaches with respect to deficits and
welfare measures carry over to estimates of efficiency gain. For example,
when the rural HYV price is reduced 30 percent, the single market model
estimates an efficiency gain which is 28 billion won larger than that of the
multi-market model. The reasons for this difference are two-fold. First, the
single-market model overestimates deficit reduction. This accounts for most
of the difference between the estimates (25 billion won). Also, the single-
market analysis consistently overestimates gain to consumers when prices fall,
and underestimates loss to producers. lf
V. AN ALTERNATIVE APPROACH
The preceeding analysis reveals that in the Korea case only certain
interactions and market interdependencies prove quantitatively significant.
substitution possibilities in production coupled with price endogenity and the
lJ ~1ote that, in failing !'o take into account the effect of a decrease in
trarlitional rice price, the sin~le market model underestimates loss to
producers. Because at the same time it underestimates gain to rural and urban
consumers, this insufficiency of the sin~le mar~et appro~ch has little effect
on the estimate of efficiency gain.
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dependence of fertilizer demand on output price are quantitatively il!lportant
interactions. 0n the other other hand, substitution poss~bilities i~
consumption and the "profit" effect prove less important. Had one possess·ed
this information in advance, it would have been a relatively simple matter to
incorporate the major interactions within the fram~work of consumer surplus
analysis. We demonstr.ate this point below, but first we examine the question
of how, in the absence of a model, one might begin to identify those
interactions which warrant inclusion.
Testing for Interactions
In principle, one can link the change in any variable of policy
interest with the change in any given policy instrument. The variables that
may be of policy interest include production, consumption, and fertilizer use
.
(positive variables), and government budg~t deficits, urban and rural welfare,
and deadweight loss (normative variables). The possible policy instruments
are the urban and rural prices of HYV rice, the urban and rural prices of
barley, and the farmgate price of fertilizer.
Consider first the positive variables. Any of the interactions noted
in Section III could be of importance. Let us examine the profit effect, that
is, the effect of a change in the price of an output or input on profits and
thence on total household income and consumer demand. In particular, do we
think that a change in the price of fertilizer will work through profits and
income to affect demand for, say, HYV rice? First, we note that fertilizer
costs are only 6.6 percent of average farm profits and that farm profits are
only 13 percent of average household full income. It follows immediately that
any change in the price of fertilizer is unlikely to have a lar~e impact on
householri full income. Second, we know that income elasticities of demand for
~ 18 -
staples are usually ~ess than one so that, whatever the percentage change in
household incone, the percentage change in consumption of MYV rice will be
even smaller. JJ EKperimentation with plausible numbers reveals quickly that
this interaction is unlikely to be i~portant and can, therefore, be dropped.
This is not to suggest that this effect will be unimportant in other
contexts. In fact, there is considerable microeconomic evidence to suggest
that it often will he important. ~evertheless, in the Korean context, it
seems safe to ignore this particular-interaction, not only for changes in the
price of fertilizer but also for changes in output prices.
Now let us turn to input - output linkages. The single-market
analysis reveals a substantial reduction in•the production of HYV rice as its
price is reduced. Since HYV rice is a major user of fertilizer, a reduction
in production can be expected to have significant implications for fertilizer
demand. It follows that _the price of HYV rice may be an importan.t determinant
of fertilizer demand. On the other hand, since fertilizer accounts for only a
small part of total costs, a change in the price of fertilizer is unlikely to
have a big impact on output. Y Simple linear regressions of fertilizer
l/ For marginal changes, the elasticity of HYV consumption with respect to
the price of fertilizer equals the elasticity of HYV consumption with respect
to income (<1) times the share of profits in total income (very small) times
the ratio of fertilizer cost to net profit (also small).
1:./For a marginal change, the elasticity of the demand for fertilizer with
respect to the price of the output equals the elasticity of output with
respect to the price of fertilizer weighted by the ratio of the value of
output to the cost of fertilizer. Thus, even if the elasticity of output with
respect to the price of fertilizer is small, the elasticity of fertilizer
demand can still be large if the ratio of the value of output to the cost of
fertilizer is large.
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demand on own-price and the price of HYV, and of HYV on own price and the
price of fertilizer, reveal the diffe~ent degrees of interaction clearly.
In the above cases, one can rely on information about shares - the
share of profits in full income, the share of fertilizer costs in the total
value of output - to guide judgements about the importance of particular
interactions. For substitution possibilities in both consUl!lption and
production, howe,er, there is little one can do other than make judgements
about the size of the cross-price elasticities. With respect to consumption,
demand studies often reveal relatively small cross-price effects. While this
can not be treated as a universal conclusion, we, nevertheless, choose to
ignore substitution possibilities in consumption in the remainder of the
analysis.
On the production side, however, it is worth investigating the
ultimate destination of 'the resources released from HYV production. Since
barley is grown in a different season, it cannot be considered a production
substitution for HYV rice. Traditional rice, on the other hand, is an obvious
substitute. Furthermore, for the multi-market analysis, the price of
traditional rice is treated as an endogenous variable. This is not a result
of the model but an input into the construction of the multi-market model.
The information that led to this decision was derived from outside the model
and may, therefore, be assumed to be available to the single-market analyst.
A siople linear regression of production of traditional rice on the price of
- 20 -
HYV rice does, indeed, reveal an important association (see Appendix C). ]J
Accordingly, in the augmented singlc-:nark~t approach presented belri;;, this
interaction is incorporated.
The interactions that prove imprrtant for the positive analysis may
or may not prove important fo-r the normative analysis. The presence of
substitution possibilities by themselves is not sufficient to cause serious
errors in the single-market approach. Consider, for example, the combination
of strong substitution possibilities between HYV rice and traditional rice and
the price endogeneity of traditional rice. The im~ortance of these
interactions for the normative analysis depends on the object of interest. If
one is interested in household welfare, then these interactions are especially
important because they involve an induced change in the price of a commodity
that plays a significant role in the incomes of rural households and in the
expenditures of both rural and urban households. Had the price change been
small (which it was not) or had the commodity whose price changed been of
little importance in consumption and production (which it was not), this
interaction would have proved unimportant for the normative analysis. As far
as household welfare is concerned, therefore, the only relevant interactions
are those that lead to large induced price changes for major consumption or
production items.
Now let us examine the consequences of· the same interaction for
measures of government revenue. Since the induced price ch~nge occurs in a
lf For a marginal change, the elasticity of traditional rice output with
respect to the price of HYV rice equals the elasticity of traditional rice
output with respect to its own price times the elasticity of the price of
traditional rice with respect to the price of HYV rice. This latter
elasticity (the general equilibrium effect) is one in the Korean case. This
is probably unusually large so that this effect may often be much less
important than it is here.
- 2l -
market which is free of ~overnment inter,,ention - traditional rice is neither
taxed 11or subsidized - government r't!v,mue is 1Jn,.1ffected by :l1is i:tteraction.
If the primary concern, therefore, is with govern~ent revenue, this particu!ar
interaction could be ignored and one would focus one's attention on changes i~
production or consumption of items that are heavily subsidized or taxed. In
the·Korean case, this implies that it is more important to worry about
interactions that affect fertilizer use (heavily subsidized) than those that
affect production and consumption of traditional rice.
Finally, if the focus of attention is deadweight loss, then cne
should concentrate on changes in consumption and production that occur in
distorted markets. Again, in the· particular case examined here, this would
suggest a focus on the use of (heavily subsidized) fertilizer. Major price
changes occurring in non-distorted markets (traditional rice, for example) do
not affect deadweight loss.
An Augmented Single-Market Approach
To demonstrate these points, we augment the single-market analysis of
Section IV to take into account those interactions which an analyst might
identify as important for positive and normative analysis: the response of
fertilizer demand to change in a controlled output price, and the response of
traditional rice production and consumption to change in rural HYV price.
Table~ presents a compariso" between the multi-market and an augmented
single-market model's est:imates of the changes in production and consumption
expected to accompany change in controlled prices for those cases vher• the
single-market analysis was clearly deficient. Note that the augmented single-
muket model effectively cloH~ the ~•ps betweei, the multi-riarl(et ~odel 's
estimates and those of the single market model presenttd 1~ S.ction tV.
- 22 -
The significance of thes..: changes for normative anal~1sis can be seen
in Table 7. Taking into account the effect of change in out?UC price on input
demand brings the single market ·deficit estimates more into line with those of
the multi-market model's. Note, however, that in failing to take into account
the effect of a change in fertilizer price on barley and HYV production, the
single-market model continues to underestimate the change in the deficit
resulting from increase in fertilier price. (See Foot-no ... e 1, pa 15 e 15.)
Further, incorporating the effect of change in the rural HYV price on the
traditional rice market substantially improves the single marlcet .::i,del 's
estimates of rural and urban welfare change. The remaining differences
between the model's estimates of welfare change are due to the fact that the
single-market model approximates welfare change by measuring the area beneath
Marshallian demand curves. Hence the gain to rural consumers when HYV and
. .
.barley prices are reduced continv.es to be ovet !Stimated by the single-mark.et
model. Note, however, that the changes incorporated in the single-mark.et
analysis have an almost negligible effect on estimates of efficienrs ga~n.
Tabliit 6
Predictions of Consumption and Production
Percent Change in Price of:
Rural HYV Fertilizer All P:ices lf
Percent Effect on: lJ -10 -30 l9.. -
30
-
10
-30
Traditional MM1,I '• .6 15.l 0 -0.1 5.6 1a.s
Rice Production SM3/ 0 0 0 0 0 0
As?'JJ S.4 16.l 0 0 S.4 16.1
Use of Fertilizer !iM -11.3 -31 .4 -9.9 -24.8 -22.s -63.3
SM 0 0 -13.4 -40.0 -13.4 -40.1)
ASM -9.6 -28.7 -1.s -22.0 -23.1 -69.2
l,I Prices are moved in the direction required to reduce the deficit. That is
rural HYV and barley prices are reduced and urban HYV, urban barley.and
fertilizer release.prices are i~creased.
JJ Base values for the analysis (in 1000 metric tons) are: HYV production -
3577.l, traditional rice production - 2110.8; Fertilizer use in barley and
rice production - 882.9;
1/ MM - multi-market analysis; SM - stngle-market.analysis; ASM - augmented
single-market analysis.
-;;~-
Table 7
Predictions of Welfare Gains anti Losses
Percent Chan~e in Price of:
Rural HYV Fertilizer All Prices 1/
Percent Effect on: 2/
HYV Production M~ef
-
-10
-42.4
-30
-92.6
10
-4.S
30
-11.8
10 30
-184.7
-80.7
sr:J./ -46.3 -·100.2 -1 .8 -3.5 -81.5 -190.6
ASMlf -45.9 -99.2 · -2.3 -5.8 -81.1 -187.7
Average Rural Welfare MM -2.7 -7.S -o. 1 -0.3 -3.3 -8.8
SM -().8 -1.S -0.1 -0.2 -1 .2 -2.2
ASM -1.7 -4.2 -o. 1 -0.3 -2.1 -s.o
Average Urban Welfare MM 0.2 .0.5 0 0 -0.2 -0.3
SM 0 0 0 0 -0.2 -0.7
ASM 0.3 o.~ 0 0 o.o 0.3
Efficiency Gain MM 1,356 2,965 144 381 2,591 5,834
(in 100 million won) SM 1,685 3,242 58 112 2,650 6,163
ASM 1,621 3,203 73 183 2, 86? 6,065
l./ Prices are moved in the direction required to reduce the deficit. That is
rural HYV and barley prices are reduced, and urban HYV, urban barley and
fertilizer release prices are increased.
1:./ Base values for the analysis are: ·Government Budget Deficit: 3246
hundred million won; Average Rural Real Disposable Income: 29900 won;
Average urban Real Disposable 23900 Income.
1/ MM - multi-market analysis; SM - single-market analysis; ASH - augmented
single-market analysis.
- 25 -
rv. CONCLUSION
0ur conclusions can be su~marized easily:
i) Single market analysis that fails to allow for interactions usually
encountered in the agricultural sector can yield misleading
predictions for both positive variables (e.g. the change in
traditional rice production following a change in the rural price of
HYV rice) and for normative variables (e.g. the change in the deficit
following a change in the price of fertilizer).
ii) Interactions that proved important in the Korean case are
substitution possibilities in production, the price endogeneity of
traditional rice, and the link between output price and fe.rtilizer
demand.
iii) A straightforward extension of consumer surplus analysis to
incorporate these interacttons yielded results reasonably close to
those of the multi-market model for the variables of interest.
This exercise suggests th,;.:: che anal;yst should be very wary of
results produced by a single-market/consumer surplus approach. If, for
reasons of time and resources, the analyst is unable to prepare a multi-market
model, considerable effort should be devoted to exploring the likely
consequences of omitted interactions and, where these prove significant, to
extending the analysis along the lines suggested in this paper. Finally, fro~
a research perspective, it would be extremely valuable to investigate whether
th~ interactions that proved unimportant in the Korean case can also be
expected to be insignificant in other situations,
- 26 -
APPENDIX A Compensating Variation
The indirect utility function consistent with the AIDS model employed in t~e·
multi-market approach is:
(1)
where income (Y) refers to full income and includes wage income, value of
leisure time, crop profits (rural sector only) and other income. Profits ar2
expressed:
(2)
for all crops (n), inputs (i), output prices (P) and input prices (W). (PI)
refers to the AIDS price index, which is a function of the prices of crops and
leisure.
From the indirect utility function (1), compensating variation, E, is
derived:
(3)
This measure of welfare change is exact, but provides useful information only
when the AIDS cost function is concave and strictly quasi-concave in prices.
As this is not true of the Korea AIDS cost function in the price range in
which simulation takes place, an approximation to welfare loss must be
employed. The approximation chosen here is change in real disposable income
deflated by the AIDS price index.
- 27 -
( 4)
(DY) refers to nominal full income minus the value of leisure.
~ote that this approximation is equivalent to compensating variation
provided two assumptions hold. First, it is assumed that demands are
hornothetic (i.e., Bn = o for all n). In addition, it is assumed that the
value of leisure is not affected by change in controlled or endogenous prices.
- 28.-
APPENDIX B: Consumer and Producer Surplus lJ
D~finirion of Compensating Variation
-1-
Differentiate l wrt all prices:
Example: For i th price,
-2-
(If producer prices are not affected, dy0 /dp0 • Q .• If consUt11er prices are
i
not affected,
By Roy's Identity, C
i
•
dE
0
-3-
0
~sumption_,!_ dv/dy1 ,:, dv/dy
0
-ci + dy /dp~ • dE/dp~ -4-
-l
Since E •
pl
J
Po
2 .... dE
dP +
pl pl
1J 2
Po
3 .... dE
dP -s-
Pl
0 po
2 .... dP l 1 po po
l 2
po
3 ••••
dP
2
2 ••••
lJ See Glaister (1974) for a similar argument.
- 29 -
l
+ •••• Pnd dE
dP
dP n
•••• Pn n
pl dy
Po Po ) ~
E = I
J
Po
C (P 1 2 .... y)
- dP
1
(Pl' - 2 •••• dp
l
.,
p .,
1
- Pn° C
1
(P 1 • • • •, p
n'
y) - dy
dPn
1
(p1 .... Pn> dp -6-
1 l 1
E .., - 6CS, (Pl' 00
•l ,
0
p2····> - ecs 2 (P 2' 0
p 2' p 1'
0
?3••··>
-7-
+ ty
Assumption 2
Set c~ 1 • o for all 1 where d? 1 , some arbitrarily small constant
Assumption 3
Assume independent price changes.
E .. - r6 . , Po.
csj ( P 1 o -1:j )
. , Pk + 6y -8-
.1 J
The change in money income (6y) is derived:
-9-
- 30 -
where (i) denotes each output whose price undergoes change and (f) denotes
fertilizer. ~oting that, from the profit function, d 1Ti/dp~ = x and
i'
differentiating (9) with respect to initial outp~t und input prices yie!ds:
dni
- --= - L X f i = - ,cf -10-
dP~ :r '
Expressing (9) as
~ 1
(Pl' P2,
1 • ·p~ ) ~
n dp -11-
dP
l1
and substituting from (10) yields:
-12-
Given that each x 1 denotes an output supply curve and xf denotes an input
demand curve, and again assumin~ independent price changes, we can express
t:.y as:
Compensating variation can now be expressed:
- 31 -
APPENDIX C: Regression Results
A data set for single market analyses was generated by simulating the
results of the multi-marKet model for 37 different sets of controlled
prices. For each simulation, a controlled price was changed by 5-30 percent
from its initial level. For 6 of the simulations, all controlled prices were
varied by 5-30 percent. OLS regressions were performed on this data set, and
the coefficients of these regressions were employed in the singl~ market
analysis of Section IV. All coefficients were significant on 95 percent
confidence interval.
Supply HYV = -2088.27 + 14.99 * Rural Price HYV (R 2 • 0.918)
Supply Barley = 1375.27 + 10.94 * Rural Price Barley (R2 - 0.993)
Demand Fertilizer .. 190.8.36 - 11.13 * Rural Price Fertilizer (R 2 • o•. 524)
Urban Demand HYV = 2904.05 - 2.48 * Urban Price HYV
Urban Demand Barley~ 213.15 - 0.4 * Urban Price Barley (R 2 • 0.360)
Rural Demand HYV • 1501.25 - 1.01 * Rural Price HYV (R 2 • 0.997)
Rural Demand Barley• 501.27 - 0.62 * Rural Price Barley (R 2 • 0.360)
In Section V, the single market model is augmented to take into
account the effect of rural HYV price on production and consumption of
traditional rice and ~he effect of rural HYV and barley prices on demand for
fertilizet. The following regressions were run on the same set of tUUlti-
- 32 -
market similation results, and the coefficients were employed in the au~mented
si~gle ~arket analysis of Section V. All coefficients were sig~ificant on a
95 percent confidence interval.
Supply Trad. Rice = 3249.75 - 3.02 * Price Rural HYV (R 2 = 0.967)
Rural Demand Trad. Rice= 953.99 - 0.62 * Price Rural HYV (R 2 = 0.99;)
Urban Trad. Rice = 2033.56 - 2.16 * Price Rural HYV (R 2 = 0.946)
Demand Fertilizer~ 172.61 - 6.68 * Rural Price Fertilizer
+ 2.2 * Rural Price HYV + 1.95 * Rural Price
Barley (R 2 = 0.987)
- 33 -
References
Braver;nan, Avishay, Jeffrey s. Hammer and Choorg Yong Ahn, "Government Deficit
Reduction and Alternative Agricultural Pricing Policies in Korea", CPD
Discussion Paper No. 1983-2 (revised), August, 1983.
Glaister, Stephen, "Generalized Consumer Surplus and Public Transport
Pricing", Economic Journal, December, 1974, Vol. 84, No. 336, pp. 849-
867.
Zabalza, A.~ "Cocpensating and Equivalent Variations, and the Deadweight Loss
of Taxation", Economica, August, 1982, Vol. 49, No.____, pp. 355-359.