Discussion Paper No.402
Economies of Scale in Raw Milk Production: Evidence fromJapanese Farm-level Data
Ayano SATO
Faculty of Law, Aoyama Gakuin University
Taiyo YOSHIMI
Faculty of Economics, Chuo University, Japan
Takatoshi ITO
School of International and Public Affairs, Columbia
University; NBER, the United States; and National
Graduate Institute for Policy Studies, JapanMay 2024

INSTITUTE OF ECONOMIC RESEARCH
Chuo University
Tokyo, Japan

Economies of Scale in Raw Milk Production: Evidence fromJapanese Farm-level Data§
Ayano SATO#
Faculty of Law, Aoyama Gakuin University
Taiyo YOSHIMI
Faculty of Economics, Chuo University, Japan
Takatoshi ITO
School of International and Public Affairs, Columbia University; NBER, the United States; andNational Graduate Institute for Policy Studies, Japan

Abstract: Raw milk production in Japan is subject to various restrictions, including mandating sales to agricultural
cooperatives, limits to inter-regional mobility of raw milk, and differentiated prices of raw milk for different dairy
products with no say from raw milk farmers. These institutional barriers contribute to inefficiency in production. This
paper estimates a translog cost function of raw milk production from individual Japanese dairy farms. Using newlyavailable farm-level data from 2008 to 2017, we examine the degree of scale economies in raw milk production. Ourfindings indicate the following: (i) Economies of scale do exist in raw milk production in Japan. The total cost
increases only by 0.67% for a 1% increase in production. (ii) Substitutability exists between labor and equipment,suggesting the potential for improving productivity by introducing more mechanization (automation). Simulation
analyses, based on the estimated cost function, are conducted to measure the impacts of removing institutional
rigidities (multiple prices; regional division of markets) on the profitability of dairy farms by farm scale and region.
Results show that removing institutional rigidity tends to increase the profitability of Japanese dairy farms in general,but the magnitude of the effect impact varies across farm scales and regions.
Keywords: Dairy industry; Farm-level analysis; Agricultural policy; JapanJEL Classification: Q12; Q16; Q18§

We would like to thank Takamune Fujii, Kota Minegishi, Shinsuke Uchida and the participants at 2022 spring meeting ofJapanese Economic Association for their comments. All remaining errors are our own.
#
Corresponding author: Ayano Sato; Address: 4-4-25 Shibuya, Shibuya-ku, Tokyo, 150-8366, Japan. Tel: +81-3-34098627; E-mail: ayano.sato@aoyamagakuin.jp.
11 Introduction
Japan’s raw milk production has been declining. This decline is often explained as an inevitabledecline in milk consumption. However, raw milk can be used to produce more dairy products.
Moreover, drinking milk, if high quality with low costs with skillful marketing, can be exported. A
drop in milk consumption can be explained partly by the decreasing population and partly by highcosts due to heavy regulation on production and distribution. High production costs make Japanese
dairy products internationally uncompetitive and “protection” from imports of dairy products, such asbutter, has been maintained.
According to the Statistical Survey on Milk and Dairy Products (Gyunyu Nyuseihin Tokei
Chosa), raw milk production declined from 8.65 million tons in 1997 to 7.60 tons in 2021, a 12.1%
drop in 24 years. During the same period, the number of raw milk-producing cows declined from 1.2
million to 0.8 million. The number of dairy farms decreased from 39.4 thousand to 13.8 thousand, anapproximately 65% drop. The number of dairy farms has declined more than the production volume,
suggesting that smaller farms in terms of cows have exited. This exit of smaller farms is the firstsuggestive evidence of scale economies in raw milk production. One region, Hokkaido, the region withthe highest raw production in Japan, has more large-scale farms than other regions. If various
regulations are preventing farmers from increasing their raw milk production, taking down regulations
will make the dairy industry as a whole become more prosperous in Japan.
Raw milk production and distribution in Japan is regulated by the Ministry of Agriculture,
Forestry and Fisheries (MAFF). Major regulations are in three categories: First, Japan is divided into
ten regions, each of which has only one “designated raw milk producer organization” (the producer
organization hereafter), or a regional agricultural cooperatives federation. Shipment of raw milk acrossthe regional boundary is extremely limited unless an importing region requests such sales. Moreover,there is a monopsony distribution channel from dairy farms to wholesalers, and only a monopoly
wholesaler in each region can sell milk, with the limited exception of independent farms’ sales. Second,2

within each of the ten regions, the producer organization functions as a monopolistic intermediary tocollect raw milk from almost all dairy farms in the region and to deliver that to dairy products
manufacturing firms, that produce a variety of dairy products, such as drinking milk, butter, cheese,and skimmed milk powder from raw milk. Third, the producer organization negotiates prices of raw
milk sold to dairy products manufacturing firms. Still, prices of the same raw milk differ dependingon which dairy products the raw milk is used. For example, raw milk for drinking milk commands thehighest price, while raw milk for cheese and butter is priced lower. Then, the payment for the raw milk
from the producer organization to each dairy farm is based on the average sales prices for different
dairy products. This average price is designated as the “pooled price” that the producer organization
calculates from the raw milk volume used for each dairy product reported by the dairy processing firms,
added to the subsidy from the government. The subsidy is supplied only to the usage of raw milk fordairy processing products other than drinking milk. These regulations combined work toward
preserving the inefficient production of raw milk.
Multiple prices exist for one good, raw milk, for different dairy products and regions. If there
is surplus raw milk in one region, raw milk can be discarded without compensation, instead of being
shipped to other regions to cause price competition. Therefore, depending on the product mixes, thepool price of raw milk may vary from one region to another. In Hokkaido, which hosts many dairy
processing firms, there is more production of lower-priced dairy products; therefore, the pooled priceis lower. The pooled prices for other regions are higher. Since the shipment of raw milk across theregional boundary is restricted, no arbitrage works. Therefore, Hokkaido farmers suffer from lower
pooled prices of raw milk due to their locations. Their lower production costs achieved through scaleeconomies are punished instead of rewarded because of these barriers. Another barrier exists forimporting butter and other dairy products under government quantitative control. Imports of theseproducts are allowed only for the Agriculture & Livestock Industries Corporation (ALIC), and allimported butter and other products distributed in Japan pass through ALIC before being wholesaled to3

dairy manufacturers. If the import volume exceeds the current access volume (137 thousand tons), a
high-rate tariff of more than 100% will be added to the imports, virtually restricting the import volume
to 137 thousand tons. We do not explicitly consider this issue. Nevertheless, this import restriction isan essential background of this paper since it discourages innovation among Japanese dairy productmanufacturers.
These regulations and rigidities are well-known among agricultural economists in Japan.
However, how these rigidities affect the efficiency of raw milk production and profitability of dairy
farms yet to be rigorously analyzed, mainly due to the availability of microdata. The paper’s novelty
is to utilize data from large-scale samples of individual dairy farms (the farm-level data). The farmlevel data are collected for the “Milk Production Cost Statistics” (the milk production cost statistics
hereafter). The statistics for the period 2008–2017 became available to the authors with special
permission for academic use. 1 The data are used to estimate a translog cost function of raw milk
production. In addition, the study will be carried out to simulate the impact of hypothetical institutionalchanges. In particular, we examine whether the Japanese dairy industry can improve productivity bypromoting mergers of small- and medium-scale farms into large-scale farms, which may be enforced
if regulatory barriers such as restrictions on cross-border shipment of raw milk among the ten regions.
The scale of dairy farms is smaller in Japan than in other countries, such as Australia and New Zealand,
which have strong dairy industries. For example, according to the Dairy Farm Monitor Project (DFMP)
of Daily Australia, which conducts a comprehensive survey of the Australian dairy industry, theaverage number of cows per farm in Victoria, Australia, in 2019–2020 was 415.5.2 According to a
MAFF Survey of Agricultural Management Statistics, the average number of cows per farm in theJapanese dairy industry in 2019 was 58.7, just one-seventh the figure reported for Victoria.
In addition, our analysis uncovers the potential for substitutability among factors of production.

MAFF provided farm-level data to conduct this study. In this paper, we independently edit the raw information for our
research purpose.
2
Results of the DFMP survey are published on the following website.
(https://www.dairyaustralia.com.au/dairytas/industry-statistics/dairy-farm-monitor-project)
4
1

We focus on the substitutability of capital and labor in raw milk production and discuss whether
Japanese raw milk production can achieve increased productivity through the promotion of automation.
In the dairy industry in Japan, labor shortages and a lack of successors have become acute. Identifying
the extent to which labor can be replaced by machines is an important policy issue. According to
Yoshimi and Sato (2021), there are significant differences (based on a test of difference in means at a
1% level of significance) among regions in the ratio of farm equipment costs to production costs forJapanese dairy farms: 3.9% in Hokkaido (30,000 yen per milking cow) versus 2.9% in regions otherthan Hokkaido (26,000 yen per milking cow).3 The higher equipment costs, which are a result of more
capital investment, suggest the employment of labor-saving technology. By examining the differencesin productivity between more-mechanized farms and less-mechanized farms, we can infer changes in
the industries if and when hypothetical regulatory changes are made and when the external
environment changes.
Simulation analyses based on three scenarios will be performed using the parameters estimatedby the translog cost function estimation. First, we simulate how much farms’ profits would improve if
the allocation of factors of production were revised so that all farms could achieve cost minimization.
Recall that real-world production may not result from optimized production due to regulatory barriers.
Second, we simulate the total cost savings for Japan in a hypothetical case where the entire production
could be done at the largest farms only. The simulation analysis corresponds to a scenario that smalland medium-scale farms with relatively low profitability are consolidated (merged) into large farms totake advantage of scale economies. Third, focusing on the regulatory change, we conduct simulations
to measure the impact of introducing a uniform national pooled price on farms’ profit margins.
The rest of the paper is organized as follows. Section 2 surveys the existing studies in theliterature. Section 3 describes the raw milk production cost statistics which form the basis for the panel
data, as well as the cost structures for farms. In Section 4, we perform estimates of translog cost

Yoshimi and Sato (2021) use the same farm-level data as this study to examine the cost structures of Japanese raw milk
production.
5
3

functions to examine economies of scale and the elasticity of substitution among different cost items.
In Section 5, simulation analyses are conducted to derive specific policy recommendations. Section 6
concludes.

2. Literature
Earlier studies of the productivity of the Japanese dairy industry include Kamata (2011) on
Hokkaido dairy farms from 1995 to 2003. Sato (2019) examined the productivity of the Japanese dairy
farming industry. Fujii and Kondo (2001), using data on Hokkaido dairy farms from 1968 to 1994,
found that land rent and purchased feed prices had an important impact on in-house (self-) produced
feed production and grassland demand, and that expansion of a farm scale contributed to a decrease in
the average cost of raw milk production. However, all these studies used aggregate data published in
the Statistical Survey on Farm Management and Economy (Nogyo Keiei Tokei Chosa), which does notallow us to examine the heterogeneity among farms’ production cost structure. This study is uniqueand the first in the literature to focus on the heterogeneity of the farms, taking advantage of the newlyavailable microdata of individual farms.
In other countries, many studies have used farm-level data to examine the productivity of dairy
farms. Kompas and Che (2006) examined the efficiency of raw milk production using informationfrom 252 farms in New South Wales and Victoria, Australia, gathered in 1996, 1998, and 2000. They
showed that the critical determinants of differences in dairy farm efficiency are the type of dairy shed
used and the proportion of irrigated farm area. They also pointed out that dairy production follows
constant returns to scale. Neal and Roche (2019) examined the case of New Zealand. They identified
the top quartile of observations based on operating return on assets as a proxy for farms achieving theirpotential to compare with the remaining farms. They found that the greater profitability of the top
quartile was associated with greater pasture, greater self-feed crop, and greater production per cow.
Notably, greater profitability was not associated with greater use of imported feed.

6Other researchers focused more on a policy impact on the efficiency of dairy farms.4 De Frahan
et al. (2011) examine the impact of eliminating production quotas and increased income compensation
on farms’ production and income using information from 143 farms in the Wallonia region of Belgium
for 1996–2006 obtained from the Farm Accountancy Data Network (FADN) database. The FADN
database is frequently used in this literature. For instance, Cechura et al. (2021) examined the impactof abolishing milk quotas in the European Union (EU) member states on the productivity andefficiency in European milk production with the same dataset. They revealed that the main driver of
an increased trend in total factor productivity is the scale effect while abolishing milk quotas also has
a positive impact. Sidhoum et al. (2022) investigated the effects of European agri-environmental
schemes on farm-level eco-efficiency using the farm-level data of Germany, France, Italy, and theNetherlands from 2006 to 2011 obtained from the same database. They found a considerable
improvement in eco-efficiency for dairy and crop production. As an example of non-EU countries,
Kumar et al. (2020) used farm-level data from dairy farmers in India's Bihar state to investigate theimpact of the adoption of food safety measures on milk production and profitability of dairy farms. We
also aim to contribute to the literature by simulating the impact of several policy changes on Japanesefarms’ profitability.

3.

Data

3.1 Overview of the farm-level data and construction of a panel data
This paper presents analyses of panel data composed of farm-level milk production coststatistics. These statistics are compiled as part of the Agricultural Management Survey and Livestock
Production Cost Statistics conducted by the Statistics Department of MAFF. They are a core metric
generated by the Statistics Law for analyzing dairy farming in Japan. Article 13 and Article 61, Item 1
Many studies examined a policy impact on the dairy industry without using farm-level data. For example, Lips and Rieder(2005) conducted a country-level analysis of the impact of the abolition of raw milk quota in the EU. Klootwijk et al.
(2016) simulated the impact of a new manure policy in the Netherlands on farm structure, including profitability and the
distribution of inputs. They also focus on the policy impact on environmental variables such as nitrogen, phosphate
surpluses, and greenhouse gas emissions.
74

of the Statistics Law in Japan stipulate penalties for survey targets who refuse to report or report falsely.
The survey targets farms who keep at least one milking cow and sell raw milk. The data are determinedbased on a stratified sample survey. The purpose of the milk production cost statistics is to understandthe production status and cost breakdown of each farm, the financial conditions of agriculture workers,
and others. Each farm responds to a survey questionnaire that includes information on the volumes
and values of their main products, usually raw milk, by-products, and the cost of each expense item toproduce by-products. Other survey items include labor hours by operation and age of workers, volumes
and values of feed and other commodities, land area, buildings, and the number of vehicles and farmequipment owned, among others. These milk production cost statistics are the only available farmlevel statistics on dairy farms in Japan, and their reliability is high. We first construct an annual
unbalanced panel dataset based on the milk production cost statistics data from 2008 to 2017. The
number of farms which have been sampled at least once (for more than one year) during the sample
period of the farm-level data in question is 389 in Hokkaido and 441 in other regions. Table 1 shows
the number of farms per year of sampling as well as the number of farms which have been sampled
for two consecutive years and the rate of farm replacement each year. The number of farms sampled
in all sample periods is 213, representing about a quarter of the farms in the sample.5 Table 2 shows
the mean, median, and standard deviation of the number of cows and raw milk yield kept by thedesignated group for the entire sample period. 6 Because of the design of the statistical survey inquestion, Hokkaido accounts for about half of the total sample. The average number of cows andaverage raw milk yield are both about 1.7 times higher in Hokkaido than in other regions.

The review of sample farms is generally conducted two years after the census revision, which is done every five years.
The census was revised in 2010 and 2015, resulting in a higher replacement rate of sample farms in 2012 and 2017. For
other years, there were basically no changes to the sample farms, but some farms were replaced because of business closuresor other reasons.
6
Okinawa Dairy Cooperatives is the only applicable prefectural body in Okinawa Prefecture. Therefore, if the tabulation
results for the designated organization in question alone are posted, the possibility remains that individual sample farms
could be identified due to the small sample size. Accordingly, Table 2 lists the results for this designated organization as asingle group, the Kyushu Seinyuhanren.
85

3.2 Overview of Cost Structures
We use seven cost items that account for 85.9% of total production costs (not excluding byproduct value) in the milk production cost statistics: self-produced feed, purchased feed, labor (familylabor and hired labor), equipment (vehicles and farm equipment), buildings, land rent (land rent paid
plus imputed rent for owned land), and cow depreciation.7 The other items which make up the total
production costs include production management, seeding, bedding, heat and power, other materials,
veterinary fees and medicines, rent and fees, property taxes and public charges, interest paid, andinterest on equity capital. However, because these other cost items account for only a small percentage
of total costs, and because calculating unit costs for the purpose of estimating cost functions is difficult,they are dropped from the subsequent analysis and estimation.
Panel (a) of Table 3 shows the average cost, pooled price, and actual production cost breakdown(average values for the entire sample period; average cost and pooled price are per 100 kg of raw milk)
for the entire country (all samples), by herd scale (small farm group, medium farm group, large farmgroup), and by Hokkaido and other regions (i.e., “excluding Hokkaido”). 8 The pooled price for
Hokkaido is distinctively lower than in other regions, suggesting that raw milk in Hokkaido is used
more for producing daily products other than drinking milk than in the rest of Japan. In this study,
farms less than the first quartile are considered small farms, farms above the first less than the third
quartiles are considered medium farms, and farms above the third quartile are considered large farms,
based on the number of cows kept for the full year. Specifically, small farms are those with less than
By-product values are excluded from the overall production costs in the milk production cost statistics, but individual
cost items include the costs invested in the production of by-products. Therefore, if we use the total cost of production as
stated, we find a sample in which the total cost of the seven items used in this study exceeds the total cost of production.
To avoid this difficulty, the denominator used here is not the total input production cost as it is, but the total input production
cost excluding by-product value.
8
The most recent agriculture and forestry census conducted within the sample period of this study (2008–2017) is the 2015
one, and the sample extraction for the 2017 individual data is based on this 2015 agriculture and forestry census. Figure
A1 in the Appendix compares the 2017 sample of our panel data with the distribution of the number of cows kept in the2015 Census of Agriculture and Forestry based on a full survey, for Japan, Hokkaido, and in other regions. The figure
shows that the distribution of the number of cows in the milk production cost statistics and the census is generally similar,
although there are some deviations depending on the number of cows. Furthermore, Figure A2 presents the distribution of
the cost of major production inputs (per 100 tons of raw milk) by Hokkaido and other regions. The figure shows that thecost distribution differs across Hokkaido and other regions. Due to this, we show the empirical results separately for
Hokkaido and other regions.
97

29.7 cows, medium-scale farms are those with between 29.7 and 68.7 cows, and large farms are thosewith more than 68.7 cows. The average cost per 100 kg of raw milk across all farms is 7,251.1 yen.
Those costs for small, medium, and large farms were 9,048.8 yen, 6,924.5 yen, and 6,111.6 yen,respectively, indicating that average costs were the lowest for large-scale farms. From these costs, it
can be inferred that larger farms produce raw milk at lower costs. While the average cost in regions
other than Hokkaido is 8,292.6 yen, the cost in Hokkaido is 6,552.8 yen, which is 1,739.8 yen lower.
One of the reasons for this is that there are more large-scale in Hokkaido than in the other regions. The
average number of cows in Hokkaido is 64.1 compared to 35.7 in the other regions. Pooled prices for
raw milk are lower in Hokkaido than in the other regions. These lower prices reflect the fact that
Hokkaido produces more raw milk destined for products of relatively low purchase prices. In contrast,
the other regions produce more raw milk intended for drinking, with a higher purchase price.
Panel (a) of Table 3 also shows the share of each cost item. Purchased feed is the item with thelargest share regardless of farm scale or region. However, the share of purchased feed is also larger forsmaller farms. A more striking difference is observed between Hokkaido and other regions. The
average purchased feed cost is 42.2% of total costs in the other regions compared to 27.7% in Hokkaido.
On the other hand, the share of self-produced feed costs was 7.8% in other regions but was significantly
higher in Hokkaido, at 18.3%. Therefore, in Hokkaido, farms can use a large amount of self-produced
feed, while in other regions farm operations are highly dependent on purchased feed. The expense itemwith the second largest share in all categories is labor, with 27% of the total sample. The share of laborcosts is smaller for larger farms. In other words, the larger the farms are, the less labor-dependent theyare. Conversely, larger farms have higher equipment and building costs. Thus, they produce more
capital-intensively than small farms. The share of cow depreciation costs is greater for larger farms
that have a higher number of cows.

10

4. Estimating Economies of Scale and Elasticities of Substitution between Factors
In this section, we estimate translog cost functions (a la Christensen, Jorgenson and Lau, 1973),
which allows us to detect both scale economies and cross-price elasticities between inputs.

4.1 Estimation of translog cost functions
Assuming the 𝑛 factors of production of one product, the translog cost function can be written
as follows9𝑛1
ln 𝐶 = ln 𝑘 + 𝑎 ln 𝑞 + 𝑑(ln 𝑞)2 + ∑ 𝑏𝑟 ln 𝑤𝑟
2
𝑟=1
𝑛
𝑛
1 𝑛
+ ∑ ∑ 𝑓𝑟𝑠 ln 𝑤𝑟 ln 𝑤𝑠 + ∑ 𝑔𝑟 ln 𝑞 ln 𝑤𝑟 .
2 𝑟=1 𝑠=1
𝑟=1

(1)

In that equation, 𝐶 is the total cost incurred by the farm to produce the raw milk, 𝑞 is the amount of
raw milk produced, and 𝑤𝑟 is the price per unit of the production factor 𝑟.10 For this study, 𝑛 = 7 isused as 𝑤1 for self-produced feed cost (per 100 kg), 𝑤2 for purchased feed cost (per 100 kg), 𝑤3 forlabor cost (per hour of family and hired labor), 𝑤4 for equipment cost (per vehicle and piece of farmequipment), 𝑤5 for building cost (per square meter), 𝑤6 for land rent (sum of land rent paid per 1a andimputed rent for owned land) and 𝑤7 for depreciation cost (per cow head).
Table 4 shows the derivation method and descriptive statistics for each “calculated” factor
price. 11 Descriptive statistics are calculated by excluding both the lower and upper 1% of the
distribution of each factor price because of the presence of outliers. The necessary and sufficientconditions for the cost function are (a) non-diminishing with respect to element prices, (b) first-orderhomogeneous with respect to element prices, (c) concave with respect to element prices, and (d)The by-products of Japanese raw milk producers consist mainly of manure and calves. According to the data in this paper,by-product production value as a percentage of total raw milk production value is 13.4% for the full sample. This paper
does not consider farm by-products and focuses only on raw milk production. Ray (1982) presents additional details for
estimating a translog cost function assuming multiple products.
10
The translog cost function is derived by taking the logarithm of both sides of the “true” cost function in general form andperforming Taylor’s quadratic approximation. Ray (1982) provides more information.
11
Each factor price is calculated by dividing the total amount of each cost item by the quantity of its inputs. The total valueof each cost item is then deducted from the by-product value multiplied by the percentage of each cost item within the total
cost. Figure A3 in the Appendix shows the distribution of those factor prices.
119continuous with respect to element prices.12 From condition (b), we transform equation (1) using thedairy cow depreciation cost (𝑤7 ) as the reference price as follows.13
ln

𝑛−1
𝐶
1
𝑤𝑟
= ln 𝑘 + 𝑎 ln 𝑞 + 𝑑(ln 𝑞)2 + ∑
𝑏𝑟 ln
𝑤7
2
𝑤7
𝑟=1

1 𝑛−1 𝑛−1
𝑤𝑟 𝑤𝑠
+ ∑
∑
𝑓𝑟𝑠 ln ln
2 𝑟=1
𝑤7 𝑤7
𝑠=1
𝑛−1

+∑
𝑟=1

𝑔𝑟 ln 𝑞 ln

(2)

𝑤𝑟
.
𝑤7

Also, by organizing equation (2) together with Shepherd’s complement, the following cost-sharing
equation can be derived as
𝑐𝑠𝑖 =

𝑛−1
𝑤𝑖 𝑥𝑖
𝑤𝑠
= 𝑏𝑖 + ∑𝑓𝑖𝑠 ln+ 𝑔𝑖 ln 𝑞,
𝐶
𝑤7
𝑠=1

where 𝑖 = 1, ⋯ , 𝑛 − 1.

(3)Here, 𝑥𝑖 represents the input of factor 𝑖. Because the sum of the cost shares of all production factors is
1, ∑𝑛𝑖=1 𝑐𝑠𝑖 = 1 is established. There are six independent cost-sharing equations.
Using the unbalanced panel data described above, we estimate the parameters of thesimultaneous equations consisting of equations (2) and (3) using the one-way Seemingly Unrelated
Regressions (SUR) system with random effects by Generalized Least Squares (GLS). 14 In theestimation, we impose the symmetry of factor prices 𝑓𝑟𝑠 = 𝑓𝑠𝑟 as a constraint with respect to all 𝑟 and𝑠.15 For the estimation, we remove the first percentile at both ends of the distribution for all series inorder to exclude outliers.16
Estimations are conducted by scale (the small, medium, and large farm groups) and by region(Hokkaido and other regions). The reason for dividing the sample by district (Hokkaido and otherregions) and by scale (small, medium, and large) for the estimation is that we expect that production
Ray (1982) explains this point.
See Kumbhakar (1996) and Weill (2013).
14
SUR estimation is used in cases in which the error terms in the simultaneous equations may be correlated with each other(inter-equations correlation). Also, in panel data estimation, there may be correlations (intra-individual correlations) in theerror terms because of unique effects. Chapter 6 of Baltagi (2021) shows that feasible SUR-GLS estimators are
asymptotically consistent and efficient when the simultaneous equations are estimated through SUR using panel data.
15
If the production technology is homothetic, then 𝑔𝑟 = 0 would be imposed as a constraint for all r. However, thisconstraint is not required in this study.
16
Since this study uses farm-level data, the issue of outliers, such as for reasons of misdescription, is expected to be moresignificant than in studies using aggregate data. Factor prices and production volumes are divided by their respective sample
averages for use in the estimation. See Croissant and Millo (2019) for a description of this procedure.
12
12
13

technology differs by district and by scale. Table 5 shows that 𝑎 and 𝑏𝑟 are positive at the 1%
significant level in all estimations irrespective of the scale and region. Thus, we can confirm that thenecessary and sufficient conditions for the use of the translog cost function: “(a) non-diminishing withrespect to factor prices” and monotonicity with respect to output, are satisfied. Wald tests for the fullsample and all subsamples by scale and region reject 𝑔𝑟 = 0, indicating that the related production
function is not homothetic. Also, 𝑑 = 0, and 𝑓𝑟𝑠 = 0 are rejected, suggesting that the cost function
does not exhibit the Cobb–Douglas form.

4.2 Economies of scale and elasticity of substitution between factors
Economies of scale is generally defined as the incremental value of costs being less than z times
when production output is z times greater. To verify this condition, we define the economies of scale
indicator called 𝑆𝐴𝐿 as follows.17
𝑆𝐴𝐿 =𝑛
𝜕 ln 𝐶− 1 = (𝑎 + 𝑑 ln 𝑦 + ∑ 𝑔𝑟 ln 𝑤𝑟 ) − 1.
𝜕 ln 𝑞
𝑟=1(4)

𝑆𝐴𝐿 can be calculated using the estimated parameters, the observed production, and factor prices foreach farm. The condition under which economies of scale operate is that 𝑆𝐴𝐿 takes a negative value,
as shown below.
𝑆𝐴𝐿 < 0.

(5)

Figure 1 shows the distribution of 𝑆𝐴𝐿 for Hokkaido farms and other regions. Observe that𝑆𝐴𝐿 is below zero for all sample farms. Table 6 also shows 𝑆𝐴𝐿 for national data, and disaggregatedby scale region. The results suggest that the average value of 𝑆𝐴𝐿 is below zero regardless of scales
and regions, suggesting that economies of scale generally exist for Japanese raw milk producers,
irrespective of the farm scale or geographic region. Figure 1 also shows that 𝑆𝐴𝐿 tends to be closer to

Because this paper focuses on a single product (raw milk), the distinction between so-called Partial Scale Economies
and Overall Scale Economies is inapplicable.
13
17

zero for farms with larger numbers of livestock, suggesting that there is more room for small-scale
farms to improve their profit margins by increasing the number of cows than large-scale farms.
In the translog cost function, the self-price elasticity 𝑒𝑖𝑖 and cross-price elasticity 𝑒𝑖𝑗 of demand
for factor 𝑖 concerning factor 𝑗 are obtained, respectively, as follows.18
𝑒𝑖𝑖 =𝜕𝑥𝑖 𝑤𝑖= 𝜎𝑖𝑖 𝑐𝑠
̂ 𝑖,
𝜕𝑤𝑖 𝑥𝑖𝑒𝑖𝑗 =𝜕𝑥𝑖 𝑤𝑗= 𝜎𝑖𝑗 𝑐𝑠
̂ 𝑗.
𝜕𝑤𝑗 𝑥𝑖(6)Here, the hat symbol represents the estimated value of each parameter. In addition, 𝜎𝑖𝑖 and 𝜎𝑖𝑗
represent the Allen–Uzawa estimates of the partial elasticity of substitution, which are given as𝜎𝑖𝑖 =𝑓̂𝑖𝑖 + 𝑐𝑠
̂ 𝑖2 − 𝑐𝑠
̂𝑖
,
2
𝑐𝑠
̂𝑖

𝜎𝑖𝑗 =

𝑓̂𝑖𝑗 + 𝑐𝑠
̂ 𝑖 𝑐𝑠̂𝑗.
𝑐𝑠
̂ 𝑖 𝑐𝑠̂𝑗(7)

Table 6 lists the own-price and cross-price elasticities for each production factor obtained fromequation (6). Three interesting results of the analysis are obtained. First, focus on 𝑒43 shown in thetable. In Japan as a whole, a 1% increase in labor prices will result in a 0.28% increase in the demandfor equipment, suggesting that a certain degree of substitutability between labor and equipment exists,
and that mechanization can increase scales of production without necessarily requiring additional labor
input. The cross-price elasticity is smaller for larger farms, 0.22%, compared to small farms, 0.33%. A
slightly smaller elasticity is obtained for Hokkaido, 0.27% in Hokkaido, compared to other regions,
0.30%. Second, focusing on 𝑒12 , a 1% increase in the price of purchased feed would result in a 0.33%
increase in the demand for self-supplied feed in Japanese farms. For this cross-price elasticity, thedifference between Hokkaido and other regions is substantial: 0.28% for Hokkaido and 0.42% for the
rest of Japan. In Hokkaido, which has a vast land area, the use of self-supplied feed has traditionallybeen high. Therefore, changes in purchased feed prices may have a small effect on the demand for selfsupplied feed. Third, focus on 𝑒62 . A 1% increase in purchased feed prices results in a 0.33% increasein demand for land for Japanese farms, suggesting a need for more land to produce self-produced feed
as demand for it increases in line with the rising price of purchased feed. Again, the difference between
18

Ray (1982) presents a detailed derivation of price elasticity.
14

Hokkaido and other regions is remarkably pronounced, with 0.27% in Hokkaido compared to 0.41%
in the rest of the country.
Conversely, cross-price elasticities among equipment, buildings, and land are estimated to below. For example, a 1% increase in equipment prices has a smaller effect on the demand for building
costs (0.05%, see 𝑒54 of the “All” column) and on the demand for land (0.05%, see 𝑒64 of the “All”
column). Therefore, the substitutability between these factors of production is smaller than for pairs
such as labor and equipment or self-produced feed and purchased feed.

5. Simulation Analysis
In this section, we use the results of the translog cost function estimation in the preceding
section to perform three simulation analyses. First, we examine how much farms’ profits would
improve in the case that the allocation of (some) factors of production were modified so that the farms
were able to achieve cost minimization. Second, we will examine how much hypothetical mergers ofsmall- and medium-scale farms into larger-scale farms would reduce production costs and increase
profit margins. Third, we will examine the impacts of introducing a uniform national integrated pooled
price integrated for raw milk, combined with or without the elimination of subsidies for milk forprocessing on farms’ profitability.

5.1 Revision of production factor allocation and farm profits
In this section, we compare the actual profits observed in the data to those that would result if
the allocations of the seven major items were revised to achieve cost minimization. The observed profit
Π𝑖,𝑡 of the farm 𝑖 in period t is defined as follows.
Π𝑖,𝑡 = 𝑝𝑖,𝑡 𝑞𝑖,𝑡 − 𝐶𝑖,𝑡 (𝒘𝒊,𝒕 , 𝑞𝑖,𝑡 )(8)where 𝑝𝑖,𝑡 and 𝑞𝑖,𝑡 respectively stand for the observed pooled price and output of farm 𝑖 in period t,

15

𝒘𝒊,𝒕 is the observed cost vector of each production factor, and 𝐶𝑖,𝑡 (𝒘𝒊,𝒕 , 𝑞𝑖,𝑡 ) is the total cost.19 Also,
given the observed output, the profit realized under an allocation of factors of production thatminimizes the costs estimated in the previous section is calculated as follows.
∗∗
Π𝑖,𝑡= 𝑝𝑖,𝑡 𝑞𝑖,𝑡 − 𝐶𝑖,𝑡(𝒘𝑖,𝑡,𝑟 , 𝒘𝑖,𝑡,𝑘 , 𝑞𝑖,𝑡 ).

(9)∗
To be comparable with the realized profit of each farm, the total cost 𝐶𝑖,𝑡is calculated here byusing the actual value (𝒘𝑖,𝑡,𝑘 ) as it is, except for the cost vector 𝒘𝑖,𝑡,𝑟 of the production factors (7 main∗
items) that is estimated to minimize costs. In other words, 𝐶𝑖,𝑡(𝒘𝑖,𝑡,𝑟 , 𝒘𝑖,𝑡,𝑘 , 𝑞𝑖,𝑡 ) represents the total∗
cost of partial cost minimization for the seven major items only. That is, Π𝑖,𝑡
represents the profit

calculated based on the partially cost-minimized total costs.
Figure 2 displays the distribution of observed and estimated partial cost-minimized profits, andpanel (b) of Table 3 reports each cost-minimized share. Panels (a) and (b) of Table 7 show theirrespective descriptive statistics. First, the average actual profit margin by scale shows higher returns
for large farms, followed by medium and small farms, in that order. The profit margins of small farms
are negative, indicating that business conditions are tough for them.20 The average actual profits inother regions are larger than in Hokkaido. One reason might be that the pooled price in Hokkaido islower than that in the other regions, while Hokkaido farms have better cost efficiency. On the other
hand, the coefficient of variation, defined as the ratio of the standard deviation to the mean, is 8.51 for
Hokkaido and 5.20 for other regions. This indicates that the variance of actual profits is greater in
Hokkaido than in the other regions.
Next, the profit calculated based on the partially cost-minimized total cost of production
according to equation (9) (profit from optimizing the allocation of factors under a given production

The observed pooled price is reported based on the following definition. Firstly, various expenses are subtracted fromthe milk payments from dairy manufacturers plus subsidies. Those expenses include the costs incurred for collecting anddelivering milk, sales commissions, and other shipping and selling costs. This amount is then divided by 100 kilograms ofraw milk production (milk fat content 3.5% equivalent), which constitutes the observed pooled price.
20
Total costs include the wage costs of family labor as well as external labor. The wage cost of family labor is an imputed
calculation and is different in nature from other cost items. One reason that many small farms are able to continue to operate
despite negative profit margins might be that the primary cost bearers are family members.
16
19

volume and price) shows an improvement in the mean and median values compared to the profit
observed across all groups. As shown in Panel (b) of Table 7, the improvement in total profit waslargest for medium-scale farms, with 48% for large farms, 153% for medium-scale farms, and 25% forsmall farms, by scale.21 By region, the profit improvement effect of the revision of input allocation
would be greatest in Hokkaido, at 199% compared to 74% in other regions. In other words, Hokkaido
farms and medium-scale farms are expected to benefit the most from cost minimization.
Table 8 reports the number and share of deficit-running farms by scale and region in eachsimulation scenario. Row i of panel (a) of the table shows the number of farms that show losses(deficits) in the actual data. Row i of panel (b) shows the number of deficit-running farms in acounterfactual case in which production is conducted with the cost-minimized combination of
production inputs. First, the percentage of deficit-running farms would become lower in the
counterfactual cases. The degree of reduction is highest among medium farms, followed by large-scale
farms and small farms. Among small farms, the actual ratio of the deficit-running farms is highest:
74%. Although cost minimization is taken into account, the ratio of loss-making farms remains almost
the same for small farms, while it decreases by about 3-4% for medium and large farms. Looking at
the result by region, the percentage of loss-making farms in Hokkaido was slightly higher than in otherregions, at 53.1%, based on actual profits. However, in a counterfactual case of cost minimization, thepercentage of loss-making farms will be lower in Hokkaido, at 47.3%, than in other regions, because
the rate of improvement would be greater in Hokkaido than elsewhere in Japan.
Rows ii of panels (a) and (b) display the number of farms that have been in the sample for morethan four years and have reported a deficit in profit over the same period in actual and counterfactual
cost-minimizing cases, respectively.22 First, by scale, the percentage of loss-making farms in actual
data is highest for small farms, followed by medium, and large farms, in that order. In the
Where the profit improvement rate is defined as (cost-minimized profit – actual profit)/actual profit.
If profit deficits persist for multiple years, even after cost minimization, the company might be forced to exit the market
abruptly (bankruptcy or business closure). For this study, although the sample replacement in the census is five years, weused four years as a guideline, given that the number of eligible farms would be greatly reduced if we narrowed the sample
to farms selected for more than five years.
17
21
22

counterfactual cost-minimizing case, the ratio of loss-making farms among medium- and large-scale
farms is lower, while it remains relatively unchanged or higher for small-scale farms. By region, theratio of loss-reporting farms is higher in Hokkaido by 11.1% point compared to other regions in actual
data. In the counterfactual scenario of cost minimization, the percentage of loss-making farms in
Hokkaido would decrease by 10.4% compared to the actual data. However, there is no substantial
reduction in the percentage of loss-making farms in regions outside Hokkaido. These simulation results
suggest that 50% of farms in Japan are making losses in actual data and that even in the counterfactual
scenario of cost minimization through input reallocation for small farms and regions outside Hokkaido,
which have a high concentration of small-scale farms, the situation would not be significantly
improved.

5.2 Cost savings by merging small and medium farms
As explained in the previous section, profit margins, especially for small farms, do not improve
much even in case of implementing cost minimization via reallocation of input. However, the analysis
suggests that increasing scale can significantly increase farms’ productivity and profitability. In thissection, a simulation will be conducted for a counterfactual scenario in which small- and mediumscale farms merge to form a larger farm without changing their total production (and, therefore, theiraggregated number of cows). The simulation assumes that small- and medium-scale farms in proximity
would merge within each of ten regions. The total production of all small and medium farms in a region
is divided by the average production for a large farm to obtain the new number of large farms after the
consolidation. We use parameters obtained from estimates for large farms’ cost function for postmerger productivity. Next, we examine the effect of consolidation on farms’ profit by examining how
much the total costs incurred by the hypothetical new large farms are reduced relative to the total costs
incurred by the small and medium farms before the merger. For example, in the case of Hokkaido, thetotal production of 2,005 small-scale and medium-scale farms is approximately 1,014 million
18

kilograms, which is divided by the average production of 919 thousand kilograms of large-scale farms
to arrive at the number of new large-scale farms after consolidation at 1,104. In this case, theassumption is that approximately two small to medium-scale farms will be merged to create one newlarge farm.
Under this assumption, the cost-minimized profit is calculated as follows.
𝑠𝑖𝑚∗
∗
Π𝑖,𝑡
= 𝑝𝑠𝑖𝑚 𝑞𝑠𝑖𝑚 − 𝐶𝑖,𝑡(𝒘𝑖,𝑡,𝑟 , 𝒘𝑠𝑖𝑚,𝑘 , 𝑞𝑠𝑖𝑚 )(10)where 𝑝𝑠𝑖𝑚 is a value generated from a normal distribution consisting of the mean and standard
deviation of the pooled prices experienced by small-scale and medium-scale farms and 𝑞𝑠𝑖𝑚 , holding
the total output of small-scale and medium-scale farms being constant.23 Similarly, for costs 𝒘𝑠𝑖𝑚,𝑘other than the seven main items, values generated from a normal distribution consisting of the meanand standard deviations for large farms were used.
Table 7 summarizes the simulation results based on equation (10). It compares the number ofsmall- and medium-scale farms, total revenue, total cost, total profit, and coefficient of variation offarms' profit in the simulated post-merger case to the actual data, i.e., pre-merger case.. The number ofsmall- and medium-scale farms in Hokkaido would decrease from 2,005 to 1,104 due to theconsolidation. The total revenue slightly differs between pre-merger and post-merger as we used the
distribution of pooled prices (not exactly the same pooled price in the pre-merger case) in the postmerger case. Total profit would increase about 7.6-fold because total costs would be reduced by 7% asa result of small- and medium-scale farms improving their cost efficiency after mergers. Similarly, inother regions, the total number of farms would decrease by about two-thirds, from 1,678 to 588, but
the total profits would increase about ten times because the total costs would be reduced by 31%.
In practice, mergers of small and medium farms do not usually proceed smoothly because ofHere, we use the distribution of pooled prices for small and medium farms before consolidation, rather than for large
farms. This is done for this study because whether the purchases made are for drinking milk or for raw milk for processing
depends mainly on the presence of plants for raw milk processing near the farm’s location. Therefore, we assume here that
there is no change in location after the merger and that pooled prices follow the pre-merger pooled price distribution forsmall- and medium-scale farms.
19
23

various institutional and geographical constraints. The simulation results here should be taken to show
the maximum benefits. But the results presented here suggest that it is possible to increase profits
without changing an overall production volume in Japan. Although the number of farms closing
businesses will most likely increase in the future due to the aging of farmers, a smooth transition fromsmall and medium family-run farms to large-scale corporate-run farms will promote an increase in
overall profit margins for dairy farming in Japan. Table 9 also shows that the coefficient of variationof total profits would decrease after consolidation in both Hokkaido and other regions. This decreaseof the coefficient of variation implies that the profit gaps between farms may narrow as they becomelarger scale.

5.3 Introduction of the national uniform pooled priceAs discussed in the Introduction, the purchase prices of raw milk by dairy processing firms
vary by dairy products, with higher prices for drinking milk and lower prices for milk intended for
products like cheese and butter. As a result, the pooled price for farms in regions other than Hokkaido,
which primarily produce milk for drinking, is higher than the pooled price for farms in Hokkaido,
which primarily produces milk for processing. 24 A natural question is why Hokkaido farms or its
designated producer organization do not “export” raw milk to the rest of Japan, where the pooled priceis higher. The cross-regional border movement of milk is likely self-regulated by the ten designatedproducer organization. There are exports from Hokkaido to other regions at the request of anotherregion although the amount of exports is limited.25 It seems that they have formed a cartel not tocompete. In other words, these product-specific price systems inhibit competition among farms acrossregions, combined with a restricted cross-border milk movement, reducing consumers’ benefits ofFor farms producing milk for processing, the pooled price, including subsidies from designated organizations, is thepurchase price of milk.
25
For example, according to The Daily Dairy News (Nikkan Rakuno Nyugyo Sokuho), the share of raw milk exports from
Hokkaido to other regions out of the total production of Hokkaido is approximately 11.5 percent in 2021. Kanagawa,Ibaraki, and Kyoto are major importers from Hokkaido in order and those prefectures import 24.4, 13.1 and 13.0 percent,respectively, out of total domestic exports of Hokkaido. Tokyo, the largest economic prefecture, imports limited amountfrom Hokkaido (1.1 percent) while it mainly imports from other periphery prefectures such as Gunma and Tochigi.
20
24having inexpensive milk. From the producer side, Hokkaido farms on average are, on average, costeffective because they have achieved a large scale, but their cost advantage is partly offset by being
forced to accept lower pooled prices just because more dairy products manufacturing firms that
produce butter and cheese exit in Hokkaido compared to other regions. This predicament for Hokkaido
farms is caused by market segmentation between regions in this industry.
This section considers a counterfactual case in which product-specific prices for raw milk are
eliminated, and a uniform nationwide pooled price is introduced. Regarding national subsidies, we
assume two cases: one in which there is no change in the subsidies in this section, and the other inwhich the subsidies are eliminated in the next section.
First, one can consider a subcase of no change in national subsidies. One can use the observed
national average pooled price of 8,413 yen (per 100 kg of raw milk) for 𝑝𝑠𝑖𝑚 in the profit function
equation (10).26 This hypothetical raw milk price is calculated as the sum of the total milk payments
made by dairy manufacturers to dairy farms and the total national subsidy for raw milk used inprocessed products, divided by total raw milk production. Therefore, the simulation is for eliminatingproduct-specific raw milk prices and introducing a one price for raw milk, but maintaining the national∗
subsidy.27 In addition, the cost is minimized to 𝐶𝑖,𝑡(𝒘𝑖,𝑡,𝑟 , 𝒘𝑠𝑖𝑚,𝑘 , 𝑞𝑠𝑖𝑚 ) for the seven main items.

Panel (c) of Table 7 displays the simulated statistics of the farm profits under the above scenario
when a uniform price for raw milk is introduced, regardless of the products or region for which raw
milk is used. Panel (b) of the table shows the counterfactual case of cost minimization by adjusting
inputs, but no change in raw milk pricing. A comparison of results in panels (b) and (c) allows us tounderstand the effect of introducing uniform national pooled pricing in addition to cost minimization.
First, introducing a uniform national pooled price would improve total profit by an average of 122%
and 73% for medium and large farms, respectively. In contrast, small farms would widen their losses

We also simulate farm profits using both 7,992 yen (95% of 8,413yen) and 8,834 yen (105% of 8,413 yen) other than
8,413 yen. Nevertheless, the results do not change qualitatively.
27
The subsidy amounts were obtained from the ALIC website.
(https://www.alic.go.jp/r-keiei/raku03_000003.html)
21
26

by 46% because Hokkaido, where the pooled price is low due to a higher percentage of raw milk being
processed for dairy products other than drinking milk, benefits most from introducing a uniform
national pooled price. In other regions, where raw milk tends to be more for drinking milk, the actual
pooled price for raw milk is higher than in Hokkaido, and because most small-scale farms are locatedoutside of Hokkaido, in a counterfactual case of uniform national pooled price would be averse to them.
Hokkaido is expected to see a 183% improvement in profits, while profits in other regions will decreaseby 117%. This difference in profits represents a huge contrast. The reason is the same as the comparisonby scale.
The coefficients of profit variation are smaller in this counterfactual case than in case (b) forall scales. Introducing the uniform national price of raw milk would reduce the disparity in profits
among farms. This reduced disparity holds for Hokkaido but not for other regions. In summary, in acounterfactual case where the total amount of subsidies is kept constant at the current level and a
uniform pooled price is introduced nationwide, medium-scale and large-scale farms anywhere andthose in Hokkaido would benefit from higher profits, whereas small farms and those in other regions
would undergo a reduction in profits.

5.4 Uniform price with elimination of subsidies for raw milk for non-drinking dairy products
Panel (d) of Table 7 shows the simulation results of introducing the uniform price for raw milk
but also abolishing the subsidy system simultaneously. This simultaneous introduction of uniform
prices and subsidy abolishment might be a more realistic hypothesis because subsidies are meant topartially compensate for lower prices of raw milk destined to non-drinking dairy products. Here, the“pooled price without subsidies” is equal to “the total pooled price received by all farms minus thetotal amount of subsidies (i.e., only the total amount paid by dairy manufacturers)” divided by “total
raw milk production nationwide.” This virtual pooled price 𝑝𝑠𝑖𝑚 is 8,090 yen. Again, as in panel (c) of
Table 7, we assume that the allocation of costs has been revised so that the farms achieve cost22

minimization. Accordingly, a comparison of panels (c) and (d) shows the impact of the abolition of thesubsidy program. Not surprisingly, eliminating the subsidy program alone would reduce farms’ profits,
regardless of scale or region. Regions other than Hokkaido would be particularly affected, with a 258%
decrease in profit margins. However, the profit reduction impact would be relatively small for
Hokkaido and large farms, at around -22%.
The government may judge that an introduction of uniform raw milk price would beaccompanied by eliminating subsidies, because the subsidies are intended as partial compensation of
the lower prices of raw milk that are used for non-drinking dairy products. 28 A combination of anational uniform raw milk price and the eliminating subsidies is shown in panel (d), in comparison
with panel (b). A comparison of (b) and (d) shows that that while small-scale farms and farms in regions
other than Hokkaido would still have negative profit margins, large-scale farms in any region and any
scale farms in Hokkaido would benefit most. This disparity of benefits is natural since the Hokkaido
farms are discriminated against in the pooled price system, being forced to have large proportion of
raw milk used for non-drinking dairy products, and being prohibited to export to other regions where
the pooled price is higher.

6. Summary and Concluding Remarks
The main results of the paper are presented below. First, economies of scale exist in raw milk
production. The total cost increases only 0.67% for a 1% expansion in production for the entire sample.
That is, the rate of increase in total cost is smaller compared to the rate of increase in production. This
result indicates that the average cost would decrease and that the production efficiency would increaseas the scale of each farm expands. Scale economies are observed regardless of the scale of the farm

One might think that the financial resources made available by abolishing the subsidy system can be used for incomecompensation to loss-making farms. The actual value of subsidies (sample average) is 24.1 billion yen per year according
to the calculation using the data obtained from the ALIC website. The number of farms that run a continuous deficit overfour years is estimated to be 7,065 using the share of deficit-running farms calculated in this research (45%) and the total
number of dairy farms in Japan obtained from the Census of Agriculture and Forestry (15,700). If a total of 24.1 billion
yen in subsidies per year were to be distributed as income compensation to these 7,065 continuously loss-making farms,
the per-household income would be 3.41 million yen. As a reference, Japan’s average income is 4.41 million yen in 2018.
23
28

household or the location, either in Hokkaido or other regions.29 Second, several interesting results are
obtained regarding the elasticities of substitution among factors of production. An estimated crossprice elasticity indicates that a 1% increase in the price of labor will result in a 0.28% increase in the
demand for equipment. Therefore, a certain degree of substitutability exists between labor andequipment. The results of this analysis suggest that introducing labor-saving technology(mechanization or automation) may increase profits. Another result is that a 1% increase in the priceof purchased feed would result in a 0.33% increase in the demand for self-produced feed. This crossprice elasticity is less pronounced for larger farms. The difference between Hokkaido and other regions
was remarkable, the cross-elasticity between the purchased feed and self-produced feed is 0.28% in
Hokkaido in contrast to 0.42% in the rest of Japan. This disparity is expected because the use of selfproduced feed has already been high in Hokkaido, so changes in purchased feed prices do not have asignificant impact on the demand for self-produced feed. The analysis also showed that a 1% increasein purchased feed prices would result in a 0.33% increase in demand for land. This increase can beinterpreted as evidence of the demand for more land to produce self-produced feed when the price ofpurchased feed increases.
The results of the simulation analysis are explained below. First, when the allocation of factorsof production is optimized to achieve cost minimization, farms’ profits improve regardless of the scaleor region. Large farms improved their profit margins by as much as 48%. Even small farms, many ofwhom are producing milk with deficits in the actual data, could reduce their deficits by as much as
25%. Comparing Hokkaido and other regions, the improvement was 74% in regions other than
Hokkaido and 199% in Hokkaido. This difference is attributable to the greater share of large-scale
farms in Hokkaido than in other regions. Second, if small-scale and medium-scale farms wereconsolidated to become larger-scale farms, costs could be reduced by 7% in Hokkaido and 31% in

Hokkaido is Japan's major production prefecture of dairy products; economies of agglomeration might work more in that
prefecture than in other prefectures. Therefore, we show some of our results for Hokkaido and other regions considering
the quantitative difference between Hokkaido and other prefectures.
24
29

other regions. Third, the introduction of a uniform national raw milk price would improve profits forlarge- and medium-scale farms while decreasing profits for small-scale farms. This expected effect is
attributable to the fact that the pooled price for Hokkaido where less small-scale farms are present islower than the rest of Japan. In addition, the elimination of the subsidy will reduce farms’ profit
margins, but introducing a uniform national raw milk price in parallel with the elimination of thesubsidy could offset the negative effect of eliminating subsidies in some regions.
The analysis and simulations in the paper are confined to that of a cost function. This limitation
is valid when demand for raw milk is held constant. The analysis of farms cost structure when theexternal conditions and policies change needs to be expanded to a demand analysis if the full
implications of policies are explored. Benefits of higher profits in some cases would most likely be
distributed to consumers by lowering the (uniform) raw milk prices. Examination of this lowering ofprices is anticipated as the next step of research. Also international comparisons of the cost function
and regulatory reforms are left as subjects for future research.

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Lips, M. and Rieder, P. Abolition of raw milk quota in the European Union: A CGE analysis at themember country level, Journal of Agricultural Economics, Vol. 56, (2005) pp. 1–17.
Neal, M. and Roche, J.R. Profitable and resilient pasture-based dairy farm businesses in New Zealand,
Animal Production Science, Vol. 60, (2019) pp. 169–174.
Ray, S. C. A translog cost function analysis of U.S. agriculture, American Journal of Agricultural
Economics, Vol. 64, (1982) pp. 490–498.
Sato, A. The Cost Structures of Dairy Farming in Japan - Are there Economies of Scale? [Nihon no
rakuno no hiyokozo – kibo no keizai ga arunoka (in Japanese)] Takasaki Keizai Daigaku Ronso,Vol. 62(2), (2019) pp. 133–137.
Sidhoum, A. A., Canessa, C. and Sauer, J. Effects of agri-environment schemes on farm-level ecoefficiency measures: Empirical evidence from EU countries, Journal of Agricultural Economics,
26

Vol. 74, (2022) pp. 551–569.
The Daily Dairy News [Nikkan Rakuno Nyugyo Sokuho] (2023), Special Issue for the Dairy Data,[Shiryo tokushu 101 (in Japanese)], The Daily Dairy News Co., Ltd.
Weill, L. Bank competition in the EU: How has it evolved? Journal of International Financial Markets,
Institute and Money, Vol. 26, (2013) pp. 100–112.
Yoshimi, T. and Ayano, S. Cost Structures of Milk Production: An Overview Using The farm-level
Data, [Seinyuseisan no hiyokozo – kohyodata ni yoru gaikan (in Japanese)] Keizaigaku Ronsan,
Vol. 62, Nos. 1, 2, 3, (2021) pp. 153–176.

27

Table 1: Frequency and continuity of sample farm selection
Frequency

Continuity
Number of farmers

Years of sampling

Number of farmers

Periodsampled for two

Replacement rate (%)

consecutive years
1 year111

2008-2009

463

6.5

2 years66

2009-2010

457

6.0

3 years67

2010-2011

467

4.5

4 years102

2011-2012

411

15.4

5 years73

2012-2013

461

6.1

6 years58

2013-2014

458

6.5

7 years34

2014-2015

460

5.2

8 years31

2015-2016

474

3.9

9 years75

2016-2017

374

23.7

10 years

213

Note: The replacement rate is defined as “the percentage of farms sampled in one year which are not sampled in thesubsequent year.” For example, the replacement rate in the row for “2008–2009” is calculated as “the percentage of
farms sampled in 2008 which were not sampled in 2009.”

28

Table 2: Farm size by the producer organization
NumberProducer organization in each block

Prefectureoffarmers

Hokuren Federation of Agricultural

Hokkaido

2,428

Cooperatives
Other organizations

Touhoku Seinyuhanren

Others2,428

Akita, Aomori, Fukushima,

525

Iwate, Miyagi, Yamagata
Hokuriku Rakuren

Fukui, Ishikawa, Niigata,

60

ToyamaKanto Seinyuhanren

Chiba, Gunma, Ibaraki,

752

Kanagawa, Saitama, Shizuoka,
Tochigi, Tokyo, Yamanashi
Toukai Rakuren

Kinki Seinyuhanren

Aichi, Gifu, Mie, Nagano

Hyogo, Kyoto, Nara, Osaka,

215

140

Shiga, Wakayama
Shikoku Seinyuhanren

Ehime, Kagawa, Kochi,

85

Tokushima
Chugoku Seinyuhanren

Hiroshima, Okayama, Shimane,

182

Tottori, Yamaguchi
Kyushu Seinyuhanren

Fukuoka, Kagoshima,

and Okinawa Dairy Cooperatives

Kumamoto, Miyazaki, Nagasaki,

469

Oita, Okinawa, Saga
All

4,856

Number

Raw milk yieldof cows(100kg)

Mean

66.6

6,222

Median

58.4

5,228

S.D.

39.8

4,345

Mean

39.2

3,667

Median

30.8

2,825

S.D.

33.0

3,388

Mean

30.1

2,679

Median

26.1

2,202

S.D.

20.6

2,044

Mean

26.5

2,438

Median

27.7

2,377

S.D.

11.3

1,103

Mean

42.9

4,026

Median

32.7

2,868

S.D.

42.1

4,378

Mean

51.0

4,979

Median

42.2

4,408

S.D.

38.8

3,811

Mean

36.6

3,376

Median

30.0

2,852

S.D.

26.5

2,512

Mean

28.3

2,635

Median

27.9

2,616

S.D.

15.0

1,485

Mean

38.4

3,710

Median

29.5

2,842

S.D.

29.5

3,288

Mean

42.7

4,010

Median

35.5

3,279

S.D.

28.4

2,865

Mean

52.9

4,945

Median

44.1

4,018

S.D.

39.1

4,100

Note: Descriptive statistics for the entire sample period (2008–2017). The number of farms included in the sample atleast once represents the overall number of farms included in the sample. S.D. indicates standard deviation.

29

Table 3: Breakdown of costs (Actual vs. Cost-minimized)
All

Small

MediumLarge

Hokkaido

Excluding
Hokkaido(a) Actual value
Average number of cows

52.7

20.4

46.7

97.1

64.1

35.7

Number of observations

3448

860

1726

864

2064

1384

Milk yield (100kg)

4833.1

1744.54197.89186.85851.73314.2Average cost (yen/100kg)

7251.19048.86924.56111.66552.88292.6Pooled price (yen/100kg)

8153.88737.78068.07743.07446.99207.9

Self-supplied feed

0.141

0.104

0.146

0.168

0.183

0.078

Purchased feed

0.336

0.351

0.327

0.337

0.277

0.422

Equipment

0.044

0.038

0.043

0.050

0.046

0.040

Building

0.024

0.020

0.023

0.030

0.025

0.023

Labor

0.270

0.331

0.273

0.204

0.259

0.287

Land rent

0.037

0.033

0.038

0.038

0.047

0.022

Cow depreciation

0.148

0.123

0.149

0.173

0.163

0.127

Average cost (yen/100kg)

7240.88883.6

6813.85957.76517.48285.5

Marginal cost (yen/100kg)

4790.25390.63745.43396.64109.15720.7

Lerner index (the degree of monopoly)

0.407

0.372

0.528

0.558

0.444

0.374

Self-supplied feed

0.133

0.093

0.133

0.164

0.173

0.076

Purchased feed

0.339

0.350

0.325

0.311

0.285

0.416

Equipment

0.050

0.043

0.050

0.059

0.054

0.046

Building

0.028

0.026

0.028

0.035

0.029

0.027

Labor

0.260

0.321

0.273

0.208

0.246

0.280

Land rent

0.038

0.037

0.041

0.045

0.048

0.023

Cow depreciation

0.152

0.129

0.151

0.178

0.165

0.133

Cost share(b) Cost-minimized value

Cost share

Note: Average values for the entire sample period (2008–2017).

30

Table 4: Descriptive statistics of factor prices and their derivation methods
Element

Mean

S.D.

MedianMax.

Min.

w1: Self-supplied 1,454

910

1,214

5,145

330

Number ofobservations
3,446

feed

Derivation method
Divide the total

Unit
Yen per 100kg

expenditure for selfsupplied feed by the
total input quantity(weighted average)

w2: Purchased

5,938

960

5,973

8,571

2,814

3,446

feed

Divide the total

Yen per 100kg

expenditure forpurchased feed by
the total input
quantity (weighted
average)w3: Labor

1,549

127

1,574

1,323

76

3,446

Divide the sum of

Yen per hourfamily labor andemployed labor by
the total hours
worked by those two
types of workers(weighted average)
w4: Equipment

95,07381,31071,443546,976

23,766

3,446

Divide the sum of car Yen per unit
expenses andagriculturalequipment cost by
the total input
quantity of those twoitems (weighted
average)w5: Building

522

387

429

2,083

120

3,446

Divide total building Yen per 1
cost by the building

square meterarea (weighted
average)w6: Land rent

367

257

282

1,323

76

3,446

Divide the sum of

Yen per 1 areland rent paid andimputed rent for
owned land by the
total land area
(weighted average)
w7: Cow

91,537

26,386

89,636

201,539

52,836depreciation

3,446

Divide the total

Yen per cow

depreciation cost by
the number of cows

Note: S.D. denotes standard deviation. The table reports the average of the 99th percentile as the maximum (Max.)and the average of the 1st percentile as the minimum (Min.) to ensure the confidentiality of individual farm
information.
31

Table 5: Estimation results of translog cost functions
ALL
Estimate

Small
S.E.

Estimate

MediumS.E.

Estimate

Large

S.E.

Estimate

Hokkaido

S.E.

Estimate

S.E.

Excl. Hokkaido
Estimate

S.E.

In k

17.2930.011 ***

16.5220.027 ***

17.1520.015 ***

17.7980.019 ***

17.3820.013 ***

17.0570.017 ***

a

0.667

0.011 ***

0.597

0.022 ***

0.566

0.020 ***

0.599

0.024 ***

0.659

0.015 ***

0.696

0.016 ***

d

0.043

0.011 ***

0.011

0.030

0.237

0.048 ***

0.420

0.060 ***

0.123

0.018 ***

0.057

0.016 ***

b1

0.133

0.003 ***

0.093

0.006 ***

0.133

0.004 ***

0.164

0.005 ***

0.173

0.003 ***

0.076

0.004 ***

b2

0.339

0.005 ***

0.350

0.012 ***

0.325

0.007 ***

0.311

0.009 ***

0.285

0.004 ***

0.416

0.007 ***

b3

0.260

0.003 ***

0.321

0.009 ***

0.273

0.005 ***

0.208

0.005 ***

0.246

0.004 ***

0.280

0.006 ***

b4

0.050

0.001 ***

0.043

0.002 ***

0.050

0.001 ***

0.059

0.002 ***

0.054

0.001 ***

0.046

0.002 ***

b5

0.028

0.001 ***

0.026

0.002 ***

0.028

0.001 ***

0.035

0.002 ***

0.029

0.001 ***

0.027

0.001 ***

b6

0.038

0.001 ***

0.037

0.004 ***

0.041

0.002 ***

0.045

0.002 ***

0.048

0.001 ***

0.023

0.002 ***

f11

0.029

0.001 ***

0.024

0.002 ***

0.030

0.002 ***

0.034

0.003 ***

0.038

0.002 ***

0.019

0.002 ***

f22

0.071

0.003 ***

0.105

0.008 ***

0.058

0.004 ***

0.068

0.005 ***

0.045

0.003 ***

0.125

0.006 ***

f33

0.115

0.003 ***

0.131

0.008 ***

0.119

0.005 ***

0.089

0.006 ***

0.114

0.005 ***

0.133

0.006 ***

f44

0.036

0.000 ***

0.032

0.001 ***

0.037

0.000 ***

0.040

0.001 ***

0.038

0.000 ***

0.033

0.001 ***

f55

0.017

0.000 ***

0.015

0.000 ***

0.016

0.000 ***

0.023

0.000 ***

0.017

0.000 ***

0.017

0.000 ***

f66

0.018

0.000 ***

0.020

0.001 ***

0.016

0.001 ***

0.023

0.001 ***

0.030

0.001 ***

0.013

0.000 ***

Note: ***, **, and ** denote that the null hypothesis of a t-test (coefficient of zero) is rejected at the 1%, 5%, and 10% significance levels, respectively. S.D.
indicates standard deviation.

32

Table 5: Estimation results of translog cost functions (continued)
ALL
Estimate

Small
S.E.

MediumEstimate

S.E.

Estimate

Large

S.E.

Estimate

Hokkaido

S.E.

Estimate

S.E.

Excl. Hokkaido
Estimate

S.E.

f12

0.008

0.001 ***

0.000

0.003

0.012

0.002 ***

0.013

0.003 ***

0.009

0.002 ***

0.004

0.002

f13

-0.0170.001 ***

-0.0130.002 ***

-0.0230.002 ***

-0.0110.002 ***

-0.0200.001 ***

-0.0130.002 ***

f14

-0.0040.000 ***

-0.0020.001 ***

-0.0030.000 ***

-0.0080.001 ***

-0.0050.000 ***

-0.0010.001

f15-0.0030.000 ***

-0.0010.001 *

-0.0030.000 ***

-0.0050.001 ***

-0.0040.000 ***

-0.0010.000 **

f16

-0.0030.000 ***

-0.0020.001 ***

-0.0030.000 ***

-0.0050.001 ***

-0.0050.000 ***

-0.0010.000 ***

f23

-0.0240.003 ***

-0.0450.007 ***

-0.0180.004 ***

-0.0190.004 ***

-0.0080.003 **

-0.0560.005 ***

f24

-0.0120.001 ***

-0.0120.002 ***

-0.0120.001 ***

-0.0100.001 ***

-0.0100.001 ***

-0.0140.001 ***

f25

-0.0080.001 ***

-0.0090.001 ***

-0.0070.001 ***

-0.0070.001 ***

-0.0060.001 ***

-0.0110.001 ***

f26

-0.0020.001 ***

-0.0070.001 ***

0.000

0.001

-0.0030.001 ***

-0.0010.001-0.0060.001 ***

f34

-0.0120.001 ***

-0.0120.002 ***

-0.0130.001 ***

-0.0090.001 ***

-0.0120.001 ***

-0.0120.001 ***

f35

-0.0040.001 ***

-0.0030.001 **

-0.0050.001 ***

-0.0060.001 ***

-0.0050.001 ***

-0.0030.001 ***

f36

-0.0060.001 ***

-0.0040.002 **

-0.0050.001 ***

-0.0050.002 ***

-0.0130.001 ***

-0.0030.001 **

f45

0.000

0.000 **

0.000

0.000 **

0.000

0.000

-0.0010.000 ***

0.000

0.000

-0.0010.000 *

f46

-0.0020.000 ***

-0.0020.000 ***

-0.0020.000 ***

-0.0020.000 ***

-0.0020.000 ***

-0.0010.000 ***

f56

0.000

0.000

0.000

0.000

0.000

0.000

-0.0010.000 **

0.000

0.000

0.000

0.000

g1

0.010

0.002 ***

0.002

0.005

0.008

0.005

0.009

0.007

0.014

0.003 ***

-0.0070.003 **

g2

0.071

0.003 ***

0.057

0.007 ***

0.087

0.007 ***

0.089

0.009 ***

0.086

0.004 ***

0.073

0.005 ***

g3

-0.0480.003 ***

-0.0230.005 ***

-0.0580.005 ***

-0.0460.005 ***

-0.0600.004 ***

-0.0330.004 ***

g4

-0.0220.001 ***

-0.0210.002 ***

-0.0160.002 ***

-0.0270.003 ***

-0.0210.001 ***

-0.0220.001 ***

g5

-0.0050.001 ***

-0.0140.001 ***

-0.0010.001-0.0050.002 ***

-0.0010.001-0.0100.001 ***

g6

-0.0140.001 ***

-0.0130.001 ***

-0.0140.001 ***

-0.0140.002 ***

-0.0210.001 ***

-0.0110.001 ***

Note: ***, **, and ** denote that the null hypothesis of a t-test (coefficient of zero) is rejected at the 1%, 5%, and 10% significance levels, respectively. S.D.
indicates standard deviation.
33

Table 6: Economies of scale and price elasticity
All

Small

MediumLarge

Hokkaido

Excluding
Hokkaido

Average number of cows

52.7

20.4

46.7

97.0

64.1

35.7

Number of observations

3448

860

1726

862

2064

1384

SAL

-0.335-0.394-0.441-0.416-0.356-0.305e11-0.643-0.629-0.636-0.622-0.604-0.662e22-0.451-0.346-0.495-0.471-0.555-0.280e33-0.299-0.271-0.292-0.368-0.287-0.249e44

0.212-0.049-0.427-0.131

0.153

0.781

e55

-0.131-0.6764.770-0.1230.029-3.061e66-7.604-0.364-0.495-0.406-0.289-1.099

e12

0.334

0.352

0.333

0.316

0.278

0.417

e13

0.270

0.317

0.271

0.213

0.258

0.282

e14

0.045

0.039

0.045

0.054

0.048

0.042

e15

0.025

0.023

0.024

0.033

0.026

0.025

e16

0.039

0.035

0.039

0.044

0.049

0.023

e21

0.132

0.090

0.135

0.167

0.172

0.076

e23

0.275

0.319

0.281

0.213

0.264

0.286

e24

0.045

0.039

0.045

0.055

0.048

0.042

e25

0.025

0.023

0.024

0.033

0.026

0.025

e26

0.039

0.035

0.039

0.044

0.049

0.023

e31

0.125

0.086

0.124

0.160

0.165

0.071

e32

0.321

0.337

0.318

0.304

0.272

0.392

e34

0.045

0.039

0.045

0.055

0.048

0.042

e35

0.025

0.023

0.024

0.033

0.026

0.025

e36

0.039

0.035

0.039

0.044

0.049

0.023

e41

0.129

0.090

0.131

0.162

0.170

0.074

e42

0.327

0.351

0.323

0.308

0.274

0.408

e43

0.281

0.333

0.285

0.216

0.266

0.298

e45

0.025

0.023

0.024

0.033

0.026

0.025

e46

0.039

0.035

0.039

0.044

0.049

0.023

e51

0.129

0.090

0.131

0.162

0.170

0.074

e52

0.328

0.352

0.323

0.308

0.274

0.408

e53

0.281

0.334

0.286

0.216

0.267

0.298

e54

0.045

0.040

0.045

0.055

0.048

0.042

e56

0.039

0.036

0.039

0.044

0.049

0.023

e61

0.129

0.090

0.131

0.162

0.170

0.074

e62

0.328

0.352

0.323

0.308

0.274

0.408

e63

0.281

0.334

0.286

0.216

0.266

0.298

e64

0.045

0.039

0.045

0.055

0.048

0.042

e65

0.025

0.023

0.024

0.033

0.026

0.025

Own-price elasticity

Cross-price elasticity

Note: The definition of elasticity is as given in equation (6). Here, the reference price in the cost function estimation
as follows: element 1, self-supplied feed costs; element 2, purchased feed costs; element 3, labor costs; element 4,
equipment costs; element 5, building costs; and element 6, land rent, and dairy cow depreciation costs.
34

Table 7: Comparison of farm profit margins
By sizeAll

Small

By region

MediumLarge

Hokkaido

Excluding
Hokkaido(a) Actual value (Baseline)
Mean

1,149

-1,830

514

5,391

985

1,393

S.D.

7,943

3,239

6,059

11,869

8,381

7,237

Coefficient of variation

6.91

-1.77

11.79

2.20

8.51

5.20

Median-305-1,760

-8

3,258

-497

-95

6,912

20,58950,10833,48343,401-10,421-13,059-20,648-17,822-11,099-1,574

887

4,647

2,033

1,927

Max.
Min.
Total profit (million yen)

3,960(b) Cost-minimized estimates: the current system
Mean

2,514

-1,377

1,302

7,961

2,943

2,426

S.D.

9,933

2,824

6,004

14,488

9,930

9,531

Coefficient of variation

3.95

-2.05

4.61

1.82

3.37

4.95

Median-128-1,799

648

5,750

493

28

Max.

7,849

20,18780,74547,772

65,125

Min.

-7,287-9,753-15,217-10,236-7,4098,670-1,184

2,247

6,862

6,074

3,357

119%

25%

153%

48%

199%

74%
-416

Total profit (million yen)
Profit improvement ratecompared to (a)(c) Cost-minimized estimates: uniform pooled price with subsidies
Mean

4,602

-2,0172,886

13,780

8,337

S.D.

10,630

1,901

5,451

13,038

11,772

6,562

Coefficient of variation

2.31

-0.94

1.89

0.95

1.41

-15.77

Median1,632-2,2242,610

11,767

5,767-2,193

3,983

18,11460,02858,75443,727

Max.
Min.

-6,163-9,093-13,662-7,188-9,29015,869-1,734

4,981

11,87817,207-576

compared to (a)

301%

-10%

461%

156%

746%

-130%

compared to (b)

83%

-46%

122%

73%

183%

-117%

Total profit (million yen)
Profit improvement rate(d) Cost-minimized estimates: uniform pooled price without subsidies
Mean

3,039

-2,581

1,528

10,8086,444-1,489

S.D.

9,664

1,790

5,102

12,191

10,746

5,961

Coefficient of variation

3.18

-0.69

3.34

1.13

1.67

-4.00

Median302-2,712

1,290

8,957

4,117

-2,876

Max.

3,080

15,76053,95353,12739,388

Min.

-6,720-10,149-16,112-7,787-10,700

10,478-2,220

2,638

9,316

13,300-2,060Total profit (million yen)
Profit improvement ratecompared to (a)

165%

-41%

197%

100%

554%

-207%

compared to (b)

21%

-87%

17%

36%

119%

-161%

compared to (c)

-34%

-28%

-47%

-22%

-23%

-258%

Note: Total profits are shown in units of one billion yen. Other items are shown in units of one thousand yen. S.D.
denotes standard deviation. The table reports the average of the 99th percentile as the maximum (Max.) and theaverage of the 1st percentile as the minimum (Min.) to ensure the confidentiality of individual farm information.

35

Table 8: Numbers and shares of deficit-running farms
By size

By region
Excluding

All

Small

MediumLarge

Hokkaido

1801/3448

636/860

865/1726

300/8621095/2064

706/1384

52%

74.0%

50.1%

34.8%

53.1%

51.0%

229/42073/97

107/211

31/103

148/251

81/169

55%

75.3%

50.7%

30.1%

59.0%

47.9%

1758/3448

633/860

798/1726

269/862976/2064

689/1384

51.0%

73.6%

46.2%

31.2%

47.3%

49.8%

211/420

74/97

93/211

29/103

122/251

77/169

50%

76.3%

44.1%

28.2%

48.6%

45.6%

1471/3448

729/860

577/1726

89/862504/2064

968/1384

43%

84.8%

33.4%

10.3%

24.4%

69.9%

171/420

81/97

65/211

6/103

58/251111/169

41%

83.5%

30.8%

5.8%

23.1%

65.7%

1670/3448

788/860

709/1726

140/862615/2064

1063/1384

48%

91.6%

41.1%

16.2%

29.8%

76.8%

190/420

87/97

80/211

12/10367/251

127/169

45%

89.7%

37.9%

11.7%

26.7%

75.1%

Hokkaido(a) Based on actual profitsi. Deficit farmers / All farmers[based on the total number over the whole sample period]
ii. Farmers with a deficit for more than four years / Farmers
sampled for more than four years(b) Based on cost-minimized profits under the current
systemi. Deficit farmers / All farmers[based on the total number over the whole sample period]
ii. Farmers with a deficit for more than four years / Farmers
sampled for more than four years(c) Based on cost-minimized profits with uniform pooled
price with subsidy
i. Deficit farmers / All farmers[based on the total number over the whole sample period]
ii. Farmers with a deficit for more than four years / Farmers
sampled for more than four years(d) Based on cost-minimized profits with uniform pooled
price and zero subsidy
i. Deficit farmers / All farmers[based on the total number over the whole sample period]
ii. Farmers with a deficit for more than four years / Farmers
sampled for more than four years

Note: Row i of each panel shows the number and share of farms that show losses (deficits) in the actual data (panela) or simulations (panels b, c, and d) for the entire sample. Row ii shows those numbers and shares focusing on
farmers that are sampled for more than four years.

36

Table 9: Consolidation effects on small-scale and medium-scale farms
Hokkaido

Excluding Hokkaido

Pre-merger

Post-merger

Pre-merger

Post-merger

Number of small and medium-scale farmers

2,005

1,104

1,678

588

Total revenue

76,05575,87949,97652,244

Total cost

75,29270,07048,15233,363

Total profit

763

5,809

1,824

18,881

Coefficient of variation of the each farmer profit

19.2

2.5

5.7

0.6

Rate of profit improvement

661%

935%

Rate of cost reduction

-7%

-31%

Note: Total revenue, total profit, and total cost are shown in units of one million yen.

37

Figure 1: Distribution of SAL, an indicator of economies of scale

Source: Prepared by the author based on farm-level data. The vertical axis shows SAL. The horizontal axis shows
the number of cows.

38

Figure 2: Profit distribution after cost minimization

Note: The vertical axis and horizontal axis present the numbers of farms and the profits (million yen), respectively.

39

Figure A1: Comparison of the Census of Agriculture and Forestry and our data

Note: The 2015 Census of Agriculture and Forestry sample is being compared to the 2017 sample of the milk
production cost statistics.

40

Figure A2: The distribution of the cost of inputs per 100 tons of raw milk

Note: The vertical axis represents the cost per 100 tons of raw milk production, measured in units of 10,000 yen. The
horizontal axis indicates the range of raw milk production in units of 100 tons. In each box plot, the box's upper end
signifies the 75th percentile, the lower end represents the 25th percentile, and the central line denotes the median.
The upper (lower) end of the whisker is the largest (smallest) observation that is less (more) than or equal to the 75th
(25th) percentile plus (minus) 1.5 times the interquartile range. To ensure the confidentiality of individual data,
samples that fall outside the upper and lower ends of the whiskers are not displayed.
41

Figure A3: Factor price distributions

Note: The vertical axis represents the price of each input, measured in units of 1,000 yen. The horizontal axis indicatesthe range of raw milk production in units of 100 tons. In each box plot, the box's upper end signifies the 75th percentile,
the lower end represents the 25th percentile, and the central line denotes the median. The upper (lower) end of thewhisker is the largest (smallest) observation that is less (more) than or equal to the 75th (25th) percentile plus (minus)
1.5 times the interquartile range. To ensure the confidentiality of individual data, samples that fall outside the upperand lower ends of the whiskers are not displayed.
42中央大学経済研究所( INSTITUTE OF ECONOMIC RESEARCH, CHUO UNIVERSITY)
代表者 阿部 顕三 (Director: Kenzo Abe)
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FAX: 042-674-3278+81 42 674 3278
E-mail: keizaiken-grp@g.chuo-u.ac.jp
URL: https://www.chuo-u.ac.jp/research/institutes/economic/