Hitotsubashi University
Institute of Innovation Research

Margin Rate Rule:
A New Drug Pricing Policy in Japan

Masaoki Tamura

IIR Working Paper WP#14-03

Jun. 2014

Institute of Innovation Research
Hitotsubashi University
Tokyo, Japan
http://www.iir.hit-u.ac.jp

Margin Rate Rule:
A New Drug Pricing Policy in Japan∗
Tamura, Masaoki†

This article theoretically evaluates the drug pricing policy in Japan and suggest
an alternative more eﬃcient policy. The Japanese current pricing rule “R2 rule”
causes high drug price and social ineﬃciency that is similar to the well-known double marginalisation problem. To solve this problem, we derive an alternative pricing
rule that we name “margin rate rule”. We show that the margin rate rule improves
Pareto eﬃciency: the rule leads to both lower drug price and higher profit of thefirms. There are three notable advantages in the margin rate rule. First, the government does not have to estimate the demand function, though it has the target price.
The pharmaceutical firms, not the government, estimate drug eﬃcacy, competition,and other demand information in pricing drugs. In this sense, the margin rate rule
is a decentralised rule, and easy to manage. Second, the government can control the
profit share between the firms and pharmacies in order to encourage pharmaceuticalinnovation. Third, the government can also control the drug-price margins so that
meditations are not biased.
∗

This research was supported by Research Institute of Science and Technology for Society (RISTEX), Japan Scienceand Technology Agency (JST).
†
Institute of Innovation Research, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo, Japan. E-mail: tamuramasaoki@gmail.com

1

JEL Codes: I11; L10; L42
keywords: Japanese Pharmaceutical Market; Drug Price; Drug Pricing Policy; Double Marginalisation

1 Introduction
The characteristics of the pharmaceutical markets are diﬀerent from country to country. The U.S.
pharmaceutical market is basically the free market: there is almost no price regulation imposedby the government. Both the retail prices and wholesale prices of the drugs are determined in
the market. The government does not intervene on the price of the drugs. On the other hand,
the Japanese pharmaceutical market is the regulated market: there is price regulations on theretail price of the drugs. The government controls the retail price according to the “R2 rule” sothat appropriate meditations are given to the appropriate patients at the moderate price. However,Which is more eﬃcient pharmaceutical market, the unregulated market or the Japanese regulated
market? Is there more eﬃcient pricing rule than the current R2 rule? This paper answers to thesequestions.
In Japan, there are two discussions on the pharmaceutical markets. The first discussion is on
the drug prices: whether the drug price is high or low? On the one hand, the pharmaceuticalfirms argues that the governmental price control (R2 rule) reduces the drug prices too much, andthe drug prices in Japan are lower than those in other countries. On the other hand, patientsand health insurance companies argue that drug prices in Japan are higher than those in othercountries. It is diﬃcult to conclude whether drug prices are high or low because the market
structure and healthcare system is diﬀerent from country to country. The second discussion is on
the inventions of new drugs: the number of “made in Japan” new drugs is recently decreasing.
It implies that the price control policy reduces the profitability of new drugs, and hence, theincentives to invent new drugs.
This paper models the Japanese pharmaceutical market and evaluate the current price control2policy (R2 rule). We find that R2 rule leads to the similar allocations as the “double monopoly
problem” leads to. This results give one answer to the two discussions above. (i) drug prices are
too high. (ii) At the same time, the pharmaceutical firms’ profits and hence the incentives forinnovations are too low.
Then, we derive the alternative more eﬃcient price control rule that we name “Margin RateRule”. This rule leads to lower drug price and more profits of the firms. There are three notableadvantages in the margin rate rule. First, the government does not have to estimate the demand
function, though it has the target price. The pharmaceutical firms, not the government, estimate
drug eﬃcacy, competition, and other demand information in pricing drugs. In this sense, themargin rate rule is a decentralised rule, and easy to manage. Second, the government can control
the profit share between the firms and pharmacies in order to encourage pharmaceutical innovation. Third, the government can also control the drug-price margins so that meditations are notbiased.
There are not many literatures that theoretically analyse the pharmaceutical market, especiallyJapanese regulated pharmaceutical market. Canton and Westerhout (1999) models the Dutch
pharmaceutical market. Bhattacharya and Vogt (2003) proposes a dynamic model of pharmaceutical pricing. Tanno and Hayashi (2013) is one of few papers that investigate the Japanese
drug market from the viewpoint of industrial organisation. However, in the papers above, theeconomic consequences and eﬃciency of the governmental pricing policy are not analysed. This
paper is the first paper that evaluates the current Japanese pricing policy and proposes an alternative policy.
This paper is organised as follows. In the section 2, the structure of the Japanese pharmaceutical market is overviewed. In addition, we see the aim and actual management of the current R2
rule. In the section 3, the Japanese pharmaceutical market and R2 rule are modelled. Then, we
evaluates the R2 rule. In the section 5, we derive the alternative more eﬃcient rule that we nameMargin Rate Rule. In the section 6, we overview the characteristics of Margin Rate Rule. There
are many advantages in implementing Margin Rate Rule. The section 7 concludes this paper.

3

2 the Japanese Pharmaceutical Market
In this section, we describe the Japanese pharmaceutical market that is mathematically modelled in the next section. The structure of the industry is presented in figure 1. There arethree economic categories in this industry: 1) pharmaceutical firms and wholesalers, 2) hospitals and pharmacies, and 3) consumers. Note that the wholesalers are put in the same category
as the pharmaceutical firms. The reason is that, in the Japanese pharmaceutical market, thewholesalers do not play important roles as the price makers. The margin rate of the Japanesepharmaceutical wholesalers are about 0.67 % which is very lower than the wholesalers in otherindustries. Because the wholesalers do not aﬀect the drug prices much, we ignore the pricing of
the wholesalers.
The relationships between the three categories are vertical. The pharmaceutical firms andwholesalers sell drugs to the hospitals and pharmacies. Then, the hospitals and pharmacies
sells them to the consumers. There are 2 kinds of the prices: retail price and wholesale price.
The retail price is the price at which the hospitals and pharmacies sell drugs to the consumers.
The wholesale price is the price at which the pharmaceutical firms sell drugs to the hospitals andpharmacies. In the following, we see how both prices are determined in Japanese pharmaceuticalmarket.
In Japan, the wholesale prices are determined in the market. In most of the cases, the wholesale prices are set by the pharmaceutical firms who are the price makers, because they havethe patents for the drugs and hence monopolistic power more or less. Generally, the wholesale
prices are lower than the retail price for the pharmacies to gain the positive profit.
On the other hand, the retail prices of the drugs are set by the government. If a pharmaceuticalfirm invents a new drug and it is listed in the National Health Insurance (NHI) Drug Price List(“NHI Price List”), national health insurance is applied to the drug. At that time, the initial retailprice is determined by the government. There are two methods to determine the initial retailprice. They are 1) comparison (with drugs of similar eﬃcacy) based price setting , and 2) costbased price setting. The first method sets the similar price to other drugs of similar eﬃcacy. The

4

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7"8#0-/,#)
Figure 1: Structure of Pharmaceutical Market
second method estimates the production cost of the drug, and sets the price for the firms to gain
appropriate profit. These methods determines the initial drug prices when they first come into
the market.
In addition, and most importantly, the government revises the retail price every two years.
Typically, the government gradually lowers the retail price over time. This price reduction iscarried out according to what is called “R2 rule”. R2 rule focuses on the diﬀerence between theretail price and wholesale price. If this diﬀerence becomes larger, the rule decreases the retailprice so that the retail price is 2% higher than the wholesale price.
Consider the following example. The initial retail price of one drug that is set by the government (by comparison-based or cost based price setting) is 100 yen, and the initial whole saleprice of the drug that is determined in the market is 98 yen. However, the wholesale price isaﬀected by the competition, entry of other firms to the market, and inventions of drugs withsimilar eﬃcacy. Suppose that other firms would invent new drugs with similar eﬃcacy and thecompetition among firms would become intense. Then, the wholesale price would decrease from98 yen to 90 yen. Then, the diﬀerence between the retail price (100 yen) and the wholesale price5

(90 yen) becomes larger than before. As a result, “R2 rule” decreases the retail price from 100
yen to 92 yen i.e. 2% higher than the wholesale price.To be accurate, new prices of the drugs
are revised according to






Weighted Average (
)
2%
of




New Retail Price =  × 1 + VAT Rate + Old Retail Price. Wholesale Price (1)

The key lies in the competition among firms. Because the wholesale prices are determinedin the market, the variations of the wholesale prices reflect the actual market competition. To
set the retail prices, the R2 rule monitors the wholesale prices, and hence, the actual market
competition. Applying the R2 rule, the government can set the retail price to reflect the actual
competition. If the competition is fierce and the wholesale prices get lower, the retail prices also
get lower.
Why does the government adopt this R2 rule? The government announces that the R2 rule isapplied so that meditations are not “biased”. We should notice that the profit for one drug (i.e.
margin) of the hospitals and pharmacies is as follows. margin = retail price − wholesale price.
The government is concerned that if the margin varies across drugs, hospitals tend to prescribe
drugs with high margin, which can be regarded as “biased” meditations. Therefore, the Japanese
government adjust the profit to 2% for all drugs.
Actually, the government is lowering the retail prices over time according to the R2 rule. The
monopolistic firms take into consideration the R2 rule and compete with other firms in drug
pricing. Then, we raise the questions. What is the economic consequence of the R2 rule? Does
the R2 rule lead to high or low drug prices? In the next section, we model the Japanese drug
market and evaluate the R2 rule.

6

3 The Model of the Pharmaceutical Market
In this section, the pharmaceutical market is modelled. In the subsection 3.1, as a benchmark,we model the hypothetical case in which the market faces no governmental regulation. In thesubsection 3.2, we model the actual case in which the market has the price regulation, R2 rule.
Finally, in the subsection 3.3, we compare both cases.
As we see in figure 1 in the previous section, there are 3 economic categories in the market:
the pharmaceutical firms and wholesalers, the hospitals and pharmacies, and the consumers. In
this paper, we denote the pharmaceutical firms and wholesalers as the “firms”, the hospitals andpharmacies as the “pharmacies”, and the consumers as the “consumers”. The relationships
between categories are vertical. The firms sell drug i to the pharmacies at the wholesale price
Wi , and pharmacies sells it to the consumers at the retail price Pi .

3.1 Hypothetical Unregulated Market
First, we consider the hypothetical unregulated market as a benchmark. There are 3 economic
agents: the firms, the pharmacies, and the consumers. We assume that the firms and pharmacies
are the price makers, especially, the monopolists. The wholesale price Wi and retail price Pi
are therefore the monopoly price. Note that we can relax the assumption that the firms andpharmacies are monopolists. it is necessary for this study to assume that they are just pricemakers. Assuming that they are oligopolists does not change the results and conclusions of ourmodel.
We model the consumers, the pharmacies, and the firms in order. In short, the Figure 2 ismodelled backward, i.e. from the bottom to the top. First, the consumers, given retail prices(Pi ), buy drugs from the pharmacies to maximise the utility that consists of the quantities of nkinds of drugs (Xi , i = 1, 2, ..., n) and the quantity of one kind of consumption good (C). We∂ U(·)
assume that the consumers’ utility function takes the normal form, i.e. ∂U(·)∂Xi > 0, ∂2 X < 0,2i7∂U(·)∂2 U(·)∂C > 0, and ∂2 C < 0. Then, consumer’s maximisation problem is()
max U X1 , X2 , ..., Xn , C(2)s.t.ΣPi Xi + C = I(3)where I denotes the income of the consumers. Solving this problem, we obtain the inverse
demand function Pi = Pi (P1 , P2 , ..., Pi−1 , Pi+1 , ..., Pn , Xi ) for drug i.

Next, the pharmacies are the price makers. Given the wholesale prices (Wi ), other drug prices
P1 , P2 , ..., Pi−1 , Pi+1 , ..., Pn , and the inverse demand functions Pi = Pi (P1 , P2 , ..., Pi−1 , Pi+1 , ..., Pn , Xi )of the consumers, the pharmacy i purchase drugs i from the firms, and monopolistically sell themto the consumers to maximise the profit1 . Then, pharmacy i’s maximisation problem is()
max Pi P1 , P2 , ..., Pi−1 , Pi+1 , ..., Pn , Xi Xi − Wi Xi
Xi(4)

Note that, for each pharmacy i, the amount of purchase is equal to the amount of sale. Solving
this problem, we obtain
Wi =∂Pi (P1 , P2 , ..., Pi−1 , Pi+1 , ..., Pn , Xi )Xi, which is rewritten as∂Xi

Wi = MRi .

(5)
(6)

In the first line, the left hand side is the wholesale price, and hence, marginal cost of the pharmacies. The right hand side represents the marginal revenue (MRi ) of the pharmacies. Noticethat this function is also regarded as the factor demand function of the pharmacies. Since Wi isgiven, the right hand side determines the factor demand Xi .

1

Note that we assume a hypothetical market in order to compare with the Japanese economy. Here, we makean assumption that the pharmacy i has monopolistic power only on the drug i. Though this is not a realistic
assumption, this does not aﬀect our results.

8

Finally, the firms are also the price makers. Given the factor demand function Wi = MRi , thefirm i produces drugs i, and monopolistically sell them to the pharmacy i to maximise the profit.
Then, the firm i’s maximisation problem is
max MRi Xi − ci (Xi )(7)∂ci (Xi ) ∂MRi
=
.
∂Xi
∂Xi

(8)

Xi

Solving this problem, we obtain

The left hand side is the marginal production cost of the firms. The right hand side represents
the marginal revenue of the firms. It is important that the marginal revenue of the firms is thederivative of the marginal revenue of the pharmacies, MRi . The equation (8) determines theequilibrium Xi , and hence Wi and Pi for all i.
This model clearly leads to the classical double marginalisation problem: the pharmacies’
marginal revenue (MRi ) means the factor demand of the pharmacies. Then, the firms’ marginal∂ci (Xi )irevenue is one more derivative of MRi , i.e. ∂MR∂Xi . This explanation is shown in figure 2. ∂Xi =
∂MRi
∂MRi
′
∂Xi determines the equilibrium Xi . Note that, In the figure, we denote ∂Xi as MR . What isthe consequence of double marginalisation? We see that• the price is higher than the single monopoly, and• the social profit in this economy is lower than the single monopoly
Note that the social profit refers to the total profit (the pharmacies’ profit plus the firms’ profit) inthe economy. In addition, the the single monopoly refers to the situation where the firms produce
the drugs and sell them directly to the consumers. In other words, in the single monopoly, therei (Xi )
is no wholesalers in the economy. In this case, ∂c∂X
= MR determines the equilibrium Xi . Fromithe two characteristics of the double marginalisation, we can say that the double marginalisation
is Pareto ineﬃcient to the single monopoly because both the consumers’ surplus and producers’

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Figure 2: Double Marginalisation
surplus are lower than the single monopoly.
For the comparison to the Japanese market, we give an alternative representation of this economy in which we does not use inverse demand functions, but use demand functions. The
firms and pharmacies’ maximisation problems are solved with respect to the prices, not thequantities. First, the consumers solve the same problem as before. the demand function is
Xi = Xi (P1 , P2 , ..., Pn ).
Next, the pharmacy i’s maximisation problem is()()
max Pi Xi P1 , P2 , ..., Pn − Wi Xi P1 , P2 , ..., Pn .
Pi

(9)Note that the amount of the pharmacy’s purchase is equal to the amount of the pharmacy’s sales
for each i. When Wi is given, the pharmacies put some mark up on Wi and set Pi = (1 + mi )Wi
where mi denotes the mark up rate. This Pi = (1 + mi )Wi determines the consumers’ demand
Xi = Xi (P1 , P2 , ..., Pi , ..., Pn ) that is equal to the pharmacies’ factor demand. Therefore the factor

10demand of the pharmacy i can be written as[]
Xi = Xi P1 , P2 , ..., (1 + mi )Wi , ..., Pn .

(10)

Finally, the pharmaceutical firm i’s maximisation problem is
[
]
( [
])
max Wi Xi P1 , P2 , ..., (1 + mi )Wi , ..., Pn − ci Xi P1 , P2 , ..., (1 + mi )Wi , ..., Pn .
Wi

(11)

Solving this problem, we obtain the equilibrium Wi , Xi , and Pi . Here, in a diﬀerent way, we
can explain why double marginalisation occurs. We focus on the revenue of the maximisation
problem above. For the firms to set Wi , the pharmacies’ mark up rate is just a disturbancebecause it does not increase the first term Wi (the gain for selling one drug), but decrease the[]second term Xi P1 , P2 , ..., (1 + mi )Wi , ..., Pn (the amount of sales). Then, the firms’ marginal
revenue with respect to Xi is smaller than the single monopoly. As a result, the equilibrium Xi islower and the retail price Pi is higher than the single monopoly.

3.2 Japanese Regulated Market
Next, we model the Japanese regulated market. There are 3 economic agents: firms, pharmacies,and consumers. For simplicity, we assume that firms are the price makers, especially, monopolists. The wholesale price Wi is therefore monopoly price. However, Pi is determined by thegovernment. As seen in the previous section, the Japanese government revises the drug prices
according to the R2 rule:
0.98 × Pi = Wi .

(12)

It controls the retail price Pi so that Pi is 2% higher than Wi . The notable feature of this R2 ruleis that the adjustment 2% is fixed rate and applied to all drugs. We conclude that this kind of
fixed rate rule causes ineﬃciency.

11

We model the consumers, the pharmacies, and the firms respectively. First the consumers
behave the same as before. Given the retail prices (Pi ), the consumers buy drugs from the pharmacies to maximise the utility that consists of the quantities of n kinds of drugs (Xi , i = 1, 2, ..., n)
and the quantity of one kind of consumption good (C). Then, consumer’s maximisation problem
is()
max U X1 , X2 , ..., Xn , C(13)

s.t.ΣPi Xi + C = I(14)

We obtain the demand function Xi (P1 , P2 , ..., Pn ) for drug i.

Next, we consider the pharmacy’s behaviour. It should be noticed that under the R2 rule,
pharmacies are no longer the price makers, but the price takers. When Wi is determined by
the firms, Pi is automatically determined by the R2 rule (12). Given the retail prices (Pi ) andthe wholesale prices (Wi ), the pharmacies buy the drugs from the firms and sell them to theconsumers to maximise the profit. Their profit is written as()()
Pi Xi P1 , P2 , ..., Pn − Wi Xi P1 , P2 , ..., Pn .

(15)

The amount of the pharmacy s purchase is equal to the amount of the pharmacy s sales foreach i. For the pharmacies, Wi , Pi , and hence Xi are determined exogenously. Then, the factor
demand of the pharmacies can be written as()
Wi, ..., Pn .
Xi = Xi P1 , P2 , ...,
0.98

(16)

Finally, the firms are the price makers. Given the R2 rule (12) and the factor demand functions,the pharmaceutical firm i produces drugs i, and monopolistically sell them to the pharmacies to12

maximise the profit. Then, the pharmaceutical firm i’s maximisation problem is
(
)
[ (
)]
Wi
Wi
max Wi Xi P1 , P2 , ...,, ..., Pn − ci Xi P1 , P2 , ...,, ..., Pn
Wi
0.98
0.98

(17)

Solving this problem, we obtain the equilibrium Wi , Pi , and Xi .
It is important that, in this economy, the firms decide all prices (Wi and Pi ) in eﬀect. Thisfeature reflects the actual behaviour of the firms in the market. It is often reported in the newspapers, magazines, and their statements that the firms are concerned about the government’s pricerevisions when they determine the Wi . Consider the situation in which the firms are planning todecrease the wholesale price to sell a large amount of the drug i to the pharmacies. However, thefirms expect that it would make the government revise the retail price lower. If this price revision would decrease the profit, the firms would give up decreasing the wholesale price. In short,taking into account the governmental price revision (the R2 rule) on the retail price, the firms
determine the wholesale price in reality. In other words, the firms aﬀect not only the wholesale
price, but also the retail price.

3.3 Comparison
In the previous section, we model both Hypothetical unregulated market and Japanese regulated
market. What is the diﬀerence in terms of economic welfare? Which is more eﬃcient system?
The answer is that the Japanese regulated market is equivalent to the hypothetical unregulated
1market when (1 + mi ) = 0.98
. This section presents this result.

Note that we solve the model backward. The order is, (i) the consumers’ problem, (ii) the
pharmacies’ problem, and then (iii) the firms’ problem. What determines the equilibrium inthe end is, therefore, the firms’ problem. We focus on the firms’ problem. Let us rewrite themaximisation problem (11) of the firms in the hypothetical unregulated market.
{ [
[
]
]}
max Wi Xi P1 , P2 , ..., (1 + mi )Wi , ..., Pn − ci Xi P1 , P2 , ..., (1 + mi )Wi , ..., Pn .
Wi

13

On the other hand, the maximisation problem (17) of the firms in Japanese regulate market under
the R2 rule is .
(
)
[
]
Wi
Wi
max Wi Xi P1 , P2 , ...,, ..., Pn − ci Xi (P1 , P2 , ...,, ..., Pn ) .
Wi
0.98
0.98
We can easily confirm that the Japanese market under the R2 rule is equivalent to the hypothetical unregulated market, when
(1 + mi ) =

1
.
0.98

(18)

We can say that the Japanese fixed rate rule (the R2 rule) cause the same social ineﬃciency
as the well-known double marginalisation problem. The drug price is higher, and hence theconsumers’ surplus is lower than the single monopoly. Regardless of the high price, the social
profit is lower, and hence the produces’ surplus is lower than the single monopoly.
We can derive some important implications for the two discussions that we introduce in thesection 1. The discussions are as follows.
1. Are the drug prices in Japan high or low?
2. Is there enough incentives for pharmaceutical innovations in Japan?
Here, we can answer these questions. For the first question, the R2 rule raises the drug price toohigh. For the second question, the R2 rule reduces the incentives for innovations because the R2
rule reduces the social profit from the new drug.

4 The Answer: Margin Rate Rule4.1 Derivation of the Margin Rate Rule
We see that the R2 rule leads to the social ineﬃciency. We ask whether there is an alternative
more eﬃcient rule than the R2 rule. In this section, we suggest one alternative pricing rule that14

we name “Margin Rate Rule”. To derive this new rule, we suppose that the government replace
the R2 rule (12) by the new rule,
Pi = αi (Wi ),(19)

where αi denotes a pricing rule that depends on Wi . In other words, by monitoring the wholesale
price Wi , the government sets the retail price Pi . Note that the R2 rule also depends on Wi , asseen in (12). The other environments are the same as in the Japanese regulated market in thesubsection 3.2. Under this new rule, the pharmaceutical firm solves
[
]
[ (
)]
max Wi Xi P1 , P2 , ..., αi (Wi ), ..., Pn − ci Xi P1 , P2 , ..., αi (Wi ), ..., Pn .
Wi

(20)

We want to find a new rule Pi = αi (Wi ) that yields the same allocation and profit as the single
monopoly. My suggestion, margin rate rule, is the answer.
Proposition (Margin Rate Rule). Margin rate rule, α(Wi ) = Ai (Wi − ci ) + ci where Ai is anarbitrary constant and ci is the marginal cost of production, is the pricing rule that yields thesame allocations as the single monopoly.
Proof. Under the pricing rule Pi = α(Wi ), the firms solve
[
]
( (
))
max Wi Xi αi (Wi ) − ci Xi αi (Wi ) .

(21)

[
]
[
]
[ (
)] [
]
Xi αi (Wi ) + Wi α′i (Wi )Xi′ αi (Wi ) − c′i Xi αi (Wi ) Xi′ αi (Wi ) α′i (Wi ) = 0.

(22)

Wi

The first order condition isOn the other hand, the single monopoly faces the following first order condition.
(
)
[
]
[ (
]
)] [
Xi αi (Wi ) + αi (Wi )Xi′ αi (Wi ) − c′i Xi αi (Wi ) Xi′ αi (Wi ) = 0.

15

(23)

If both (22) and (23) take the same form, the allocations under the rule are the same as the single
monopoly. Then, we obtain the following first order diﬀerence equation with respect to α(Wi ).
[ (
[ (
)]
)]
Wi α′i (Wi ) − c′i Xi αi (Wi ) α′i (Wi ) = αi (Wi ) − c′i Xi αi (Wi )(24)

Solving this first order diﬀerence equation yields
αi (Wi ) − ci = Ai (Wi − ci ),(25)

where Ai is an arbitrary constant and ci is the marginal cost of production, which we assume
constant for simplicity. We call this rule as the “margin rate rule”.

□

Under this margin rate rule, the economy achieves the same allocations as the single monopoly.
Because the single monopoly is Pareto eﬃcient to the double marginalisation, applying the margin rate rule is better than the R2 rule in the sense of economic eﬃciency. However, we additionally have to discuss whether the single monopoly is the better than any other allocations ornot. In the standard price theory, the economy is the most eﬃcient when the price is equal to themarginal cost, i.e. in the perfect competition. However, in the pharmaceutical market, it is nottrue that the perfect competition is best, because we have to take into account the incentives forinnovations. We can say that, at least, moderate monopolistic profit is necessary to invent new
drugs. In this sense, whether the lower price than the single monopoly is more eﬃcient or not
is still an open question in economics. Therefore, our suggestion targets the single monopoly
where the allocations are at least Pareto eﬃcient to the double marginalisation.

4.2 Why do we name our rule as “Margin Rate Rule”
Here, we see why we name our rule as margin rate rule. The Japanese drug pricing rule controls
the retail price based on the wholesale price. From the pharmacies’ point of view, it controls the−Wiipharmacies’ mark-up rate that is defined by PiW= αi (WWi )−W. First, the R2 rule sets the mark-upi
i

16

rate asαi (Wi ) − Wi Wi /0.98 − Wi=
≈ 0.02.
Wi
Wi

(26)

In words, the R2 rule adjust the pharmacies’ mark-up rate to 2%. Next, the margin rate rule sets
the mark-up rate as][
Ai (Wi − ci ) + ci − Wi
αi (Wi ) − Wi=
Wi
Wi
Wi − ci= (Ai − 1)
.
Wi

(27)
(28)

In words, the margin rate rule sets the pharmacies’ mark-up rate proportional to the firms’ marginrate. Here, the margin rate means the same as the learner index. This is the reason why we callour rule as margin rate rule.

5 Why is the Margin Rate Rule efficient?
In the previous section, we derive an alternative pharmaceutical pricing rule, “margin rate rule”.
In this section, we see the intuitions for why “margin rate rule” yields more eﬃcient allocations
than the R2 rule.

5.1 Individual Firms’ Margin vs Social Margin
As we see in the section 3, the R2 rule leads to the higher drug price than the single monopoly.
Then, the R2 rule leads to the lower social profit than the single monopoly, because the social
profit (=the firms’ profit + the pharmacies’ profit ) is maximised under the single monopoly.
This is because, under the R2 rule, maximising the firms’ profit is not equivalent to maximising
the social profit. As is seen in the section 3, both the double marginalisation and R2 rule cause
this problem.
On the other hand, the margin rate rule leads to the same drug price and the same social profit17

as the single monopoly. This is because, under the margin rate rule, maximising the firms’ profit
is equivalent to maximising the social profit. To confirm this claim, we transform the marginrate rule to the following.
α(Wi ) − ci = Ai (Wi − ci ).

(29)

The left hand side represents the margin of the firms for selling one drug. The right hand side
represents the constant multiplication of the social margin (= the firms’ margin + the pharmacies
margin) for selling one drug. To sum up, the margin rate rule controls the retail price P=alpha sothat the firms’ margin is proportional to the social margin. Therefore, the firms set their margin
that maximises the social margin and profit. The margin rate rule leads to the same drug priceand the same social profit as the single monopoly. This is one explanation why the margin rate
rule guides to the single monopoly.

5.2 Margin Rate Rule as Variable Rate Rule
The R2 rule sets the retail price by adding 2% to the wholesale price. The added percentage, 2%, is fixed whatever the wholesale price level is. On the other hand, under the margin rate rule,
the added percentage is variable according to the wholesale price level. In this sense, the marginrate rule is regarded as the variable rate rule, while the R2 rule is regarded as the fixed rate rule.
Figure 3 shows the relationship between the wholesale price and the added percentage for both
the R2 rule and the margin rate rule.

First, the R2 rule adds the fixed percentage, 2%. Second, the higher the wholesale price is, thehigher percentage the margin rate rule adds to the wholesale price. What does it mean for thefirms? Note that, under the R2 rule, the firms raises the wholesale price and hence the retailprice above the single monopoly level. However, under the margin rate rule, the firms havelower incentives to raise the wholesale price. Suppose that the firms raised the wholesale price18

/0*1.*2,3,.*45.*%&'()*+,!'-$,!"#$%
R2 !"#$%.*%
Figure 3: R2 Rule vs Margin Rate Rulesignificantly. Then, as seen in Figure 5, the margin rate rule would add the higher percentage
and hence set the higher retail price than the R2 rule. The consumers’ demand for the drugs
would become lower. As a result, the firms would gain less profit. In contrast, if the firms
lowered the wholesale price significantly, then the margin rate rule would add lower percentage
and the firms would gain more profit. In summary, under the margin rate rule, the firms lower
the wholesale price to avoid government’s high-percentage adding to the wholesale price. Thisis another explanation why the margin rate rule leads to lower drug prices than the R2 rule.

6 Advantages of Margin Rate Rule
Besides the result that margin rate rule is more eﬃcient than the R2 rule, there are additionally
three advantages in the margin rate rule. First, applying the margin rate rule does not require
the demand information of the consumers, though the monopoly pricing normally requires it.
Second, margin rate rule can divide the profit arbitrarily between the firms and pharmacies. The
government can encourage innovation in new drugs. Third, the government can achieve the19

“unbiased meditations”. Applying the margin rate rule requires only cost information. In thissection, we study both advantages in detail.

6.1 No Need for Demand Estimation
The first advantage is that the margin rate rule does not require demand information including
drug eﬃcacy, competition, and price elasticity of demand. Consider an alternative method forthe government to set the single monopoly price: at the time of price revision, the government
estimates the hypothetical single monopoly prices and arbitrarily sets them for all drugs. Whatkinds of information would the government need for such estimations? To estimate the single
monopoly price, the government would need to estimate the demand function and the marginalcost. It requires the drug eﬃcacy, the competition level among firms, price elasticity of demand,and the production cost of the drugs. In short, the government would need both the demand andcost information. However, for the estimations the government would pay a large amount oftime and money, and the accuracy of them would be unclear.
On the other hand, managing the margin rate rule does not require the demand information.
The reason is that, under the margin rate rule, not the government, but the firms themselvescalculate the drug eﬃcacy, the competition level, and the price elasticity of demand to maximise
the profit. Not the government, but the firms face the demand curves and set the price. The
government only adjusts the relative margin: it adjusts the margin of the firms proportional to thesocial margin as seen above. In this sense, the margin rate rule can be regarded as a decentralised
pricing rule. It implies that the market (i.e. the firms) is superior to the government in pricing
the drugs.
Managing the margin rate rule only requires the cost information, the marginal cost to produce
a drug as seen in α(Wi ) = Ai (Wi − ci ) + ci . Of course, the government has to put eﬀort into
this estimation. However, as seen in the next section, the Japanese governement is currently
estimating the production cost for some kinds of new drugs. Therefore, we can say that the
government do not need to pay a large amount of additional time and money to manage the20margin rate rule. We discuss this point in the next section.

6.2 Arbitrary Distribution of the Social Profit and Encouragement of
Innovation
We show that the margin rate rule works to stimulate pharmaceutical Innovation by dividing thesocial profit arbitrarily between the firms and pharmacies. At the beginning, we should noticethat Ai in margin rate rule α(Wi ) = Ai (Wi − ci ) + ci is an arbitrary constant. This is because
we solve the first order diﬀerential equation when we derive the margin rate rule. What would
happen when the government controls Ai ? In principle, controlling Ai does not aﬀect the size ofthe social profit. Whatever value Ai takes, the margin rate rule guides to the single monopoly,and hence, it does not aﬀect the equilibrium value of Xi , Pi , and the size of the social profit.
However, it aﬀects the distribution of the social profit between the firms and pharmacies. Thisis because the value of Ai clearly aﬀects the equilibrium value of the remaining variable, Wi . If
the government announces higher Ai than before, then the equilibrium value of Pi remains thesame, but Wi becomes lower. Here, it should be noted that (i) the margin of the firms is Wi − ci ,and the margin of the pharmacies is Pi − Wi , and (ii) The margin determines the share of thesocial profit that they gain when Xi is unchanged. Then, we can restate our claim as follows.
• The higher Ai the government announces, the higher share of the social profit pharmacies
gain, and the lower share of the social profit the firms gain.
• The lower Ai the government announces, the lower share of the social profit pharmacies
gain, and the higher share of the social profit the firms gain.
Note that controlling Ai does not reduce the size of the social profit.
Why does the government take into account the distribution of the social profit? There are
two answers to this question. First, there is a positive relationship between the pharmacies’
share of the social profit and pharmaceutical innovation. The more share of the social profit thefirms gain, the more incentives for inventing new drugs they have. This is because high share21

of the social profit means high reward of inventing new drugs. Inventing new drugs stimulate
the economy in the end. Therefore, increasing the share of the firms would encourage R&D
and innovation, and hence economic growth. Second, the Japanese government cares about
the biased meditations. By controlling Ai , the government can also solve “biased” meditations
problem. This is explained in the following.

6.3 Unbiased Meditations
As we discuss in the section 2, the Japanese government is concerned about the biased meditations: if the margin would vary across drugs, hospitals and pharmacies would tend to prescribe
drugs with high margin. For the similar reason above, the margin rate rule solves this concern,by the appropriate control and announcements on Ai .
As we see above, high Ai makes low margin of the firms (Wi − ci ) and high margin of thepharmacies (Pi − Wi ). In contrast, low Ai makes high margin of the firms (Wi − ci ) and low
margin of the pharmacies (Pi − Wi ). Here, we should notice that the value Ai can vary acrossdrugs i. For the drug i the government can announce Ai , while for the drug j the government canannounce A j , Ai . Therefore, by controlling Ai and A j , the government can set the pharmacies’
margin of the drug i and j at the same level, i.e. Wi − ci = W j − c j . Then, the hospitals andpharmacies gain the same margin whatever drugs they prescribe. Note that controlling Ai does
not aﬀect the size of the social profit. As a result, the government can achieve both the eﬃcient
allocations and unbiased meditations.

7 Data Feasibility of the Margin Rate Rule
Managing the margin rate rule only requires the production cost. Then, is it possible to obtainthe cost information and manage the rule? The answer is positive because currently the Japanese
government is collecting the production cost data to set the initial price for some kinds of new
drugs.

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As we overview in the section 2, if a pharmaceutical firm invents a new drug and it is listed in
the National Health Insurance (NHI) Drug Price List (“NHI Price List”), the initial retail priceis determined by the government. There are two methods to determine the initial retail price.
1. comparison (with drugs of similar eﬃcacy) based price setting , and
2. cost-based price setting.
If the eﬃcacy of the new drug is comparable to that of the existing one in the market, the firstcomparison-based method is applied. The government compares the eﬃcacy of both drugs andsets appropriate price to the new one. On the other hand, if there is no comparable drugs in themarket, the government applies the second cost-based price setting. The government estimatesthe cost of manufacturing, sales, administration, operating, distribution, marketing and VAT.
Then, the government adds some margin to the cost for the firm to gain appropriate profit.
We put emphasis on the second pricing method. In short, currently the government is estimating the production cost for initial pricing of new drugs. Our margin rate rule requires cost
information. If the government collected cost data more broadly, then the margin rate rule could
be applied to the overall market. We conclude that the margin rate rule is feasible to manage interms of data.

8 Concluding Remarks and Extension to the Model under
Health Insurance
We evaluate the drug pricing sheme (R2 rule) in Japan, and find social ineﬃciency that is similar
to well-known double marginalisation problem. Then we suggest an alternative rule that wename “margin rate rule”. Applying margin rate rule is Pareto improving because the drug priceis lower and the total profit of firms are larger than applying R2 rule. In addition, there are threenotable advantages in the margin rate rule. First, the government does not have to estimate drugeﬃcacy, competition, and other demand information in pricing drugs. The government only

23

has to estimate the cost of drug production. In this sense, the margin rate rule is regarded as adecentralised rule. Therefore, we can say that the margin rate rule is feasible and easy to manage.
Second, the government can control the margin share between the firms and pharmacies in orderto encourage pharmaceutical innovation. Third, the government can also control the retail priceand margin share so that meditations are not biased.
Finally, we refer to the health insurance. In this paper, the eﬀect of the health insurance is notanalysed. However, the existence of the health insurance would not change the functional form
and advantages of the margin rate rule. Under the health insurance, there still exists the similar
problem to the double marginalisation. Then, applying the margin rate rule is Pareto improving.
To build a more realistic model, we are going to analyse the economy with the health insurance
in the future study.

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References
Canton, Erik, Westerhout, Ed., Model for the Dutch Pharmaceutical Market. Health Economics, Vol. 1999, Issue 5, pp391-402, 1999.
Bhattacharya, Jayanta, Vogt, William, B., A Simple Model of Pharmaceutical Price Dynamics. Journal of Law and Economics, Vol. 46, No. 2, pp. 599-626, 2003.
Tanno, Tadanobu, Hayashi, Yukinari, Current Status and Economic Analysis in JapaneseWholesalers of Prescription Drugs. Atomi University Department of Management Annals,
No. 15, 2013.

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