I

ArticlesThe Hicks-Morishima
Approach Reconsidered
Another Look at the Interdependenceof Several Markets

Yasuhiro Sakai

Shiga University / Professor Emeritus

072

Michio Morishima andJohn R. Hicks:
the Two Superstarsof Economics

There are the two economics superstars
who have greatly influenced my academic career. They are Michio Morishima, Osaka
University and London School of Economics,
and John R. Hicks, London School of Economics and Oxford University. To tell thetruth, both of them already passed away. Academically, however, they seem to be still alive:
indeed, their outstanding accomplishments
will never be forgotten in economic science.
The main aim of this paper is to reconsider andshed new light on a topic named the HicksMorishima approach to the interdependenceof several markets. Although such approachhas been rather neglected for some time, I am
sure that even now, it is worthy of serious reconsideration, presumably giving a new guide
toward an integrated grand theory of social science in the twenty-first century. No doubt,
this should be the direction of future research
to be strongly desired by both Morishima andHicks in their late years.
When I was a graduate student at the University of Rochester, I was fortunate to meetwith Mr. Masayoshi Hirota, a "very serious
man with highly samurai spirits," who so fondly
argued night and day with me about life philosophy, world matters, and of course

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economic science. According to Hirota, weshould not have any fears about the seemingly
high levels of American universities. Osaka
University seemed to be at least on a par with,and even better than, University of Rochester.
Hirota proposed me to do a joint work on general equilibrium theory with the final aim of
publishing academic papers in professional
journals of high prestige. We worked very hardby utilizing every space of the Rochester campus, namely the university library, class rooms,
student dining rooms, and the graduate student center. After some time of our joint
research, there came our final product, Hirota
and Sakai (1969), which aimed to open a newhorizon in theoretical studies in production
theory. Although our joint paper had a humble yet attractive title "On Substitution and
Scale Effects in Production Theory," it wasquite unfortunate that because of some minor
technical reasons, it missed a publication opportunity.
In hindsight, I am sure that my joint research experience with Mr. Hirota, or "Osaka
samurai scholar," has constantly given us a great
stimulus for the execution of our research project on economic theory. Indeed, having beenencouraged a great deal by the Hirota-Sakai
cooperation, I myself continued to learn many
advanced mathematical tools which were applicable not only to production theory, butalso to consumption theory as well. The final
result of my continuous research effort was thecompletion of my doctoral dissertation (1972)
Axiomatic Foundations of Consumption and
Production Theories submitted to The University of Rochester, with my main thesis advisor
being Professor Lionel W. McKenzie. After
finishing my Ph. D. work and publishing many
theoretical papers in international journals, I
could spend a happy life at Pittsburgh, inwhich Professor Asatoshi Maeshiro and hiswife Kazuko kindly helped me in many ways.
All those nice things happened to my rather
long American life in the period 1968-1976.1)
I can vividly recall that at the very end of
1973, my important meeting with Michio Morishima took place in New York City. Moreexactly, he was invited to deliver a special lecture at Econometric Society North American
Meeting at New York Hilton Hotel, with Professor Lawrence W. Klein of Pennsylvania
serving as a respectable chairman. The audience filled the hall to overflowing. Professor
Akira Takayama, a noted international economist, sat in the very front seat, taking so many
pictures. All the people seemed to have a very
happy time by enjoying the presence of thememorable trio, namely Morishima, Klein and
Takayama. Then, Morishima stood up and delivered a historical speech: "Kark Marx is so
great! I have no doubt that he is academicallystill alive after one hundred years of his death!"
In an instant, the whole audience stood up andapplauded his powerful speech.2)

1) In September 1972, I submitted my Ph.D. disserta-

Morishima of Osaka University and Lawrence Klein of
the University of Pennsylvania.

tion to the University of Rochester, with Professors Lionel W. McKenzie and James Friedman being thesis advisers. As we seen in Sakai (1972), the thesis consisted of
the two parts. The first part carefully discussed axiomatic approaches to consumption theory, the second partmathematical foundations of production theor y. I
would like to point out that Chapter 3 in Part 2, titled
An Axiomatic Approach to Input Demand Theory, wasbased on my joint work with Dr. Masayoshi Hirota withfurther refinements. Very fortunately, a still further revision of this Chapter was published in International
Economic Review, which was first published by Michio

The Hicks-Morishima Approach Reconsidered

2) More exactly speaking, Professor Morishima's invitedlecture was titled Marx in the Light of Modern Economic
Theory. It was nothing but a Walras memorial lecture at
the North American Meeting of Econometric Society.
Although it was first read at Hilton Hotel, New York, in
28 December 1973, it was later published as a leading article of Econometrica (see Morishima, 1974). It was really lucky that I myself was right there as an attentive audience. This constitutes one of never-to-be-forgotten
memories in my long academic life.

Yasuhiro Sakai073

In what follows, I would like to just pickup Hicks' great book Value and Capital (1939,1946), carefully discussing how closely Hicks
and Morishima have been connected by thismasterpiece. A famous writer Naoki Komuro(2004) once remarked:

mind was how Hicks' market laws aforementi on e d wo u l d ha d to c hang e by th e
introduction of distance and space. In mystudent days, I was literally swamped withsuch a very difficult problem.
(Morishima, 1999)

During the Second World War, Morishima
served as a naval cadet whose duty wasto
break a secret code of the enemy. When heleft home toward a battlefront, he carried an
important book with himself. That bookwas nothing but a newly published text Value and Capital by Hicks, then a rising stareconomist of the United Kingdom, one ofJapan's hostile countries. Nevertheless, Morishima, who faithfully conducted his secretmission of code breaking, dared to exert all
his energy to fully understand the Hicks
new book, and safely could return home
(Komuro, 2004)

It was quite fair to say that in those days,
Morishima stood high and alone in the Japanese academia: in fact, the research level ofMorishima went far beyond the one of any ordinary Japanese economist. He was a man ofcourage and determination. The major aim of
this paper is to reconsider Hicks' law of market
exchange in a new modern fashion, thus further extending the Hicks-Morishima approachwith my unique flavor attached to it.
I have met with Hicks several times. My
most memorable moment took place when I
attended the International Conference inHonor of J.R. Hicks, Bologna, Italy, in 1991. It
gave me a great and unforgettable memory.
The outline of this paper is as follows. The
second section will deal with s simple model ofgeneral equilibrium — the excess demand approach a la Hicks and Morishima. The third
section will discuss many non-normal cases.
The issues of instability, multiple equilibriumand non-existence will be successively taken up.
In the fourth section, we will turn to the problem of comparative statics. The impact ofparameter changes on equilibrium values will
carefully be investigated. Final remarks will bemade in the fifth section, with reference toMorishima's life-long dream of a grand synthetic approach to a so - ca lle d "symphoniceconomics."

Later in his life, Morishima (1999) got asudden surge of nostalgia for his youth:
When I [Morishima] was a Kyoto University student just after the last war, I was fondly
reading Value and Capital by J.R. Hicks.
He discovered the following law of criticalimportance: "Let the excess demand for one
good increase. Then, not only will its pricewill rise, but also the prices of other substitutive goods will rise, whereas the prices ofcomplementary goods will decline." I noticed, however, that he carelessly neglected
the undeniable truth that any economic activity including market trading had tooperate at some distance in a space. My
question which would naturally arise in my074

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II

A Simple Model ofGeneral Equilibrium:
The Excess Function
Approach a laHicks and Morishima

Saying is one thing. But doing is another.
Now let us discuss the working and performance of a simple model of g eneralequilibrium. To this end, we will adopt the exc e ss d eman d appro a c h a la Hi c k s an dMorishima. The Hicks-Morishima approach isa very effective one to shed light on interrelation of excess demand curves in the price space
for an in investigation of the working and performance of general equilibrium. Although
we focus on a simple two-good model in thispaper, its generalization to any several goodmodel would require no difficult task.
Honestly speaking, in spite of its rather
simple and ambitious framework, it is quite
unfortunate that the Hicks-Morishima approach has been long neglected in the academic
circle. I suppose that there are several reasonsfor this. First of all, the traditional generalequilibrium approach, developed by Lionel W.
McKenjie, Gerald Debreu and Kenneth J. Arrow, exclusively works with the goods spacerather than the price space. In contrast, theHicks-Morishima approach exclusively operates on the price space, thus against the current
main stream of economic theory. Next, themajority of economics readers are usually familiar with the straightforward notion ofdemand and supply curves, but not with thetwisted concept of excess demand curves. Andof course, many people prefer simplicity tocomplexity.

The Hicks-Morishima Approach Reconsidered

I suppose that Morishima would apparently agree with those reasons. In order for theexcess demand approach to become very familiar to the academic circle, we would have to doa sort of extraordinary work for publicity andsales effort. Morishima had special courage towrite a new style of economics text (1984) The
Economics of Industrial Society, in which he adopted the Hicks-Morishima approach again.
Unfortunately, history repeated itself : it again
received a rather dull response. Since I regard
myself as an "academic son" of Morishima andalso as an "academic grandson" of Hicks, I haveto be strong in the neglected stream of academia, strongly arg uing usefulness andapplicability of the Hicks-Morishima Approach.
2-1 Are A Pair of Two Goods Substitutive or Complementary ?
In reality, there seem to be many diversified markets which are more or less interlockedwith each other. If we take a simple example
from a female clothes market, it is true thatskirt and jeans markets are mutually interrelated. Their relations, however, are much more
complicated that a man in the street would
usually imagine. The demand for female cloths
may be influenced by so many possible factors.
First of all, a young stylish girl may want to be
dressed in the height of fashion: indeed, being
behind the fashion would be the most terrible
thing to do. If wearing slim jeans, but not wideskirt, becomes more fashionable than before,
then there would be so many young girls whowant to change their fashion style from skirt tojeans. Besides, if skirt becomes more expensive
due to an increased cost of fabric, then there
would be a tendency that the sale of jeans as a

Yasuhiro Sakai

075

good substitute of skirt will rise. Moreover, theoverall demand for cloths, jeans or skirt, is determined by the purchasing power of buyers.
When the economic conditions become improved (or worsened), people want to spend
more (or less) money for clothing, so that thesales of skirt and jeans will overall tend to goup (or down).
This may not be all of the story. Let us recall that we live in the world of risk anduncertainty. If we consider people's forecasts
and expectations, the demand and supply of agood should get much more complicated.
For instance, even if the price of a skirt has
risen "this week", no one can exactly tell what
will happen to that price "next week." If a
young girl expects it to rise higher next week,
she has a good incentive to buy it this week.
Besides, even if her income stays sluggish thismonth, yet she expects it to go up significantly
the next month, she might feel rich and affluent even now, possibly showing positive buying
behavior. Similar reasoning will be applicableto the supply side, not only the demand side.
In general, if the trader expects the sale to besluggish this year, but to be increasing nextyear, he is likely to positively respond to his optimistic forecast.
To sum up, human beings are complicated,and so are markets. In fact, a skirt market and ajeans market are so intricate that they cannot
simply be analyzed. It is the Hicks-Morishima
approach that can shed a nice analytical lighton the entangled interdependence of several
markets. In historical perspective, that approach was originated in Chapter 5 of Hicks(1939, 1946), and later highly developed inMorishima (1984) in many possible ways. In
our regret, however, time seems to pass too

076

slowly to recognize a masterpiece: indeed, themagnificent Hicks-Morishima approach has
been long undervalued or neglected. As I havesaid repeatedly, it is my sincere desire to revive
the approach once more and hopefully attach
some new findings and flavors to it.
2-2 A Simple Two-Good Model :The Starting PointAt the starting point of discussion, let us
begin our market model analysis with a simple
case of two goods, x1 and x2 . More specifically,
let us suppose that x1 stands for tea and x2 coffee. Further assume that the price of x1 and theone of x2 are respectively denoted by p1 and p2
It is natural to assume that the amount ofdemand for x 1 is dependent not only on p1 ,but also on p2 . Since tea and coffee are presumably in competitive relations, they areformally regarded as "substitutive" in microeconomic theory. Therefore the demand function,
D1, for good 1 may be formulated as follows:

D1 : x1 = – p1 + 0.5 p2 + 3(1)

It is supposed here that there are two different routes by which the amount of demandof coffee, x1, rises. The first route is the direct
one by means of a fall in p1, the price of coffee
per se. This may be called the "own effect" of aprice change. The second route is the indirect
one in the sense that the price rise of tea as a
substitute of coffee causes the change of demand from tea to coffee. This may be named
the "cross effect" of a price change. As is clearlyseen in Eq. (1), it is supposed that the first own
effect overpowers the second cross effect.
Concerning the supply side, we assume
that its direction of change is exactly the oppo-

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site of the demand side. More specifically, let
us consider the following linear supply function:
S1 : x1 = p1 – 0.5 p2 – 1(2)Let the price of coffee rise. Then, we obtain the following two effects. First, thedistributor intends to increase the supply ofcoffee in the market. This is the "own effect" ofa more expensive coffee. Second, when theprice of tea falls, the distributor not only wishes to sell tea less, but also he tends to sell coffee
more. This is the "cross effect" or the "spillover" effect over the two markets. Besides, it is
supposed here that the first own effect overwhelms the second cross one.
We are now in a position to introduce theconcept of an excess demand function. Notethat excess demand means "demand minus supply": namely, E1 = D1 – S1.
Thus, in the light of Eqs. (1) and (2), we
can easily derive the excess demand function
for x1 as follows:
E1 = D1 – S1 : x1 = 2p1 + p2 + 4(3)This demonstrates that the amount of excess demand for good 1 is inversely proportional
to its price (the own effect), whereas the former
amount is in direct proportion to the price ofgood 2 (the cross effect). Besides, understandably, the own effect overpowers the cross one.
Market equilibrium of good 1 is realized
when its demand and supply are just equal,
namely its excess demand completely vanishes.
It is at this equilibrium point that the price ofgood 1 ceases to change. On the one hand, if
the demand for good 1 exceeds its supply, then

The Hicks-Morishima Approach Reconsidered

the excess demand occurs, implying that theprice of good 1 must go up. On the other, if
the demand is less than the supply, then the excess supply occurs, so that the price has to fall.
This is a famous adjustment process a la Leon
Walras, which may be summarized as follows:
E1 > 0 : D1 > S1(disequilibrium)→p1 goes up.
E1 = 0 : D1 = S1(equilibrium)→p1 does notchange.
E1 < 0 : D1 = S1(disequilibrium)→p1 goesdown.
Let us take a look at Fig. 1. In the left chart(A), the straight line on the price plane represents the excess demand function: – 2 p1 + p2
+ 4 = 0. (Note that this function can also be
rewritten as p2 = 2p1 – 4.) Since the two goods
are substitutes, the line is positively sloped.
Moreover, reflecting the fact that the own effect overpowers the cross effect, the slope ofthe straight line for p1-axis should be steeper
than the one for p2-axis , so that the former
slope must exceed 45 degree.
Suppose that a pair of prices (p1, p2) lies
right on the straight line E1. Then, p1 does notchange at all, and maintains the same value as
before. Clearly, the excess demand line E1 = 0
divides the whole price plane into two areas.
In the left area where E1 > 0, p1 rises in a direction indicated by the right arrow ( →). In
contrast, in the right area where E1 < 0, p1 falls
in an opposite direction indicated by the left
arrow (←).
A similar argument will apply for good 2,
or coffee. So, we can formulate the demand ,the supply and the excess demand functions in
the following way:

Yasuhiro Sakai077

D2 : x2 = 0.5 p1 – 2p2 + 4(4)S2 : x2 = –0.5 p1 + p2 – 2(5)E2 = D2 –S2 : x2 = p1 – 3p2 + 6(6)This teaches us that the amount of excess
demand for good 2 is inversely proportional toits price p2 (the own effect), whereas the former
amount is in direct proportion to p1, the priceof good 1 (the cross effect). Besides, as before,
the own effect overpowers the cross one.
The Walras-type adjustment process forgood 2 may be formulated analogously:
E2 > 0 : D2 > S2(disequilibrium)→p2 rises.
E2 = 0 : D2 = S2(equilibrium)→p2 does notchange.
E2 < 0 : D2 < S2(disequilibrium)→p2 falls.
Let us take a look at Fig. 1 again. In theright chart diagram (B), the straight line E2 =0, or p1 – 3p2 + 6 = 0, represents the excess demand for good 2. Note that this line may be
rewritten as p1 = 3p2 – 6. This is the case inwhich the two goods are substitutes and eachown effect is dominating, so that the excess demand line is positively sloped and its "slope forp2-axis" must exceed 45 degree. The directionsof price adjustment p2 are indicated by arrows
in the figure.: namely, p2 rises in the lower area,
but falls in the upper area.
2-3 General Equilibrium of Two
Markets: The Simplest Case
We are now ready to get into the world of"general equilibrium" with the two goods, inwhich the demand and supply of each good are
just equal and the changes of prices stop moving. In other words, general equilibrium looks
like a stationary state.

(A) Excess demand for x1 :changes in(B) Excess demand for x2 : changes in

p1 and p2

p1 and p2

Fig. 1 The Relation between the Two Markets

078

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Summer / July 2020 / No.424

Now, let us carefully investigate what happens if the two chart diagrams (A) and (B) of
Fig. 1 as well as the corresponding sets of arrows are superimposed. Then, we will
immediately see that a very charming float diagram like Fig. 2 appears. At the intersection
point Q of the two excess demand lines, E1 = 0
and E2 = 0, the following two equations mustbe satisfied :–2 p1 + p2 + 4 = 0
p1 – 3p2 + 6 = 0

(7)
(8)

Solving Eqs. (7) and (8) for p1 and p2 simultaneously, we can see that a pair of
coordinates of the intersection point Q isshown by Q = (18/5, 16/5). Therefore, theequilibrium prices of p1 and p2 are respectively
18/5 (= 3.6) and 16/5 (= 3.2).3)

To sum up, the intersection point Q indicates the point of "general equilibrium" of thetwo markets. Remarkably, it should be a stable
point as well. Note that any price movements
may be shown by the arrows of the pair (p1, p2).
In whatever direction the price pair may movein Fig. 2, it is eventually destined to converge atthe equilibrium point Q.

III

Many Non-Normal Cases:
Instability,
Multiple-Equilibrium,
and Nonexistence

3-1 The Saddle-Point Equilibrium:
Substitutable Goods yet
Dominating Cross Effects
As the saying goes, saying is one thing but
doing is really another. All the foregoing analyses have just dealt with the ideal, utopian two-Fig. 2 The existence and stability of the two-good markets: An ideal state3) A group of chart diagrams like Fig. 2 were first intro-

chance.

The Hicks-Morishima Approach Reconsidered

Yasuhiro Sakai

duced by Hicks (1939). Morishima who admired Hicks
so much intended to make the chart diagrams revived,with the aim of establishing his own "new economics."
To our regret, however, such revival of the Hicks-Morishima approach has not been very successful so far. It is
our real intention that we give the approach one more079

good world in which the only one point ofgeneral equilibrium uniquely exists and its stability is also guaranteed. One might wonder ifsuch utopian world really exists. When we are
getting into the real world as it is, it is far fromperfect, with a lot of irregularities. For instance, general equilibrium might not exist atall. There would be more than one equilibrium. Besides, many other "irregular situations"
including unstable points and/or saddle points
might occur.
Suppose that there is a market equilibriumwith substitutable goods. Then, the most important question to ask is whether and to what
extent the stability of the equilibrium is guaranteed. Interesting enough, the equilibrium is
not always stable. In fact, we will see that thecross effects of price changes act as disturbing
factors of instability. In fact, if the cross effects
are strong enough to outweigh the own effects,

then the equilibrium point will become a nonstable saddle point. To clarif y such aninteresting point, let us focus on the case thatthe excess demand functions are of the following forms:
E1 : E1 = – p1 + 2p2 – 4(9)E2 : E2 = 3p1 – p2 – 6(10)The excess demand lines of good 1 andgood 2 are depicted in Fig. 3. Since we are dealing with substitutable goods, it follows thatboth lines should be positively sloped. There is
an important point we should not miss, however. Note, the cross effects are strong enoughto outweigh the own effects. Indeed, in Eq. (9)above, the absolute value 2 of the coefficient of
p2 is greater than the one 1 of the coefficient of
p1 , whereas in Eq. (10), the absolute value 3 ofFig. 3 The equilibrium point is an unstable saddle point: Thecross effect is so strong080

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the coefficient of p1 exceed the one 1 of the coefficient of p2.
As a result, in sharp contrast to the idealistic case discussed above, the slope of E1- line issteeper for p2-axis, whereas the one of E2- line
is steeper for p1- axis.
Let compare Fig. 2 and Fig. 3. Then, weclearly understand that the positional relationship of the lines E1 = 0 and E2 = 0 has been
reversed. Consequently, such reversal of locations would critically change the adjustment
processes of prices.
The coordinates of equilibrium point is Q
= (16/5, 18/5). Apart from the previous discussion, however, we can no longer say that thispoint is a stable point in its true sense. In fact,
it should be a saddle point that is unstable on
almost all paths. As is seen in Fig. 3, except only for the two stable paths, one path going
down from the North-West to Q, and another(A) The prices are declining to zero

going up from the South-East to Q, all otherpossible paths are not stable at all. This meansthat the saddle point Q should substantially beunstable.
3-2 Non-Existence of the
Two-Market Equilibrium
What we should consider next is the emergence of "non-normal situations." Since all ofthem are of vital importance, they respectively
require for very careful investigations. As thefirst example, let us examine the case in which
the excess demand functions are written as follows:

E1 : E1 = – 2p1 + p2 – 2(11)E2 : E2 = p1 – 2p2 – 2(12)Let us take a look at Fig. 4. As is seen in
Chart (A), the two excess demand lines, E1 = 0(B) The prices are expanding foreverFig. 4 Non-existence of equilibriums

The Hicks-Morishima Approach Reconsidered

Yasuhiro Sakai

081

and E2= 0, never intersect at all in the positive
coordinates of the price space. If we dared tosolve for p1 and p2 in Eqs. (11) and (12), wewould obtain a pair of NEGATIVE prices (p1,p2) = (–2, –2), which should not economicallybe meaningful. Eventually, as is shown inChart (A), both prices, p1 and p2 , tend to eventually decline toward zero along the directionsof arrows.
If we interchange the positions of the twolines, E 1 = 0 and E 2 = 0 in the left chart (A),then we immediately obtain those lines in theright chart (B). Then, we have to deal with thefollowing set of equations:
E1 : E1 = p1 + 2p2 + 4(11)E2 : E2 = 3p1 – p2 + 6(12)In Chart (B), there exist no intersectionsof the two lines in the positive price quadrant.
If we dared to simultaneously solve E1 = 0 andE2 = 0, then we would find (p1, p2) = (–16/5,–18/5), a pair of negative and economicallymeaningless prices. As a result, there are no
general equilibrium solutions, and the prices
eventually tend to rise forever as indicated byarrows.
3-3 The Case of Complementary
Goods : A Completely
New Situation
In the above, we have limited our investigation to the case of competitive or substitutable
goods. Looking at the real world, however, we
can eyewitness many other cases in which somegoods may not be mutually competitive but
rather move in the same direction. For instance, while tea and coffee are substitutes, tea

082

and sugar are complementary, and so are coffeeand sugar.
As the first example of complementary
goods, let us discuss the following excess demand functions of the two goods:
E1 : E1 = 2p1 – p2 + 4(13)E2 : E2 = – p1 – 3p2 + 6(14)Let take a close look at Eq. (13) and (14).
The, we will see that in the right-hand sides of
those equations, the values of coefficients of p1– term and p2 – term are both negative. Thismeans that both the excess demands for x1 andx2 have to increase when p1 falls, or when p2
falls. This implies that the two goods are complementary, not substitutes. Besides, we
assume here that the own effects overpowers
the cross effects. Therefore, we would rightly
conjecture that the equilibrium point Q , if itexists, must be stable. Surely, such conjecture
will turn out be right by looking at the left
chart (A) of Fig. 5.
Concerning Fig. 5, there is one more point
to watch. We must make sure that the two excess demand lines, E 1 and E 2 , are now
NEGATIVELY sloped. Since the own effects
dominate the cross effects in Chart (A), it follows that both the slope of E1 for p1 – axis andthe slope of E2 for p2 – axis should be steeper.
We will turn to the second case which isrepresented by the following pair of excess demand functions:
E1 : E1 – p1– 3p2 + 6(15)E2 : E2 – 2p1 – p2 + 4(16)Now, the cross effects are now more powerful than the own effects. As can easily be

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Summer / July 2020 / No.424

(A) Point Q is stable since the own effects are
dominating
Fig. 5 The two goods are complementary

seen in Chart (B), the slope of E1 for p2 – axis
(not for p1 – axis) is steeper while the the oneof E2 for p1 – axis (not for p2 – axis ) is steeper.
Therefore, the equilibrium point Q is an almost
unstable saddle point.
In conclusion, the power relation between
the own effects and the cross effects plays a vital role in the determination of the stability ofan equilibrium point. Whether the goods aresubstitutes or complementary, the dominanceof the own effects over the cross effects clearly
guarantees the stability of an equilibrium. On
the contrary, if the cross effects dominate theown effects, then an equilibrium point becomes an almost unstable saddle point.

IV Comparative Statics:

The Impact of Parameter
Changes on Equilibriums

Let us turn our attention to the issue of

The Hicks-Morishima Approach Reconsidered(B) Point Q is unstable since the cross effects are
dominatingcomparative statics. This is a very important
problem that was first intensively discussed by
J.R . Hicks and later greatly developed byMichio Morishima.
First of all, let us assume that the twogoods are substitutes like tea and coffee. Let us
take a look at Fig. 7. In the left chart (A), thestraight lines E1 and E2 respectively represent
the excess demand lines of good 1 (tea) andgood 2 (coffee). More specifically, let us consider the following set of equations:
E1 : E1 = – 2p1 + p2 + 4(15)E2 : E2 = p1 – 3p2 + 6(16)If we put E1 = 0 and E2 = 0 and solve forp1 and p2, we find a pair of equilibrium prices:in fact, (p1Q , p2Q ) = (3.6, 3.2).
Now suppose that because of some reasons,the popularity of tea suddenly rises among thepeople. Then, the excess demand curve E1 has

Yasuhiro Sakai

083

(A) The goods are substitutable(B) The goods are complimentary

Fig. 7 Comparative statics: changes in excess demand

to shift to the right. This implies that regarding the constant term of Eq, (15) above, it has
to change its value from 4 to (4 + α):
A change in E1 : E1 +α = – 2p1 + p2 + 4 + α(17)Let us take a look at Fig. 7. In Chart (A),the new equilibrium point R is found at the intersection of the two lines, E1 = 0 and E2 = 0.
For convenience, let us specify α = 2. Then, thecoordinates of R are calculated as (p1R, p2R) =(4.8, 3.6).
4-1 Hicksian Three Laws of Price
Changes: The Case of Substitutable Goods
In his classic Value and Capital, Hicks(1939, 1946) succeeded in deriving the very famous three laws which stood for the core of his
comparative static results. It was also remark-084

able to see that those Hicksian laws were later
developed a great deal by his successor, Morishima (1984). It is the Hicksian laws that wewill intensively investigate in this and following
subsections.
We are most interested in comparing thetwo equilibrium points, the old point Q and
the new point R. We are expected to obtainseveral results of great importance. First of all,we would like to pay attention to comparisonof the following two relations:
p1R = 4.8 > 3.6 = p1Q(18)p2R = 3.6 > 3.2 = p2Q(19)
To begin with, let us suppose that becauseof some reasons, tea becomes very popularamong the people, whence its demand suddenly increases. To take an example, the openingof the Great Britain Exhibition in Kyoto may
produce such a sudden surge for the popularity

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Summer / July 2020 / No.424

of tea in Japan. Then, its immediate effect we
can expect to have is that tea will be more expensive than before in response to the demand
increase. Not only that, there would also be
many other repercussions such as its indirect
impact on other markets including the coffee
market. Besides, those influences will invoke
the third and forth rounds of repercussions as
well. Those direct and indirect effects would
make our repercussion calculations very hardand complicated. In order to make sure of thispoint, if we patiently compute the proportional
rates of increase of the prices (in terms of percent), then we will be able to derive the following equations:(p1R – p1Q) / p1Q = (4.8 – 3.6) / 3.6 = 1/3
(20)(p2R – p2Q) / p2Q = (3.6 – 3.2) /3.2 = 1/8
(21)Clearly, the ratio (p1R – p1Q) / p1Q is greater than the ratio (p2R – p2Q) / p2Q , implyingthat the rising rate of tea exceeds the one ofcoffee.
We must bear in mind that whether or not
the excess demand functions are linear, all thecomparative static results derived above generally hold. J.R. Hick first obtained all thoseresults which Michio Morishima rightfully
called the "Hicksian Three Laws of Price
Changes." They are really outstanding consequenses of the Hicks-Morishima approach,which can be summarized as the following theorem.

The Hicks-Morishima Approach Reconsidered

Theorem 1(Hicks-Morishima on substitutable goods)

Assume that the two goods, x1 and x2, aresubstitutable and that the own effects overpower the cross effects. Then the point ofgeneral equilibrium, if it exists, must be stable.
When the excess demand for good 1, E1, increases, the following three properties must
hold:(i) The price of good 1, p1, will rise.
(ii) The price of good 2, p2, will rise too.
(iii)	The price of good 1 will rise proportionately more than the price of good 2;
namely, the price ratio (p1 /p2) will rise.
4.2 The Case of Complementary
Goods: Hicksian Three Laws
Continued
Now, let us turn to the case of complementary goods Let us assume that goods 1 and 2
respectively represent tea and sugar. Then, as
Chart (B) of Fig. 7 above tells us, the two excess demand lines, E 1 and E 2 , are both
downward sloped. If we suppose that the own
effects outweigh the cross effects, then the oldintersection point Q becomes a stable point.
Now, suppose that a sudden tea boom happens among the people, resulting in a drastic
increase in tea demand. This is the first direct
effect of tea price rise. Moreover, such rise willlead to a sequence of secondary repercussions
since it will dampen the demands for both tea
and sugar. Recall here that complementary
goods have to go in the same direction. This is
the second indirect effect. If we employ a similar reasoning, then we would also take accountof third and fourth round of repercussions thatmust have less influence than the second round.

Yasuhiro Sakai

085

In Chart (B), let us shift the excess demand
function to the right, from E1 to E1 + α. Then,since such shift changes the equilibrium point
in a right and downward direction, from Q to
R, it will have to cause a big rise in p1 together
with a small change in p2. Consequently, in absolute value terms, the rising rate of p 1 will
exceed the falling rate of p2. We omit a moredetailed calculation here.
The final results for the case of complementary goods will be summarized as thefollowing theorem:
Theorem 2(Hicks-Morishima on complementary goods）

Suppose that the two goods, x1 and x2, arecomplementary, and that the own effects overpower the cross effects. Then, the point ofgeneral equilibrium, if it exists, must be stable.
When the excess demand for good 1, E1, increases, the following three properties must
hold:(i) The price of good 1, p1, will rise.
(ii) The price of good, p2, will fall a bit.
(iii)	The rising rate of good 1 will be greaterthan the falling rate of good 2; namely,
price ratio (p1 / p2) will rise a great deal.
As I mentioned before, the exact derivation of Theorems 1 and was the main theme of
the Young Morishima. For that purpose, heliterally racked his brains. In this paper, I haveintended to limit my analysis on a simple yet
useful case of linear excess demand functions.
Besides, following the Morishima spirits, I haveoften made use of many eye-catching graphicalapproaches. I can say, however, that the extension of my analysis to the more general

086

nonlinear cases should not be so difficult, requiring for a bit more calculation and patience.

V

Morishima Towards
a New Economics

This paper may be regarded as an hommage to my two great mentors, Professors John
R. Hicks and Michio Morishima. The HicksMorishima approach wa s adopte d anddeveloped by Morishima in his book (1984).
For this book, Morishima gave an interesting
subtitle "An Introduction to New Economics."
Because it was far more than "an introduction"and contained "several new and original results," it seemed to me that the subtitle per sewas "too modest, and even cheating." In fact,
Morishima himself made several remarks :The approach of this book differs to a considerable degree from standard ecnomics. ...
This book attempts to analyze the pricemechanism in accordance with reality and at
the same time to introduce students directly
to the major problems of economics – ananalysis of the way in which the real economy operates and the best way to bring abouta change in direction in this operation.
(Morishima, 1984, Preface)
Morishma's later book (1999) could bethought of as one of his "last swans," in which
he greatly lamented the recent Japanese society
as one approaching at a "dangerous stage."
Here again, he made some intriguing remarks:
This book is the one I have constantly wanted to write for a long time. In fact, it is a sortof a "Grand Integral Social Science" in the

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Summer / July 2020 / No.424

sense that it contained economics, sociology,
education, history and many other related
fields. It could rightly be called an "Academic Symphony." .. Let us take a careful look atmany non-economic fields such as the worldsof politics, religion, and ideology. Then you
will see that many main actors such as political, religious , and military bosses may playvery large roles in our society. Unfortunately,
economics and other related fields are so
powerless to investigate those important
problems. So, I should say that the existingsocial science remains in an under-developed
state, thus lacking its very essential core."(Morishima, 1999, Appendix)

⦿Hirota, M. and Sakai, Y. (1969) Notes on Substitution

and Scale Effects in Production Theory, unpublishedmanuscript, University of Rochester.

⦿Komoro, N. (2004) Economics Super Stars: Seminar on

the History of Economic Thought, in Japanese. Diamond
Publishers, Tokyo.

⦿Morishima, M. (1974) “Marx in the Light of Modern

Economic Theory,” Econometrica, Vo.42, No.4, pp.611632.

⦿Morishima, M. (1984) The Economics of Industrial Soci-ety, Translated by Anthony, Clark and Hunter. Cambridge University Press..

⦿Morishima, M. (1999) Relying on your Intellect Makes

you Harsh and Rigid, in Japanese. Iwanami Publishers,
Tokyo.

⦿Morishima, M. (1999) Why Will Japan Collapse? (inJapanese). Iwanami Publishers, Tokyo.

⦿Sakai, Y. (1972) Axiomatic Foundations of Consumption

and Production Theories. Ph.D. dissertation thesis, University of Rochester.

Honestly speaking, the right way toward
the "Grand Integral Social Science" a la Morishima seems to be too far for me to take. Evena right direction for the road has not beenfound yet. A few years ago, when I published
my book (2010) The Economic Thought of Risk
and Uncertainty written in Japanese, I sent one
copy to Professor Tetsuya Nose, a close friendof Morishima. Nose immediately replied tome, "This looked like 'an academic symphony' ala Morishima! " This was really the highest
praise on my academic work.
I sincerely hope that this paper would serve
very well as one small step toward Morishima's
dream of establishing the Grand Integral Social
Science. I strongly believe in the following
golden saying: "Life is an adventure! Life is really a challenge! "References
⦿Hicks, J. R (1939, 2nd ed. 1946) Value and Capital, Ox-

ford University Press.

The Hicks-Morishima Approach Reconsidered

Yasuhiro Sakai

087

The Hicks-Morishima Approach Reconsidered
Another Look at the Interdependence of Several Markets

Yasuhiro Sakai

This paper aims to shed some new light on
the Hicks-Morishima approach to the interdependence of several markets. In spite of its
rather simple and ambitious framework for theinterdependence of several markets, it is quite
unfortunate that this approach has been rather
neglected in the academic circle. I suppose that
there are several reasons for this. First, the traditiona l g enera l e quilibrium approachdeveloped by Lionel W. McKenzie, Gerald Debreu and Kenneth J. Arrow exclusively works
with the good space rather than the price space.
In contrast, the Hicks-Morishima approachbased on Hicks' classical book Value and Capital exclusively operates on the price space, thus
against the current main stream of economic
theory. Next, the majority of economics readers are usually familiar with the straightforward
notion of demand and supply curves, but notwith the twisted concept of excess demand
curves. It is one of my main purpose to mendsuch unfortunate tendency, presumably proceeding toward the establishment of a new
grand system of social science. We can learn
new lessons from old teachings.
Keywords: J.R. Hicks, M. Morishima, Valueand Capital, excess demand curves, generalequilibrium analysis, comparative statics
JEL Classification B31, C62, D51

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The Hicks-Morishima Approach Reconsidered

Yasuhiro Sakai

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