The Hicks-Morishima Approach Reconsidered

Articles I Michio Morishima and John R. Hicks: the Two Superstars of Economics

There are the two economics superstars The Hicks-Morishima who have greatly influenced my academic ca- Approach Reconsidered reer. They are Michio Morishima, Osaka University and London School of Economics, and John R. Hicks, London School of Eco- Another Look at the Interdependence nomics and Oxford University. To tell the of Several Markets truth, both of them already passed away. Aca- demically, 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 and shed new light on a topic named the Hicks- Yasuhiro Sakai Morishima approach to the interdependence Shiga University / Professor Emeritus of several markets. Although such approach has been rather neglected for some time, I am sure that even now, it is worthy of serious re- consideration, 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 and Hicks in their late years. When I was a graduate student at the Uni- versity of Rochester, I was fortunate to meet with Mr. Masayoshi Hirota, a "very serious man with highly samurai spirits," who so fondly argued night and day with me about life phi- losophy, world matters, and of course

072 THE HIKONE RONSO Summer / July 2020 / No.424 economic science. According to Hirota, we completion of my doctoral dissertation (1972) should not have any fears about the seemingly Axiomatic Foundations of Consumption and high levels of American universities. Osaka Production Theories submitted to The Universi- University seemed to be at least on a par with, ty of Rochester, with my main thesis advisor and even better than, University of Rochester. being Professor Lionel W. McKenzie. After Hirota proposed me to do a joint work on gen- finishing my Ph. D. work and publishing many eral equilibrium theory with the final aim of theoretical papers in international journals, I publishing academic papers in professional could spend a happy life at Pittsburgh, in journals of high prestige. We worked very hard which Professor Asatoshi Maeshiro and his by utilizing every space of the Rochester cam- wife Kazuko kindly helped me in many ways. pus, namely the university library, class rooms, All those nice things happened to my rather student dining rooms, and the graduate stu- long American life in the period 1968-1976.1) dent center. After some time of our joint I can vividly recall that at the very end of research, there came our final product, Hirota 1973, my important meeting with Michio Mor- and Sakai (1969), which aimed to open a new ishima took place in New York City. More horizon in theoretical studies in production exactly, he was invited to deliver a special lec- theory. Although our joint paper had a hum- ture at Econometric Society North American ble yet attractive title "On Substitution and Meeting at New York Hilton Hotel, with Pro- Scale Effects in Production Theory," it was fessor Lawrence W. Klein of Pennsylvania quite unfortunate that because of some minor serving as a respectable chairman. The audi- technical reasons, it missed a publication op- ence filled the hall to overflowing. Professor portunity. Akira Takayama, a noted international econo- In hindsight, I am sure that my joint re- mist, sat in the very front seat, taking so many search experience with Mr. Hirota, or "Osaka pictures. All the people seemed to have a very samurai scholar," has constantly given us a great happy time by enjoying the presence of the stimulus for the execution of our research proj- memorable trio, namely Morishima, Klein and ect on economic theory. Indeed, having been Takayama. Then, Morishima stood up and de- encouraged a great deal by the Hirota-Sakai livered a historical speech: "Kark Marx is so cooperation, I myself continued to learn many great! I have no doubt that he is academically advanced mathematical tools which were ap- still alive after one hundred years of his death!" plicable not only to production theory, but In an instant, the whole audience stood up and also to consumption theory as well. The final applauded his powerful speech.2) result of my continuous research effort was the

1) In September 1972, I submitted my Ph.D. disserta- Morishima of Osaka University and Lawrence Klein of tion to the University of Rochester, with Professors Lio- the University of Pennsylvania. nel W. McKenzie and James Friedman being thesis ad- 2) More exactly speaking, Professor Morishima's invited visers. As we seen in Sakai (1972), the thesis consisted of lecture was titled the two parts. The first part carefully discussed axiom- Marx in the Light of Modern Economic . It was nothing but a Walras memorial lecture at atic approaches to consumption theory, the second part Theory the North American Meeting of Econometric Society. mathematical foundations of production theory. I Although it was first read at Hilton Hotel, New York, in would like to point out that Chapter 3 in Part 2, titled 28 December 1973, it was later published as a leading ar- , was An Axiomatic Approach to Input Demand Theory ticle of (see Morishima, 1974). It was real- based on my joint work with Dr. Masayoshi Hirota with Econometrica ly lucky that I myself was right there as an attentive au- further refinements. Very fortunately, a still further re- dience. This constitutes one of never-to-be-forgotten vision of this Chapter was published in International memories in my long academic life. Economic Review, which was first published by Michio

The Hicks-Morishima Approach Reconsidered Yasuhiro Sakai 073 In what follows, I would like to just pick mind was how Hicks' market laws aforemen- up Hicks' great book Value and Capital (1939, tioned would had to change by the 1946), carefully discussing how closely Hicks introduction of distance and space. In my and Morishima have been connected by this student days, I was literally swamped with masterpiece. A famous writer Naoki Komuro such a very difficult problem. (2004) once remarked: (Morishima, 1999)

During the Second World War, Morishima It was quite fair to say that in those days, served as a naval cadet whose duty wasto Morishima stood high and alone in the Japa- break a secret code of the enemy. When he nese academia: in fact, the research level of left home toward a battlefront, he carried an Morishima went far beyond the one of any or- important book with himself. That book dinary Japanese economist. He was a man of was nothing but a newly published text Va l - courage and determination. The major aim of ue and Capital by Hicks, then a rising star this paper is to reconsider Hicks' law of market economist of the United Kingdom, one of exchange in a new modern fashion, thus fur- Japan's hostile countries. Nevertheless, Mor- ther extending the Hicks-Morishima approach ishima, who faithfully conducted his secret with my unique flavor attached to it. mission of code breaking, dared to exert all I have met with Hicks several times. My his energy to fully understand the Hicks most memorable moment took place when I new book, and safely could return home attended the International Conference in (Komuro, 2004) Honor of J.R. Hicks, Bologna, Italy, in 1991. It gave me a great and unforgettable memory. Later in his life, Morishima (1999) got a The outline of this paper is as follows. The sudden surge of nostalgia for his youth: second section will deal with s simple model of general equilibrium — the excess demand ap- When I [Morishima] was a Kyoto Universi- proach a la Hicks and Morishima. The third ty student just after the last war, I was fondly section will discuss many non-normal cases. reading Value and Capital by J.R. Hicks. The issues of instability, multiple equilibrium He discovered the following law of critical and non-existence will be successively taken up. importance: "Let the excess demand for one In the fourth section, we will turn to the prob- good increase. Then, not only will its price lem of comparative statics. The impact of will rise, but also the prices of other substi- parameter changes on equilibrium values will tutive goods will rise, whereas the prices of carefully be investigated. Final remarks will be complementary goods will decline." I no- made in the fifth section, with reference to ticed, however, that he carelessly neglected Morishima's life-long dream of a grand synthet- the undeniable truth that any economic ac- ic approach to a so-called "symphonic tivity including market trading had to economics." operate at some distance in a space. My question which would naturally arise in my

074 THE HIKONE RONSO Summer / July 2020 / No.424 II A Simple Model of I suppose that Morishima would apparent- General Equilibrium: ly agree with those reasons. In order for the The Excess Function excess demand approach to become very famil- Approach a la iar to the academic circle, we would have to do Hicks and Morishima a sort of extraordinary work for publicity and sales effort. Morishima had special courage to Saying is one thing. But doing is another. write a new style of economics text (1984) The Now let us discuss the working and perfor- Economics of Industrial Society, in which he ad- mance of a simple model of general opted the Hicks-Morishima approach again. equilibrium. To this end, we will adopt the ex- Unfortunately, history repeated itself : it again cess demand approach a la Hicks and received a rather dull response. Since I regard Morishima. The Hicks-Morishima approach is myself as an "academic son" of Morishima and a very effective one to shed light on interrela- also as an "academic grandson" of Hicks, I have tion of excess demand curves in the price space to be strong in the neglected stream of aca- for an in investigation of the working and per- demia, strongly arguing usefulness and formance of general equilibrium. Although applicability of the Hicks-Morishima Ap- we focus on a simple two-good model in this proach. paper, its generalization to any several good model would require no difficult task. 2-1 Are A Pair of Two Goods Sub- Honestly speaking, in spite of its rather stitutive or Complementary ? simple and ambitious framework, it is quite In reality, there seem to be many diversi- unfortunate that the Hicks-Morishima ap- fied markets which are more or less interlocked proach has been long neglected in the academic with each other. If we take a simple example circle. I suppose that there are several reasons from a female clothes market, it is true that for this. First of all, the traditional general skirt and jeans markets are mutually interrelat- equilibrium approach, developed by Lionel W. ed. Their relations, however, are much more McKenjie, Gerald Debreu and Kenneth J. Ar- complicated that a man in the street would row, exclusively works with the goods space usually imagine. The demand for female cloths rather than the price space. In contrast, the may be influenced by so many possible factors. Hicks-Morishima approach exclusively oper- First of all, a young stylish girl may want to be ates on the price space, thus against the current dressed in the height of fashion: indeed, being main stream of economic theory. Next, the behind the fashion would be the most terrible majority of economics readers are usually fa- thing to do. If wearing slim jeans, but not wide miliar with the straightforward notion of skirt, becomes more fashionable than before, demand and supply curves, but not with the then there would be so many young girls who twisted concept of excess demand curves. And want to change their fashion style from skirt to of course, many people prefer simplicity to jeans. Besides, if skirt becomes more expensive complexity. due to an increased cost of fabric, then there would be a tendency that the sale of jeans as a

The Hicks-Morishima Approach Reconsidered Yasuhiro Sakai 075 good substitute of skirt will rise. Moreover, the slowly to recognize a masterpiece: indeed, the overall demand for cloths, jeans or skirt, is de- magnificent Hicks-Morishima approach has termined by the purchasing power of buyers. been long undervalued or neglected. As I have When the economic conditions become im- said repeatedly, it is my sincere desire to revive proved (or worsened), people want to spend the approach once more and hopefully attach more (or less) money for clothing, so that the some new findings and flavors to it. sales of skirt and jeans will overall tend to go up (or down). 2-2 A Simple Two-Good Model : This may not be all of the story. Let us re- The Starting Point call that we live in the world of risk and At the starting point of discussion, let us uncertainty. If we consider people's forecasts begin our market model analysis with a simple and expectations, the demand and supply of a case of two goods, x1 and x2 . More specifically, good should get much more complicated. let us suppose that x1 stands for tea and x2 cof- For instance, even if the price of a skirt has fee. Further assume that the price of x1 and the risen "this week", no one can exactly tell what one of x2 are respectively denoted by p1 and p2 will happen to that price "next week." If a It is natural to assume that the amount of young girl expects it to rise higher next week, demand for x 1 is dependent not only on p1 , she has a good incentive to buy it this week. but also on p2 . Since tea and coffee are pre- Besides, even if her income stays sluggish this sumably in competitive relations, they are month, yet she expects it to go up significantly formally regarded as "substitutive" in microeco- the next month, she might feel rich and afflu- nomic theory. Therefore the demand function, ent even now, possibly showing positive buying D1, for good 1 may be formulated as follows: behavior. Similar reasoning will be applicable to the supply side, not only the demand side. D1 : x1 = – p1 + 0.5 p2 + 3 (1) In general, if the trader expects the sale to be sluggish this year, but to be increasing next It is supposed here that there are two dif- year, he is likely to positively respond to his op- ferent routes by which the amount of demand timistic forecast. of coffee,x 1, rises. The first route is the direct To sum up, human beings are complicated, one by means of a fall in p1, the price of coffee and so are markets. In fact, a skirt market and a per se. This may be called the "own effect" of a jeans market are so intricate that they cannot price change. The second route is the indirect simply be analyzed. It is the Hicks-Morishima one in the sense that the price rise of tea as a approach that can shed a nice analytical light substitute of coffee causes the change of de- on the entangled interdependence of several mand from tea to coffee. This may be named markets. In historical perspective, that ap- the "cross effect" of a price change. As is clearly proach was originated in Chapter 5 of Hicks seen in Eq. (1), it is supposed that the first own (1939, 1946), and later highly developed in effect overpowers the second cross effect. Morishima (1984) in many possible ways. In Concerning the supply side, we assume our regret, however, time seems to pass too that its direction of change is exactly the oppo-

076 THE HIKONE RONSO Summer / July 2020 / No.424 site of the demand side. More specifically, let the excess demand occurs, implying that the us consider the following linear supply func- price of good 1 must go up. On the other, if tion: the demand is less than the supply, then the excess supply occurs, so that the price has to fall. S1 : x1 = p1 – 0.5 p2 – 1 (2) This is a famous adjustment process a la Leon Walras, which may be summarized as follows: Let the price of coffee rise. Then, we obtain the following two effects. First, the E1 > 0 : D1 > S1(disequilibrium)→p1 goes up. distributor intends to increase the supply of E1 = 0 : D1 = S1(equilibrium)→p1 does not coffee in the market. This is the "own effect" of change. a more expensive coffee. Second, when the E1 < 0 : D1 = S1(disequilibrium)→p1 goes price of tea falls, the distributor not only wish- down. es to sell tea less, but also he tends to sell coffee more. This is the "cross effect" or the "spill Let us take a look at Fig. 1. In the left chart over" effect over the two markets. Besides, it is (A), the straight line on the price plane repre- supposed here that the first own effect over- sents the excess demand function: – 2 p1 + p2 whelms the second cross one. + 4 = 0. (Note that this function can also be We are now in a position to introduce the rewritten as p2 = 2p1 – 4.) Since the two goods concept of an excess demand function. Note are substitutes, the line is positively sloped. that excess demand means "demand minus sup- Moreover, reflecting the fact that the own ef- ply": namely, E1 = D1 – S1. fect overpowers the cross effect, the slope of Thus, in the light of Eqs. (1) and (2), we the straight line for p1-axis should be steeper can easily derive the excess demand function than the one for p2-axis , so that the former for x1 as follows: slope must exceed 45 degree. Suppose that a pair of prices (p1, p2) lies E1 = D1 – S1 : x1 = 2p1 + p2 + 4 (3) right on the straight line E1. Then, p1 does not change at all, and maintains the same value as This demonstrates that the amount of ex- before. Clearly, the excess demand line E1 = 0 cess demand for good 1 is inversely proportional divides the whole price plane into two areas. to its price (the own effect), whereas the former In the left area where E1 > 0, p1 rises in a direc- amount is in direct proportion to the price of tion indicated by the right arrow (→). In good 2 (the cross effect). Besides, understand- contrast, in the right area where E1 < 0, p1 falls ably, the own effect overpowers the cross one. in an opposite direction indicated by the left Market equilibrium of good 1 is realized arrow (←). when its demand and supply are just equal, A similar argument will apply for good 2, namely its excess demand completely vanishes. or coffee. So, we can formulate the demand , It is at this equilibrium point that the price of the supply and the excess demand functions in good 1 ceases to change. On the one hand, if the following way: the demand for good 1 exceeds its supply, then

The Hicks-Morishima Approach Reconsidered Yasuhiro Sakai 077 D2 : x2 = 0.5 p1 – 2p2 + 4 (4) 0, or p1 – 3p2 + 6 = 0, represents the excess de- S2 : x2 = –0.5 p1 + p2 – 2 (5) mand for good 2. Note that this line may be E2 = D2 –S2 : x2 = p1 – 3p2 + 6 (6) rewritten as p1 = 3p2 – 6. This is the case in which the two goods are substitutes and each This teaches us that the amount of excess own effect is dominating, so that the excess de- demand for good 2 is inversely proportional to mand line is positively sloped and its "slope for its price p2 (the own effect), whereas the former p2-axis" must exceed 45 degree. The directions amount is in direct proportion to p1, the price of price adjustment p2 are indicated by arrows of good 1 (the cross effect). Besides, as before, in the figure.: namely,p 2 rises in the lower area, the own effect overpowers the cross one. but falls in the upper area. The Walras-type adjustment process for good 2 may be formulated analogously: 2-3 General Equilibrium of Two Markets: The Simplest Case E2 > 0 : D2 > S2(disequilibrium)→p2 rises. We are now ready to get into the world of E2 = 0 : D2 = S2(equilibrium)→p2 does not "general equilibrium" with the two goods, in change. which the demand and supply of each good are E2 < 0 : D2 < S2(disequilibrium)→p2 falls. just equal and the changes of prices stop mov- ing. In other words, general equilibrium looks Let us take a look at Fig. 1 again. In the like a stationary state. right chart diagram (B), the straight line E2 =

(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 THE HIKONE RONSO Summer / July 2020 / No.424 Now, let us carefully investigate what hap- To sum up, the intersection point Q indi- pens if the two chart diagrams (A) and (B) of cates the point of "general equilibrium" of the Fig. 1 as well as the corresponding sets of ar- two markets. Remarkably, it should be a stable rows are superimposed. Then, we will point as well. Note that any price movements immediately see that a very charming float dia- may be shown by the arrows of the pair (p1, p2). gram like Fig. 2 appears. At the intersection In whatever direction the price pair may move point Q of the two excess demand lines, E1 = 0 in Fig. 2, it is eventually destined to converge at and E2 = 0, the following two equations must the equilibrium point Q. be satisfied : III Many Non-Normal Cases: –2 p1 + p2 + 4 = 0 (7) Instability, p1 – 3p2 + 6 = 0 (8) Multiple-Equilibrium, and Nonexistence Solving Eqs. (7) and (8) for p1 and p2 simultaneously, we can see that a pair of 3-1 The Saddle-Point Equilibrium: coordinates of the intersection point Q is Substitutable Goods yet shown by Q = (18/5, 16/5). Therefore, the Dominating Cross Effects equilibrium prices of p1 and p2 are respectively As the saying goes, saying is one thing but 18/5 (= 3.6) and 16/5 (= 3.2).3) doing is really another. All the foregoing analy- ses have just dealt with the ideal, utopian two-

Fig. 2 The existence and stability of the two-good markets: An ideal state

3) A group of chart diagrams like Fig. 2 were first intro- chance. 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-Mor- ishima approach has not been very successful so far. It is our real intention that we give the approach one more

The Hicks-Morishima Approach Reconsidered Yasuhiro Sakai 079 good world in which the only one point of then the equilibrium point will become a non- general equilibrium uniquely exists and its sta- stable saddle point. To clarify such an bility is also guaranteed. One might wonder if interesting point, let us focus on the case that such utopian world really exists. When we are the excess demand functions are of the follow- getting into the real world as it is, it is far from ing forms: perfect, with a lot of irregularities. For instance, general equilibrium might not exist at E1 : E1 = – p1 + 2p2 – 4 (9) all. There would be more than one equilibri- E2 : E2 = 3p1 – p2 – 6 (10) um. Besides, many other "irregular situations" including unstable points and/or saddle points The excess demand lines of good 1 and might occur. good 2 are depicted in Fig. 3. Since we are deal- Suppose that there is a market equilibrium ing with substitutable goods, it follows that with substitutable goods. Then, the most im- both lines should be positively sloped. There is portant question to ask is whether and to what an important point we should not miss, how- extent the stability of the equilibrium is guar- ever. Note, the cross effects are strong enough anteed. Interesting enough, the equilibrium is to outweigh the own effects. Indeed, in Eq. (9) not always stable. In fact, we will see that the above, the absolute value 2 of the coefficient of cross effects of price changes act as disturbing p2 is greater than the one 1 of the coefficient of factors of instability. In fact, if the cross effects p1 , whereas in Eq. (10), the absolute value 3 of are strong enough to outweigh the own effects,

Fig. 3 The equilibrium point is an unstable saddle point: The cross effect is so strong

080 THE HIKONE RONSO Summer / July 2020 / No.424 the coefficient of p1 exceed the one 1 of the co- going up from the South-East to Q, all other efficient ofp 2. possible paths are not stable at all. This means As a result, in sharp contrast to the idealis- that the saddle point Q should substantially be tic case discussed above, the slope of E1- line is unstable. steeper for p2-axis, whereas the one of E2- line is steeper for p1- axis. 3-2 Non-Existence of the Let compare Fig. 2 and Fig. 3. Then, we Two-Market Equilibrium clearly understand that the positional relation- What we should consider next is the emer- ship of the lines E1 = 0 and E2 = 0 has been gence of "non-normal situations." Since all of reversed. Consequently, such reversal of loca- them are of vital importance, they respectively tions would critically change the adjustment require for very careful investigations. As the processes of prices. first example, let us examine the case in which The coordinates of equilibrium point isQ the excess demand functions are written as fol- = (16/5, 18/5). Apart from the previous dis- lows: cussion, however, we can no longer say that this point is a stable point in its true sense. In fact, E1 : E1 = – 2p1 + p2 – 2 (11) it should be a saddle point that is unstable on E2 : E2 = p1 – 2p2 – 2 (12) almost all paths. As is seen in Fig. 3, except only for the two stable paths, one path going Let us take a look at Fig. 4. As is seen in down from the North-West to Q, and another Chart (A), the two excess demand lines, E1 = 0

(A) The prices are declining to zero (B) The prices are expanding forever

Fig. 4 Non-existence of equilibriums

The Hicks-Morishima Approach Reconsidered Yasuhiro Sakai 081 and E2= 0, never intersect at all in the positive and sugar are complementary, and so are coffee coordinates of the price space. If we dared to and sugar. solve for p1 and p2 in Eqs. (11) and (12), we As the first example of complementary would obtain a pair of NEGATIVE prices (p1, goods, let us discuss the following excess de- p2) = (–2, –2), which should not economically mand functions of the two goods: be meaningful. Eventually, as is shown in Chart (A), both prices, p1 and p2 , tend to even- E1 : E1 = 2p1 – p2 + 4 (13) tually decline toward zero along the directions E2 : E2 = – p1 – 3p2 + 6 (14) of arrows. If we interchange the positions of the two Let take a close look at Eq. (13) and (14). lines, E 1 = 0 and E 2 = 0 in the left chart (A), The, we will see that in the right-hand sides of then we immediately obtain those lines in the those equations, the values of coefficients of p1 right chart (B). Then, we have to deal with the – term and p2 – term are both negative. This following set of equations: means that both the excess demands for x1 and x2 have to increase when p1 falls, or when p2 E1 : E1 = p1 + 2p2 + 4 (11) falls. This implies that the two goods are com- E2 : E2 = 3p1 – p2 + 6 (12) plementary, not substitutes. Besides, we assume here that the own effects overpowers In Chart (B), there exist no intersections the cross effects. Therefore, we would rightly of the two lines in the positive price quadrant. conjecture that the equilibrium point Q , if it If we dared to simultaneously solve E1 = 0 and exists, must be stable. Surely, such conjecture E2 = 0, then we would find (p1, p2) = (–16/5, will turn out be right by looking at the left –18/5), a pair of negative and economically chart (A) of Fig. 5. meaningless prices. As a result, there are no Concerning Fig. 5, there is one more point general equilibrium solutions, and the prices to watch. We must make sure that the two ex- eventually tend to rise forever as indicated by cess demand lines, E1 and E2, are now arrows. NEGATIVELY sloped. Since the own effects dominate the cross effects in Chart (A), it fol- 3-3 The Case of Complementary lows that both the slope of E1 for p1 – axis and Goods : A Completely the slope of E2 for p2 – axis should be steeper. New Situation We will turn to the second case which is In the above, we have limited our investiga- represented by the following pair of excess de- tion to the case of competitive or substitutable mand functions: goods. Looking at the real world, however, we can eyewitness many other cases in which some E1 : E1 – p1– 3p2 + 6 (15) goods may not be mutually competitive but E2 : E2 – 2p1 – p2 + 4 (16) rather move in the same direction. For instance, while tea and coffee are substitutes, tea Now, the cross effects are now more powerful than the own effects. As can easily be

082 THE HIKONE RONSO Summer / July 2020 / No.424 (A) Point Q is stable since the own effects are (B) Point Q is unstable since the cross effects are dominating dominating Fig. 5 The two goods are complementary

seen in Chart (B), the slope of E1 for p2 – axis comparative statics. This is a very important (not for p1 – axis) is steeper while the the one problem that was first intensively discussed by of E2 for p1 – axis (not for p2 – axis ) is steeper. J.R. Hicks and later greatly developed by Therefore, the equilibrium point Q is an almost Michio Morishima. unstable saddle point. First of all, let us assume that the two In conclusion, the power relation between goods are substitutes like tea and coffee. Let us the own effects and the cross effects plays a -vi take a look at Fig. 7. In the left chart (A), the tal role in the determination of the stability of straight lines E1 and E2 respectively represent an equilibrium point. Whether the goods are the excess demand lines of good 1 (tea) and substitutes or complementary, the dominance good 2 (coffee). More specifically, let us con- of the own effects over the cross effects clearly sider the following set of equations: guarantees the stability of an equilibrium. On the contrary, if the cross effects dominate the E1 : E1 = – 2p1 + p2 + 4 (15) own effects, then an equilibrium point be- E2 : E2 = p1 – 3p2 + 6 (16) comes an almost unstable saddle point. If we put E1 = 0 and E2 = 0 and solve for IV Comparative Statics: p1 and p2, we find a pair of equilibrium prices: The Impact of Parameter in fact, (p1Q , p2Q ) = (3.6, 3.2). Changes on Equilibriums Now suppose that because of some reasons, the popularity of tea suddenly rises among the Let us turn our attention to the issue of people. Then, the excess demand curveE 1 has

The Hicks-Morishima Approach Reconsidered 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 regard- able to see that those Hicksian laws were later ing the constant term of Eq, (15) above, it has developed a great deal by his successor, Mor- to change its value from 4 to (4 + α): ishima (1984). It is the Hicksian laws that we will intensively investigate in this and following A change in E1 : E1 +α = – 2p1 + p2 + 4 + α subsections. (17) We are most interested in comparing the two equilibrium points, the old point Q and Let us take a look at Fig. 7. In Chart (A), the new point R. We are expected to obtain the new equilibrium point R is found at the in- several results of great importance. First of all, tersection of the two lines, E1 = 0 and E2 = 0. we would like to pay attention to comparison For convenience, let us specify α = 2. Then, the of the following two relations: R R coordinates of R are calculated as (p1 , p2 ) = R Q (4.8, 3.6). p1 = 4.8 > 3.6 = p1 (18) R Q p2 = 3.6 > 3.2 = p2 (19) 4-1 Hicksian Three Laws of Price Changes: The Case of Substitut- To begin with, let us suppose that because able Goods of some reasons, tea becomes very popular In his classic Value and Capital, Hicks among the people, whence its demand sudden- (1939, 1946) succeeded in deriving the very fa- ly increases. To take an example, the opening mous three laws which stood for the core of his of the Great Britain Exhibition in Kyoto may comparative static results. It was also remark- produce such a sudden surge for the popularity

084 THE HIKONE RONSO Summer / July 2020 / No.424 of tea in Japan. Then, its immediate effect we Theorem 1 can expect to have is that tea will be more ex- (Hicks-Morishima on substitutable goods) pensive than before in response to the demand Assume that the two goods, x1 and x2, are increase. Not only that, there would also be substitutable and that the own effects over- many other repercussions such as its indirect power the cross effects. Then the point of impact on other markets including the coffee general equilibrium, if it exists, must be stable. market. Besides, those influences will invoke When the excess demand for good 1, E1, in- the third and forth rounds of repercussions as creases, the following three properties must well. Those direct and indirect effects would hold: make our repercussion calculations very hard (i) The price of good 1, p1, will rise. and complicated. In order to make sure of this (ii) The price of good 2, p2, will rise too. point, if we patiently compute the proportional (iii) The price of good 1 will rise proportion- rates of increase of the prices (in terms of per ately more than the price of good 2; cent), then we will be able to derive the follow- namely, the price ratio (p1 /p2) will rise. ing equations: 4.2 The Case of Complementary R Q Q (p1 – p1 ) / p1 = (4.8 – 3.6) / 3.6 = 1/3 Goods: Hicksian Three Laws (20) Continued R Q Q (p2 – p2 ) / p2 = (3.6 – 3.2) /3.2 = 1/8 Now, let us turn to the case of complemen- (21) tary goods Let us assume that goods 1 and 2 respectively represent tea and sugar. Then, as R Q Q Clearly, the ratio (p1 – p1 ) / p1 is great- Chart (B) of Fig. 7 above tells us, the two ex- R Q Q er than the ratio (p2 – p2 ) / p2 , implying cess demand lines, E1 and E2, are both that the rising rate of tea exceeds the one of downward sloped. If we suppose that the own coffee. effects outweigh the cross effects, then the old We must bear in mind that whether or not intersection point Q becomes a stable point. the excess demand functions are linear, all the Now, suppose that a sudden tea boom hap- comparative static results derived above gener- pens among the people, resulting in a drastic ally hold. J.R. Hick first obtained all those increase in tea demand. This is the first direct results which Michio Morishima rightfully effect of tea price rise. Moreover, such rise will called the "Hicksian Three Laws of Price lead to a sequence of secondary repercussions Changes." They are really outstanding conse- since it will dampen the demands for both tea quenses of the Hicks-Morishima approach, and sugar. Recall here that complementary which can be summarized as the following the- goods have to go in the same direction. This is orem. the second indirect effect. If we employ a similar reasoning, then we would also take account of third and fourth round of repercussions that must have less influence than the second round.

The Hicks-Morishima Approach Reconsidered Yasuhiro Sakai 085 In Chart (B), let us shift the excess demand nonlinear cases should not be so difficult, re- function to the right, from E1 to E1 + α. Then, quiring for a bit more calculation and patience. since such shift changes the equilibrium point in a right and downward direction, from Q to V Morishima Towards R, it will have to cause a big rise in p1 together a New Economics with a small change in p2. Consequently, in absolute value terms, the rising rate of p1 will This paper may be regarded as an hom- exceed the falling rate of p2. We omit a more mage to my two great mentors, Professors John detailed calculation here. R. Hicks and Michio Morishima. The Hicks- The final results for the case of comple- Morishima approach was adopted and mentary goods will be summarized as the developed by Morishima in his book (1984). following theorem: For this book, Morishima gave an interesting subtitle "An Introduction to New Economics." Theorem 2 Because it was far more than "an introduction" (Hicks-Morishima on complementary goods） and contained "several new and original re- Suppose that the two goods, x1 and x2, are sults," it seemed to me that the subtitle per se complementary, and that the own effects over- was "too modest, and even cheating." In fact, power the cross effects. Then, the point of Morishima himself made several remarks : general equilibrium, if it exists, must be stable. When the excess demand for good 1, E1, in- The approach of this book differs to a con- creases, the following three properties must siderable degree from standard ecnomics. ... hold: This book attempts to analyze the price (i) The price of good 1, p1, will rise. mechanism in accordance with reality and at (ii) The price of good, p2, will fall a bit. the same time to introduce students directly (iii) The rising rate of good 1 will be greater to the major problems of economics – an than the falling rate of good 2; namely, analysis of the way in which the real econo- price ratio (p1 / p2) will rise a great deal. my operates and the best way to bring about a change in direction in this operation. As I mentioned before, the exact deriva- (Morishima, 1984, Preface) tion of Theorems 1 and was the main theme of the Young Morishima. For that purpose, he Morishma's later book (1999) could be literally racked his brains. In this paper, I have thought of as one of his "last swans," in which intended to limit my analysis on a simple yet he greatly lamented the recent Japanese society useful case of linear excess demand functions. as one approaching at a "dangerous stage." Besides, following the Morishima spirits, I have Here again, he made some intriguing remarks: often made use of many eye-catching graphical approaches. I can say, however, that the exten- This book is the one I have constantly want- sion of my analysis to the more general ed to write for a long time. In fact, it is a sort of a "Grand Integral Social Science" in the

086 THE HIKONE RONSO Summer / July 2020 / No.424 sense that it contained economics, sociology, ⦿ Hirota, M. and Sakai, Y. (1969) Notes on Substitution and Scale Effects in Production Theory, unpublished education, history and many other related manuscript, University of Rochester. fields. It could rightly be called an "Academ- ⦿ Komoro, N. (2004) Economics Super Stars: Seminar on ic Symphony." .. Let us take a careful look at the History of Economic Thought, in Japanese. Diamond many non-economic fields such as the worlds Publishers, Tokyo. of politics, religion, and ideology. Then you ⦿ Morishima, M. (1974) “Marx in the Light of Modern Economic Theory,” Econometrica, Vo.42, No.4, pp.611- will see that many main actors such as politi- 632. cal, religious , and military bosses may play ⦿ Morishima, M. (1984) The Economics of Industrial Soci- very large roles in our society. Unfortunately, ety, Translated by Anthony, Clark and Hunter. Cam- bridge University Press.. economics and other related fields are so ⦿ Morishima, M. (1999) Relying on your Intellect Makes powerless to investigate those important you Harsh and Rigid, in Japanese. Iwanami Publishers, problems. So, I should say that the existing Tokyo. social science remains in an under-developed ⦿ Morishima, M. (1999) Why Will Japan Collapse? (in Japanese). Iwanami Publishers, Tokyo. state, thus lacking its very essential core." ⦿ Sakai, Y. (1972) Axiomatic Foundations of Consumption (Morishima, 1999, Appendix) and Production Theories. Ph.D. dissertation thesis, Uni- versity of Rochester. Honestly speaking, the right way toward the "Grand Integral Social Science" a la Mor- ishima seems to be too far for me to take. Even a right direction for the road has not been found 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 friend of Morishima. Nose immediately replied to me, "This looked like 'an academic symphony' a la 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 the interdependence 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 traditional general equilibrium approach developed by Lionel W. McKenzie, Gerald De- breu and Kenneth J. Arrow exclusively works with the good space rather than the price space. In contrast, the Hicks-Morishima approach based on Hicks' classical book Value and Capi- tal 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 not with the twisted concept of excess demand curves. It is one of my main purpose to mend such unfortunate tendency, presumably pro- ceeding 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, Value and Capital, excess demand curves, general equilibrium analysis, comparative statics

JEL Classification B31, C62, D51

088 THE HIKONE RONSO Summer / July 2020 / No.424 The Hicks-Morishima Approach Reconsidered Yasuhiro Sakai 089