Inventory, Labor and Price Movements in
Business Cycles-Based on Multi Agent Simulation
Nozomi Kichiji
Research Fellow of the Japan Society
for the Promotion of Science, Hokkaido University
Kita 9 Nishi 7, Kita-Ku, Sapporo, 060-0809, Japannkichiji@d9.dion.ne.jp

Makoto Nishibe
Associate Prof of Graduate School of Economics, Hokkaido University
Kita 9 Nishi 7, Kita-Ku, Sapporo, 060-0809, Japannishibe@econ.hokudai.ac.jp

Abstract
The purpose of this paper is to show a new understanding of business cycles by practicing multi-agent simulation in autonomous decentralized markets. In this paper we construct the model of dispersive
markets with autonomous agents that is diﬀerent from Neo-classicaleconomic models. We adopt multi-layered adjustment ﬁrms as agents.
The multi-layered adjustment ﬁrm takes a sequence of routinized behaviors in a nested time structure. In the ﬁrst layer, the ﬁrm does
quantity adjustment. In the second layer, it does price adjustment.
This paper examines the following two points. We compare thelabor market with higher rate of regular labor called Japanese type(J-type) and the other one with lower rate of regular labor called
American type (A-type) in view of volatility on business cycles. It
is found that the latter is more volatile than the former. We also
showed countercyclical movements of the production and the price at
the macro dimension.

1

1

Introduction

The purpose of this paper is to show a new understanding of the businesscycle by practicing multi-agent simulation in autonomous decentralized markets. In this paper we try to construct the model of dispersive markets withautonomous agents that are in many ways diﬀerent from well-organized andcentralized ones in orthodox economic models. General Equilibrium theory depicts the ’one-price to one-good’ type market with a price-adjusting
auctioneer. Because all selling and buying transactions are cleared oﬀ simultaneously in the market, money plays no role but means of circulation
enabling indirect exchange of goods and services.
But we observe that in reality all economic agents come in market processes with not only goods and services but also money, and buying or sellingis fulﬁlled as a separate transaction one by one in a sequence. In each transaction money must be paid from one to another agent in the opposite directionof ﬂow of goods and services. Market is not a gigantic exchange place where
all the selling and buying transactions of all kinds of goods and services aredone all at once, but an integrated and decentralized network of individual
selling and buying sequential processes. In the latter case, the interrelations among agents are not so tight but rather loose because buﬀer stocksof money or inventory create slackness both in price and quantity. Agents
do not maximize unique function of utility or proﬁt in response to the single
information with regard to change of prices, but they satisﬁce adopting routinized patterns of decisions and actions in response to such local information
with regard to change of stocks. For example, ups and downs of buﬀer inventory show the gap between the expected sales and the realized ones of
agents. Satisﬁcers have a bigger degree of freedom in their decision-making
and behavior than rational maximizers. Such agents are autonomous in thesense that they can select any possible patterns of routinized behaviors and2change them adaptively in the course of time. That is why we call such amarket ’autonomous decentralized.’ We believe that the great signiﬁcance of
inventory and money as decoupling and informational function will be shownin our model. It is now clear that we cannot but use a method of computer
simulation in order to examine working and movement of a complex system
of autonomous decentralized market.
Here we adopt multi-layered adjustment ﬁrms as agents. The multilayered adjustment ﬁrm takes a sequence of routinized behaviors in a nested
time structure. The nested time structure has three layers. In the ﬁrst
layer, the ﬁrm does quantity adjustment. In the second layer, it does priceadjustment. In the third layer, it invests to plants and equipment. But as
space is limited, we shall concentrate on the ﬁrst two layers.
The multi-layered adjustment ﬁrm regards inventories as the most important local information. Each ﬁrm has two thresholds of inventory, which areupper one and lower one. For example, when actual inventories exceed theupper threshold, the ﬁrm recognizes overproduction. When actual inventories, on the other hand, come short of lower threshold, the ﬁrm recognizes
underproduction. The ﬁrm exclusively relies on its recognition to decide its
production level.
Metzler [9] ﬁrstly opened the way to explain business cycle phenomena
based on the inventory mechanism. He thought of inventories as a destabilizing factor and demonstrated that an inventory-accelerator could produce
cycles in simple Keynesian models. According to Blinder and Maccini [4],many macro economic theorists similarly think of the inventories as a destabilizing factor, whereas the prevailing micro economic theory viewed the inventories as a stabilizing one. Thus the paradoxical problem on inventories
remains unanswered.
Many models that explain business cycle from inventories adjustment
have mostly ignored price adjustment. However, we believe that both quan-3

tity adjustment and price adjustment are indispensable to construct the theory of business cycle. We therefore employ as the unit of analysis multilayered adjustment ﬁrm: the ﬁrm equipped with both the quantity adjustment and the price adjustment mechanisms.
Such preceding papers as Reagan [10] and Blinder [3] took both quantity
adjustment and price adjustment simultaneously. They thought that inventories played an important role to cause rigidity and asymmetry in priceadjustment based on the rigorous micro foundation. In their models, when
demand rapidly increases, the ﬁrm disposes of the inventories at ﬁrst. If
the ﬁrm is not able to meet increasing demand, the ﬁrm raises the priceso that it can clear the market. On the other hand, when demand rapidly
decreases, the ﬁrm piles inventories up and make the price stay. They tried
to explain price rigidity in the downward due to asymmetry of price adjustment by these models. However, these papers neglect the interaction of thegoods market and the labor market and assume that the markets are always
cleared oﬀ. Accordingly, they could not investigate the business cycles fromthe viewpoint of the interplay of aggregate demand and supply as well as thepossibility of excess demand or excess supply in markets. In short, they do
not present a new view of market and business cycles. In contrast, our model
explores business cycles based on the modeling of autonomous decentralized
markets.
In order to understand the characteristics of our article, the developmentof the micro theory cannot be neglected. The mainstream micro theory iscalled the Production-Smoothing or Buﬀer-Stock Model. These models are
summarized to two points.
First, the ﬁrm possesses buﬀer stocks to prepare for the unanticipateddemand change. Second, the ﬁrm makes production smoothing to cope withthe change of marginal costs depending on the utilization level. It is possible
to extend this basic model (Blanchard [1]) in many ways.

4

For example, Holt, Modigiliani, Muth, and Simon [6] has presented an
extended model characterized by the loss caused by the stock out cost. In
this model two costs are clearly classiﬁed. The ﬁrst one is the cost of carrying inventories, which rises monotonically with inventories. The second oneis the expected cost of stocking out which, for any given level of expectedsales, falls with inventories. This model can thus create a positive covariance
between inventory investments and expected sales. Furthermore it explainsthat the variance of production is bigger than that of the sale. Most of
modiﬁed models are criticized because these models are only treating inventory of ﬁnished goods and there is no theoretical ground that, as assumed
in the model, the marginal cost increases with utilization level. Blinder andMaccini [4], instead of extending the Production-Smoothing or Buﬀer-Stockmodel, switch over to the (S, s) Model which can reﬂect more stylized facts.
In the (S, s) Model each ﬁrm has the upper limit (S) and the lower limit (s)of the inventory and try to maintain the normal level by increasing/decreasingorders when inventory go under/over the s/S. This model is not dealing with
the inventory of ﬁnished goods in manufacturing sectors but with that of raw
materials and supplies in manufacturing or wholesale/retail sectors, which
accounts for most of the inventories. They mainly consider the circulationof the goods, not the production of goods. Since the inventory cost is to beconstant in our model, there is no need to take the increasing marginal cost
into account.
Blinder [2] and Caplin [5] has introduced the model assuming that all
ﬁrms have the same upper limits and lower limits of inventory possession butthat each ﬁrm has a diﬀerent initial inventory and diﬀerent sales. They havemade a conclusion, however, that empirical studies on the models are too
premature to explain the contradictory relationships of the micro side andmacro side in the inventory theory.
The model of our article is more or less similar to the (S, s) Model. But it

5was invented independently of it, taking the idea from Marshall’s concept [8]of multi-layered time structure. The big diﬀerence between the (S, s) Modeland our model is that the latter sets as the unit of analysis a multi-layered
ﬁrm that undertakes the price adjustment in addition to the quantity adjustment. As explained in Section 2, we introduce both the normal cost principle
and the full cost principle from the Post-Keynesian price theory1 . The multilayered adjustment ﬁrm may be regarded as integrating manufacturing andwholesale/retails supplier vertically. Similarly, the inventories are assumed
to be a sort of compound goods that includes the ﬁnished goods as well as
raw materials and supplies. This enables us to focus on the production of
goods rather than the circulation process of goods. Furthermore, the demandis determined endogenously in our model by introducing the labor market sothat it can analyze the relation between wages and unemployment rates.
This paper examines the following two points by multi-agents computer
simulation.
1 We set two diﬀerent types of labor market: the labor market with
higher rate of regular labor called Japanese type (J-type) and the other one
with lower rate of regular labor called American type (A-type). We compare
J-type with A-type from the standpoint of macro stability. Is there any
diﬀerence on the Phillips curves between J-type and A-type?
2 As our model takes the assumption of increasing returns to scale2 , theprocess of adjustment is diﬀerent from that of the conventional decreasing
returns to scale. Can we see the counter-cyclical relation between production
and price at the macro level?
The plan of the paper is as follows. We give an outline of the modelin section 2. In section 3, we show simulation results and indicate their
1
2

Paul Downward [7]The assumption of decreasing returns to scale does not match stylized facts reported

in many empirical studies on manufacture sector. Therefore, the assumption of increasing
returns to scale, we consider, is not arbitrary but realistic.

6

implications . Lastly, we make a brief conclusion on this simulation and referto the future study.

2

The framework of the model

2.1

Time structure (Triple nested time structure)

Time structure has triple hierarchical loops of short-term, middle-term andlong-term. The unit of short term loop is week(w), the unit of middle-term
loop is month(m), the unit of long-term loop is year(y) 3 . For example, 30
years can be expressed as 30y=360m=1440w4. The multi-layered adjustment
ﬁrm adjusts utilization rate in the short-term loop, and revises the price inthe middle-term loop.

2.2Market(Dispersive market with autonomous agents)

We assume that there is only one kind of homogeneous good in this model.
Firms5 face consumers and sell their products at a certain price. Consumers
are assumed to be in a line and come in the market by turn to buy products
from ﬁrms at the current lowest price. When all products are sold out,
consumers waiting in a line simply give up purchase. At the macro level, theshort side of demand and supply is realized as sales.
X (t) = min(S (t), D(t))3(1)

The relations of variables in time structure are shown in ﬁg.15. How the ﬁrm adjusts

quantity and price is shown in ﬁg.16.
4
w is expressed as t in the following formulas.
5
We regard these ﬁrms as vertically integrated ﬁrms, each of which is composed of
manufacturing, wholesale and retail sections.

7where X(t): aggregate sales at period t, S(t): aggregate supply at period t,
D(t): aggregate demand at period t.

2.3

Supply side

2.3.1

Production function

The production function is supposed to be a linear form.
Q(i , t) = u(i , t − 1 ) ∗ Qmax (i )(2)where i: i-th agent, u: utilization rate, Qmax (i)6 : the capacity of productionof i-th ﬁrm.
Each ﬁrm increases or decreases the utilization rate when stock levelis beyond its upper threshold of inventory or under its lower threshold of
inventory. We discuss the way of adjusting utilization rate at 2.5.1.
2.3.2

Price setting

Price is not determined by an auctioneer as in centralized market. In decentralized market with autonomous agents, each ﬁrm sets its own price. In thisarticle, price setting is described by two types.
First, in case of the normal cost principlep(i , t) = nc(i ) ∗ (1 + Vmp(i , t))(3)where nc: the normal cost7 , which is constant, V mp: variable markup8 . The
price setting is done through changing V mp.
Second, in case of the full cost principlep(i , t) = k (i , t) ∗ (1 + Fmp(i ))(4)6Qmax (i) is set 200.
The value of nc is set 2.
8
The initial value of V mp is set 0.3.
78

where p(i, t): the price set by i-th ﬁrm9 , k(i, t) is the actual cost per unit,
F mp is the ﬁxed markup. The price setting is done through changing k. We
discuss the price adjustment in detail at 2.5.2.
2.3.3

Supply function

Supply is determined as the sum of production in this period and inventory
in previous period.
S (i , t) = Q(i , t) + Z (i , t − 1 )(5)where S(i, t): the supply of i-th ﬁrm at period t, Q(i, t): the production ofi-th ﬁrm at period t, Z(i, t − 1): the inventories held by i-th ﬁrm at periodt − 1. In our simulation, we assume that there is no negative inventory, that
is, Z ≥ 0.
2.3.4

Cost function per unit

This model takes the assumption of increasing returns to scale as it is a better
approximation of reality. As utilization rates rise, unit cost becomes lower.
The cost function in the case of endogenous demand isk(i, t) = Cmin + (1 − u(i, t − 1)) ∗ k0 + w(i, t − 1) ∗ Ld(i, t − 1)
+sc ∗ Z(i, t − 1)/S(i, t)(6)where k: the cost per unit, k0: the cost parameter (=1), Ld(i, t − 1): thedemand for labor per product by i-th ﬁrm, sc: inventory cost per product.
Since we assume that one unit of labor is needed for per product, (6) can be
rewritten as:k(i, t) = Cmin + (1 − u(i, t − 1)) ∗ k0 + w(i, t − 1)
+sc ∗ Z(i, t − 1)/S(i, t)
9

The initial value of p is set 2.6.

9

(7)

Cmin = 1 − Qmax ∗ set(8)Cmin means the parameter of increasing returns to capacity of production.
Cmin also depends on the capacity of production. As the capacity of production becomes larger, Cmin becomes smaller. set is increasing return to scaleparameter. In this simulation set is 0.004.

2.4

Demand side

2.4.1

Demand function

We introduce endogenous demand in this model. In this case, our simulation
is based on the following demand function.
D(t) = α ∗ I (t)/P (t)a(9)

I (t) = w (i , t − 1 ) ∗ Ld (i , t − 1 )(10)where α: a parameter for strength of demand, a: demand elasticity, P (t): thehighest price among sold goods, not the market clearing price, I(t): aggregate
wage income.
2.4.2

Labor market

Labor demand function is necessary to be introduced to build endogenous
demand model. Since the labor demand per product is assumed to be one,labor demand function is written as:
Ld (i , t) = Qmax ∗ u(i , t)

(11)Whenever labor demand exceeds a maximum regular labor (maxRL), theﬁrm displays a ﬂag. The number of ﬂag is recorded to the Upwageﬂag (UW ).
If labor demand is below a minimum regular labor (minRL), the ﬁrm displays10

a ﬂag. The number of ﬂag is recorded to the Downwageﬂag (DW ). The
maxRL is not equal to the minRL. They generally satisfy the relation as:
maxRL(i)  minRL(i)(12)

if (Ld (i, t) ≥ maxRL(i))
UW (i, t) = UW (i, t − 1) + 1(13)

if (Ld (i, t) ≤ minRL(i))
DW (i, t) = DW (i, t − 1) + 1(14)

If either UW or DW exceeds the threshold for revise of wage, wage is revisedas:if (UW (i, t) ≥ T W (i))
w(i, t) = w(i, t − 1) ∗ (1 + wc)(15)

if (DW (i, t) ≥ T W (i))
w(i, t) = w(i, t − 1) ∗ (1 − wc)(16)

where T W : the threshold for revise of wage, w(i, t)10 : nominal wage, wc: thewidth of wage revise.
If the nominal wages of all ﬁrms are not the same, the labor demand function
becomes a step function. Due to unlimited labor supply in this model, theproduction is constrained not by labor supply(Ls) but by eﬀective demand.
Ls = Ld

10(17)

The initial value of w is set 1.

11

2.5

The way of multi-layered adjustment

2.5.1

Quantity adjustment

A multi-layered adjustment ﬁrm thinks of inventories as the most important
local information. Inventories have three distinctive functions; information,
buﬀer and speculation. Inventories as information let a ﬁrm notice the gap
between the expected demand and the actual demand. Inventories as buﬀer
absorb the gap between them to make production constant. Inventories as
speculation make a proﬁt from price movement. In this article, we think thatinventories as information are most important. A ﬁrm adjusts its utilizationlevel in short-term loops. Each ﬁrm has the upper limit and the lower limitof the inventories as in the (S, s) model. S is called ’upper limit inventory
threshold value’, and s is called ’lower limit inventory threshold value’ in ourmodel. If the actual inventories go over an upper limit inventory thresholdvalue, the ﬁrm pulls down the utilization rate. Similarly, if the actual inventories go down to a lower inventory threshold value, the ﬁrm pushes up
the utilization rate. The upper limit and the lower limit of inventory threshold value become cognitive ﬁlters for the ﬁrm and can let the ﬁrm recognize
the unanticipated change in demand for its products. The ﬁrm adjusts its
utilization rate as follows.
if (Z ≥ Zuth)u(i, t) = (E(D(i, t − 1)) − (Z(i, t − 1) − Zuth))/Qmax
DP (i, t) = DP (i, t − 1) + 1

(18)
(19)

if (Z ≤ Zlth)u(i, t) = (E(D(i, t − 1)) − (Z(i, t − 1) − Zuth))/Qmax
UP (i, t) = UP (i, t − 1) + 1

(20)
(21)

12

where Zuth: the inventory upper limit threshold value, Zlth: the inventory
lower limit threshold value11 , E(D) : the expected demand, DP : Downpriceﬂag, UP : Upprice ﬂag.
Each ﬁrm estimates the expected demand based on static expectations (Itestimates demand in the present period as the same as the realized demandin the previous period).
E(D(i, t)) = D(i, t − 1)(22)

In this article, the size of upper limit threshold value becomes a buﬀer stock
to the unanticipated demand change. Moreover, when the demand increases
rapidly with the price change, it also becomes a speculative inventory although it is not necessarily intended for speculation. Therefore, three features of the inventory are embodied in this model.
2.5.2

Price adjustment

Price is adjusted in middle loops. The ﬁrm revises a price when UP exceeds aprice revision threshold value UPth and DP exceeds a price revision thresholdvalue DPth . In case of normal cost principle,
if (UP ≥ UPth )V mp(i, t) = V mp(i, t − 1) ∗ (1 + pc)(23)

if (DP ≥ DPth )V mp(i, t) = V mp(i, t − 1) ∗ (1 − pc)
where pc : the width of price revise.

11

In our simulation, Zlth is set 0. Then Z=0 holds as Z ≥ 0

13

(24)

2.6

Bankruptcy

If total proﬁt (total negative proﬁt, i.e., total loss) falls below the credit limit
to the ﬁrm, bankruptcy occurs. The credit limit is assumed to be proportional to the capacity of production. But in our model, even if bankruptcy
occurs, new ﬁrms never enter. Thus the number of the ﬁrms tends to decrease.

3

Simulation Results

3.1

Basic Parameters

Zuth, P th and T W are basic parameters in our model. Thus we need examine the relation of them. Fig.1 shows that the relation between upper
threshold of inventory and price revision threshold. Fig.1 draws three dimensional diagram on the result of ending 100 times out of 1440 turns withregard to the aggregate production, which is computed by the combination of
the parameters of price revision threshold and upper threshold of inventory.
The combination of lower upper threshold of inventory and null price revisionthreshold shows poor performance in output level. The highest output levels
cluster around relatively lower price revision threshold. Fig.2 shows the relation between T W and P th. The combination of higher T W and lower P th
gives the highest output level. If T W is lower than P th, rise of wage squeezes
ﬁrm’s proﬁt. As a result, the ﬁrm is prone to get into the red and may gobankrupt. If T W is higher than P th, the ﬁrm is able to pass the rise of wage
on the price so that it may escape from bankruptcy. We set parameters as
follows considering the relationship of these parameters.

14

3.2

Parameter Setting

The signiﬁcant results of simulations are clariﬁed in this chapter. The numberof the ﬁrm is 5. The following parameters are used.
Zuth={30,31,32,33,34}, UPth =DPth = 12, pc=0.1, T W =36, wc=0.1,
maxRL=0.8, a=1, α=1.3, sc=0. The number of turns is 1440w (1440w=360m=30y).
We focus on relationships among labor practices, wage, price, and output.
We consider that each ﬁrm regards regular labor as buﬀer inventory of labor
to unexpected change of demand and tries to preserve regular labor enough toabsorb such external shocks. Accordingly, the parameters minRL represent
the characteristics of labor practice of A-type or J-Type of ﬁrm. We simulate
two kinds of labor practice in Case 1 and Case 2 as follows.
Case 1: A-type labor practice, minRL = 0.3
Case 2: J-type labor practice, minRL= 0.6

3.3

Dynamics of the System

3.3.1

Aggregate Production

We set the diﬀerent parameters of the minRL in Case 1 and Case 2. It is
implied that minRL could also be regarded as equivalent to the ﬁxed capitalfor each ﬁrm if it is diﬃcult or, at least, it takes considerable time for the ﬁrm
to employ or ﬁre regular workers. At ﬁrst, we analyze aggregate productionlevel.
minRL is the parameter closely related to the wage revision in the downward. Ceteris paribus, as minRL becomes larger, DW is likely to increase
because the actual labor demand will more often falls below the lower limitof regular labor minRL. On the other hand, UW is closely related with
maxRL, not minRL. Thus it is more likely to revise the wage in the downward in Case 2 (J-type) than in Case 1 (A-type) although J-type tends to15

preserve more regular labor than A-type. As basic demand is minRL multiplied by nominal wage, and nominal wage is set 1 in our model, the size of
minRL expresses that of basic demand.
We can see from ﬁg.3 and ﬁg.4 that aggregate production in Case 1 (Atype) ﬂuctuates more sharply than that in Case 2 (J-type). This is due tothe advantage of the larger initial basic demand for J-type.
3.3.2

Phillips curve

We plotted the points of rate of unemployment and rate of inﬂation on themonthly basis in ﬁg.5 for A-type and ﬁg.6 for J-type. The existence domainof the points for J-type is more compact than that of A-type. This indicatesthe lower volatility for J-type than A-type. It is often observed that there
coexist the positive rate of inﬂation and the positive rate of unemployment.
Stagﬂation is not rare in our simulation. As far as we observe, it is unclear
whether the slope of Phillips curves is positive or negative in both cases.
3.3.3

Aggregate production and Price

The nominal wage tends to monotonically and geometrically increase for
type-A and type-J as seen in ﬁg.7 and ﬁg.8 . The average speed of increaseis higher for type-J than that of type-A. On the other hand, the price tend
to increase with cycles for type-A and type-J as seen in ﬁg.13 and ﬁg.14.
Type-J has steeper and deeper cycles than type-A.
The real wage moves on compound waves of short cycles and mid-term
cycles for type-A in ﬁg.9 and for type-J in ﬁg.10 . It stays within 0.8 to 1.8
for type-A and within 0.95 to 1.55 for type-J. The real wage for type-J is
more stable. The proﬁt rate also moves on the similar waves but completelycountercyclical for type-A in ﬁg.11 and for type-J in ﬁg.12. This shows thatthe real wage run counter the proﬁt rate. This can be explained as follows.
As nominal wage increases almost geometrically, the movement of real wage16

is the same as the countercyclical element in the movement of the price,
while the movement of price is isomorphic to that of variable markup as thenormal cost nc remains constant. The cyclical element in the movement ofmarkup is the same as the movement of proﬁt rate. It follows that the real
wage moves contrary to the proﬁt rate.
We also observe that the output of production and the price are countercyclical in ﬁg.13 and ﬁg.14. The production falls down abruptly on the topof price increase. This seems to show the phenomena of crises, the sudden
collapses of boom.
Our simulation does not explicitly introduce money but we actually assume that there is money stock on the side of ﬁrms or laborers. If wage arepaid in advance, ﬁrms should hold money stock necessary for payment tolaborers. Otherwise, the products cannot be bought in the goods markets.
If wages are paid late, laborers should hold money stock at initial period.
This simulation creates continuing inﬂation without increase of money supply. This is contrary to the opinion of Neo-classical school that increase of thequantity of money causes inﬂation that is the only monetary phenomenon.

4

Conclusion

1
The
basic demand for products depends on the demand for labor by ﬁrms.
More correctly, it is determined by the demand for regular workers multipliedby their nominal wage. Accordingly, the higher rate of regular workers does
not necessarily lead to the stability of basic demand for products. Truly, if
we presuppose the downward stickiness of wage, the higher rate of regular
workers means the bigger basic demand. But the reduction of nominal wage
may result in the decrease in the basic demand. Type-J with the higher rateof regular workers in most cases stays more stable with respect to the rate of
inﬂation and the rate of unemployment. In contrast, as to type-A with the17higher rate of regular workers, the unemployment rate and the inﬂation rate
are rather higher and stagﬂation is frequently observed.
2
On
the assumptions at the micro level that each ﬁrm has a production
function with increasing returns to scale, and that it has upper and lower
thresholds of buﬀer inventory for goods and labor, we ﬁnd countercyclicalmovement of the output and the price level at the macro level. This agrees
with the results obtained in many empirical studies.

References[1] Oliver J. Blanchard. The production and inventory behavior of theamerican automobil industry. Journal of Political Economy, 91:365–
400, 1983.
[2] Alan S. Blinder. Retail inventory behavior and business ﬂuctuations.
Brooking Papers on Economic Activity, 2:443–505, 1981.
[3] Alan S. Blinder. Inventries and sticky prices: More on the microfoundation of macroeconomics. American Economic Review, 72:334–349, 1982.
[4] Alan S. Blinder and Louis J. Maccini. Taking stock: A critical assessment of recent research on inventries. Journal of Economic Perspective,
5(1):73–96, 1991.
[5] Andrew S. Caplin. The variability of aggregate demand with (s,s) inventory policies. Econometrica, 53:1395–1409, 1985.
[6] John F. Muth Charles C. Holt, Franco Modigliani and Herbert Simon.
Planning Production, Inventories, and Work Force. Englewood Cliﬀs:
Prentice-Hall, 1960.
[7] P. Downward. Pricing Theory in Post Keynesian economics. Edward
Elgar, 1999.
18

[8] A. Marshall. Principles of Economics. Macmillan, 8th edition, 1920.
[9] L.A. Metzler. The nature and stability of inventory cycle. Review of
Economics and Statistics, 23:113–129.
[10] Patricia C. Reagan. Inventory and price behavior. Review of Economic
Studies, 49:137–142, 1982.

19

Multilayered Adjustment pc0.1,end-dull
J-type Demand=1.3’judgem~2.dat’

1000

Aggregate Production Level
800

Aggregate Production

10

5

0

0

10

20

30
40
Th of Stock

50

60

70

0

80

10

5

20

15

30

25

35

40

600

400

45
200

Th of Price

0
0

200

400

600

800

1000

1200

1400

week

Figure 1: The relation between Zuth

Figure 4: Case 2

and P thA-type Demand=1.3

Multilayered Adjustment pc0.1, end-dull
0.025
0.02
0.015

Aggregate Production

0.01
10Rate of Inflation

0.005

8
6
4
2

0
-0.005
-0.01

0

0

5

10

15
20
25
30
TW(wage-threshold)

35

40

45

0

5

45
40
35
30
25
20 PTH(price-threshold)15
10-0.015-0.02-0.025
-0.03
0

0.1

Figure 2: The relation between T W

0.2

0.3
0.4
0.5
Rate of Unemployment

0.6

0.7

0.8

0.7

0.8

Figure 5: Case 1

and P thJ-type Demand=1.3
0.03

A-type Demand=1.3
1000

0.02

0.01

Rate of Inflation

Aggregate Production

800

600

0

-0.01

-0.02

400
-0.03
200

-0.04

-0.05
0

0
0

200

400

600

800

1000

1200

1400

0.1

0.2

0.3
0.4
0.5
Rate of Unemployment

0.6

week

Figure 6: Case 2

Figure 3: Case 1

20

A-type Demand=1.3

J-type Demand=1.3

18

1.6

16
1.5
14
1.4

Real Wage

Nominal Wage

12
10
8

1.3

1.2

6
1.1
4
1
2
0

0.9
0

200

400

600

800

1000

1200

1400

0

200

400

600

week

800

1000

1200

1400

1200

1400

1200

1400

week

Figure 7: Case 1

Figure 10: Case 2

J-type Demand=1.3

A-type Demand=1.3

25

2

1.5
20

Profit Rate

Nominal Wage

1
15
0.5

10
0

5
-0.5

0

-1
0

200

400

600

800

1000

1200

1400

0

200

400

600

week

800

1000

week

Figure 8: Case 2

Figure 11: Case 1

A-type Demand=1.3

J-type Demand=1.3

2

2

1.8
1.5

1

1.4

Profit Rate

Real Wage

1.6

1.2

0.5

1
0
0.8

0.6

-0.5
0

200

400

600

800

1000

1200

1400

week

0

200

400

600

800

1000

week

Figure 9: Case 1

Figure 12: Case 2

21

1
36
71
106
141
176
211
246
281
316
351
386
421
456
491
526
561
596
631
666
701
736
771
806
841
876
911
946
981
1016
1051
1086
1121
1156
1191
1226
1261
1296
1331
1366
1401
1436

Aggregate Production

A-type Demand=1.3

Price Level

22

Aggregate Production

1200
Price Level
50

45

1000
40

35

800

30

600
25

20

400
15

10

200

5

0

0

week

Figure 13: Case 1

1
37
73
109
145
181
217
253
289
325
361
397
433
469
505
541
577
613
649
685
721
757
793
829
865
901
937
973
1009
1045
1081
1117
1153
1189
1225
1261
1297
1333
1369
1405
1441

Aggregate Production

Price Level

1200
60

1000
50

800
40

600
30

400
20

200
10

0

0

23

week

Figure 14: Case 2
Price Level

J-type Demand=1.3

Aggregate Production

n: agent, t: terms
t-terms(short_term)
m-term(middle_term)
l-term(long _term)Black dot means startingpointm = 4t, t = [m/4]IndexPrice:the highest price of sold goods[] means Gaussian Symbol.
t+1(m=1)(l=1)
t+4(m=2)(l=1)
t+7(m=3)(l=1)
t+10(m=4)(l=1)

Initial util(n, t)

t+2(m=1)(l=1)
t+5(m=2)(l=1)
t+8(m=3)(l=1)
t+11(m=4)(l=1)

t+3(m=1)(l=1)
t+6(m=2)(l=1)
t+9(m=3)(l=1)
t+12(m=4)(l=1)

util(n, t+1)

util(n, t+2)

util(n, t+3)

Product(n, t+1)

Product(n, t+2)

Product(n, t+3)

Firm's Cognitive Filter
Threshold of Stock(n)(Zuth)
works in shor_term_loop
Threshold of Price(n)(Pth)
works in middle_term_loop

If( Stock(n, t+1) > Zuth)
util(n,t+1)↑& upPriceflag++;
If( Stock(n, t+1) = 0 )util(n,t+1)↓& downPriceflag++;If( upPriceflag > UPth)Markup(n, t+3)↑
If( downPriceflag > DPth)
Markup(n, t+3)↓
If(upWageflag > TW)wage(n, t+3) ↑If(downWageflag > TW)wage(n, t+3) ↓Threshold of Wage(n)(TW)
works in middle_term_loop

If( laborDemand(n, t+1) > MaxRegularlabor)
upWageflag++;If( laborDemand(n, t+1) < Regularlabor)
downWageflag++;

Initial Stock(n, t)

Stock(n, t+1)

Stock(n, t+2)

Stock(n, t+3)

Supply(n, t+1)

Supply(n, t+2)

Supply(n, t+3)

Cost(n, t+1)

Cost(n, t+2)

Cost(n, t+3)

Setting NormalCost
depends on normal rate of util

NormalCost(n)NormalCost(n)NormalCost(n)Initial Markup(n, t)Markup(n, t+1)

Markup(n, t+2)

Markup(n, t+3)

Initial Price(n, t)

Price(n, t+1)

Price(n, t+2)

Price(n, t+3)

Profit(n, t+1)

Profit(n, t+2)

Profit(n, t+3)

∑Supply(n, t+1)

∑Supply(n, t+2)

∑Supply(n, t+3)

IndexPrice(t+1)
Demandgoods(n, t+1)

IndexPrice(t+2)
Demandgoods(n, t+2)

IndexPrice(t+3)
Demandgoods(n, t+3)

AggregateDemand(t+1)

AggregateDemand(t+2)

AggregateDemand(t+3)

AggregateIncome(t+1)

AggregateIncome(t+2)

AggregateIncome(t+3)

wage(n, t+1)

wage(n, t+2)

wage(n, t+3)

laborDemand(n, t+1)

laborDemand(n, t+2)

laborDemand(n, t+3)

util(n, t+1)

util(n, t+2)

util(n, t+3)

Autonomous decentralized market

Initial IncomeAggregate(t)Initial util(n, t)

24
Figure 15: Relations of Variables

pulled down
utilization rate

Stock

Upper limitof threshold
Lower limitof thresholdTimepulled up
utilization rate

Production

Time

Flags ofprice
revison in3
downward

Pricerevisionthresholdpulled price down

2
1

Flags ofprice
revision in
upward 3

Pricerevisionthreshold

Time

2
1
Time

price level

Time

25

Figure 16: Adjustment of Quantity and Price