Cybernetics and Systems Analysis, Vol. 31, No. 3, 1995

SYSTEMS ANALYSIS

DYNAMIC PRICING MACROMODELS

FOR A TRANSITION

ECONOMY V. S. Mikhalevich* and M. V. Mikhalevich

UDC 338.5

Considerable experience has been accumulated with modeling of both market and centrally planned economies. However, the economic situation in Ukraine (and other CIS countries) does not fit the assumptions on which either of these economies is based. On the one hand, the rigid central controls are gone but prices (at least partially) are still not formed by the market mechanisms of supply and demand; on the other hand, production is still highly monopolized, which exacerbates shortages of products and services to consumers, and the socio-economic conditions are in general highly unstable. The absence of a market infrastructure generates specific forms of commodity and money relations which are not treated in traditional economic theories. All these necessitate a special study of the economic laws of transition, including their mathematical modeling. Hyperinflation, financial instability, and market imbalance are characteristic features of the deep economic crisis affecting the Ukrainian economy. In order to develop effective measures for overcoming these difficulties, we need to know the reasons that lead to and aggravate the crisis, and to determine the factors that must be taken into consideration in the policy and practice of necessary reforms. The relevant processes are highly complex and multifaceted. They affect various spheres of activity (production, distribution, exchange) and various levels of aggregation. Their analysis therefore requires models based on methods of system analysis. In this paper, we examine a number of such models designed for the description of pricing processes under financial instability, which is a characteristic feature of a transition economy. The first such model [1] describing the relationship between demand, supply, and prices was stated in terms of highly aggregated indicators - - aggregate social product, produced national income, demand and supply of commodities consumed outside the production sphere, money balances held by consumers, and the price index. The purpose of modeling is to study the specific features of pricing in a market with shortages. Since we are dealing with nonstationary and rapidly changing processes, the model is dynamic in continuous time. It consists of five differential equations that determine the balance of aggregate social product, the consumption fund balance, and the money balances held by consumers. It is assumed that the total demand is the sum of permanent demand for the necessities of life and cash-paying demand for other products. The price dynamics is modeled by the Samuelson equation [2], which describes the variation of prices in response to demand and supply. The application of this aggregate approach to a transition economy may raise objections. However, for the crisis scenarios considered below, the effect of monopolistic pricing will only exacerbate the consequences. Moreover, monopolies may affect prices both directly and indirectly, by controlling supply and demand. A model of such monopolistic effects has been considered in [1]. Therefore, the Samuelson equations constructed for a pure market economy may also be adequately used to describe pricing in a transition economy. Thus, we consider a relatively closed economic system described by aggregate indicators and functioning on the time interval [0, T]. We use the following notation for this system.

*Deceased. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 116-130, May-June, 1995. Original article submitted April 26, 1995. 1060-0396/95/3103-0409512.50

9

Plenum Publishing Corporation

409

tnl

t~

t

Fig. 1. Variation of prices under the impact of emission. Let x(t) be the gross social product (GSP) of the system in constant prices at time t; 1 - - a the share of national income (NI) in GSP; R(t) the part of NI (in constant prices) used for consumption; 1~ the consumption rate; W the accumulation rate; Wo the investment rate (relative to NI) which is needed to keep a constant level of production; S(t) the cash-paying demand of consumers; D(t) the money balances held by consumers at time t; p(t) the consumer price index relative to time t = 0; m the coefficient of price elasticity [2]; b the reciprocal of the rate of return on investments; q the share of consumer incomes in NI. Then our model takes the following form:

x' = ~

( W - Wo)X, R = (I - a) W'x

(1)

(the dynamic balance of GSP and the consumption fund in constant prices), p ' = m (S - R)

(2)

s ' -- (D / p)'

(3)

D ' = pq (1 - a)x - p rain (S, R)

(4)

(Samuelson's equation),

(the equation of demand dynamics),

(the equation of consumer money balances), x (o) ffi x o, p (0) = p o, s (0) ffi s 0, z) (0) = D o

(the initial conditions for the variables in Cauchy form). The system of equations (1)-(4) cannot be solved analytically, but similarly to the particular case of the model considered in [1] it can be investigated by constructing its phase portrait. Reasoning as in [1], we note three typical situations: 1) Overproduction crisis, when the rates of growth of national income exceed the rates 6f growth of consumer money balances; the result is a stable imbalance of supply and demand, which asymptotically evolves into a constant excess of supply over demand. This situation arises when (w-

410

wo)(1 - ~)b -~ > & ;

2) Self-regulation region, wtlen the rates of growth of national income are less than the rates of growth of consumer money balances, but by a quantity that does not exceed 1. In this region, demand and supply may be balanced by market pricing mechanisms. This region is defined by the condition

~q - I ~ ( W - Wo)(l-a)b-I

~

q

.

3) Demand crisis, when the rates of growth of national income are less than the rates of growth of consumer money balances. This leads to a stable imbalance of demand and supply, which asymptotically evolves into a constant excess of demand over snpply~ This situation is defined by the inequality

(w-

wo)(l

- a ) / , - ' < ---q -

1.

Since (W - - W0)(1 -- a) b - t may be interpreted as the rate of growth (or decline) of NI, the demand crisis typically arises in cases when economic growth gives way to decline, while the nominal level of consumer incomes remains unchanged. Note that our analysis also identifies some local pre-asymptotic effects. For instance, if at the instant when market pricing mechanisms are turned on (when "price liberalization" occurs) demand exceeds supply and the model parameters correspond to the demand crisis conditions, then the model leads to the following qualitative forecast. First demand decreases and the imbalance is reduced (remission). Then, as the consumer money balances increase, demand again starts growing faster than supply, and the crisis becomes more acute. The only solution is to reduce the rate of growth of money balances and to increase the rate of growth of national income. The proposed model has been applied to simulate the inflationary processes in Ukraine in the early 1990s. Up to mid1992, the simulation results adequately fit the actual data. Since the end of 1992, however, the forecast substantially deviates from the actual process, which points to the existence of additional inflationary mechanisms in this period that are not included in model (1)-(4). The high degree of sectoral monopoly combined with the practice of pricing based on industry-average production costs has led to cost inflation. To a certain extent this is attributable to external factors (for instance, the energy prices increased by a factor of 15-20 in dollar terms during 1993), but our model of the cost-based pricing mechanism has elucidated also a number of internal factors which may cause permanent cost increases. We consider a system consisting of n material production industries. Let a/j be the input of industry i product needed to produce a unit of industryj product in constant prices; qj the share of value added in the price of industry j product; Hj the other components of price, including excess profit. Thenpj(t + At), the price of industry j product at time t + At, is expressed by the following equality given the prices Pi(t) of the products of other industries: tl

py(t + At) = Z

aqPi(t) + cliP.i(t + At) + H i, j = 1, n.

(5)

i~,l

Note that qj and Hi in (5) may also depend on t. Hence

pl(t +

At) = ~ / iI= ~ = l aiJPi(t) +

---&t--S, 1 -- q1' J =

or in vector form

p(t + at)'=-~p(O +'a,

(6)

where p is the price vector (Pl . . . . . Pn); ~ is the matrix {~/},

-

av l-q1

....

l-q/

,j=TS.

411

T A B L E 1. Simulation of the Consequences of Structural Hyperinflationary Crisis Period

Weighted Consumer money Unsatisfied demand Optimal quantity price balances as a ratio of total !of money (trillindex (billion krb.) supply of goods ion krb.) (1991 = 1) services (%)

andl

Real quantity of money (trillion krb.)

1992 I

No data

]January

1,00

250,67

109,42

0,041

February [April June August September November

5,92 5.12 8,488 11.751 1631 23,76

434,705 551,02 581,72 630,82 704,50

-6 -10 -3 13,89 6,52 -2,65 -9,31 -13,13

02,45 0212 0,351 0,486 0,692 0,984

33,79 48,039 279,224 397,03 564,543 802,73

805,91 942,19 2563 3144 3815 4551

-15,04 -18,3 -24,76 -25,36 -25,9 -26,4

1,4 1,99 11.,57 I4,45 23,40 3327

3,01 6,099 16,10I 29,665 34,82

5290 6388 7995 10184 11134 11383

-26,9 -26,67 -24,9 -22,98 -21,53 -20,77

47,298 60,17 77,98 100,62 109,131 110,627

49.2 58,0 73,0 97,0 160,0 217,0

46421

1993

January Feb~ary June August October November

2,575

1994

!January March !May July October iDecember

1141 1452 1881 . 2428 2633 2669

Consider the equation p = ~ p + ~.

(7)

Relationship (6) is a procedure for solving this equation by the simple iteration method [3]. The production property of the matrix A, i.e., the inequalities n

~ "~i1<1 for i = l, n 1=I or

tl for i==1

j= 1,--;,

is a sufficient condition for solvability of Eq. (7) and convergence of procedure (6) to its solution. If the production condition is not satisfied, the components of the vector function p(t) may increase without bound. In particular, for

1 = I-7~

we obtain from (6) the estimate 412

J=i

]ffil, n

jffi, l , n

and the prices increase at a constant rate. This inflation scenario is called a structural hyperinflationary crisis [4]. This crisis is caused by structural distortions, n

i.e., the existence of industries with a high level of costs, where ~ n

demand for their product, where ~

-aij >

1, and industries with a high level of production

i=1

a0" > 1.

i=1

Industries with a high level of costs attempt to improve their financial situation by raising the prices of their products. This price increase is amplified by the industries with a high production demand, and initiates a new round of cost increases in the high-cost industries. Analysis of interindustry balances for 1990-1991 [5, 6] has provided some evidence for this inflationary scenario in Ukraine in the early 1990s. Thus, an excessive level of costs was observed in the coal and food industries. Given the monopolistic increase of industry-average profitability, the group of high-cost industries in 1993 included also ferrous metallurgy, chemical industry, construction materials, and light industry. High production demand is typical for the products of power industry, oil and gas industry, and machine building. Almost all the material production industries were thus attracted into our scenario. The multiplier/~ calculated assuming quarterly price increases was 3.52. The government economic policy has a large effect on the development of inflationary processes during transition. In analyzing the effect of government policy on prices, we distinguish between two significant aspects. First, government policy involves conscious price controls or, most frequently, unsuccessful attempts to control prices through various subsidies, transfer payments, price "freezing," nonmarket product allocations, etc. In the process of economic transformation, pricing inevitably becomes one of the "painful" spots of the economy. Even in an ideal case transition to the market should be accomplished by a radical change of the function of prices in the economy and thus substantial changes of their magnitude. Large pre-market distortions, the lack of market infrastructure, and the dominance of the "black market" aggravate the negative consequences of these changes. Therefore, despite the critique of theoretical economists, direct price intervention by the government is still viewed by the political practitioners as the main technique of "reducing the cost of reforms, '~ softening the social tensions, limiting the destructive influence of inflation. In support of this policy we can mention that direct price controls are used, albeit on a limited scale, also in developed countries. Second, the government has a strong unconscious influence on prices through its economic policy, mainly the tax policy, the credit and money-emission policy, the budget policy, and the investment policy. The budget deficit, with the resulting money and credit emissions, is usually viewed as a strong inflationary factor [7, 8]. During the transition to the market, their effect is amplified by the high ratio between budget expenditures and national income (for instance, in Ukraine this ratio in 1992-1993 was 0.65-0.7 [9]), the use of a large part of the budget in the production sphere, chronic shortages of money under strong inflationary conditions, and other factors. With mainly cost-based pricing, the relationship between money emissions and inflationary processes acquires specific features that require special study. These two aspects are closely interrelated. Thus, subsidies for controlled prices and credit for unprofitable state-owned enterprises are one of the main causes of a large budget deficit. The attempt to reduce the budget deficit by increasing the revenues leads to higher taxes, which in turn reduce production and raise prices. As a result, the real budget revenues decrease instead of increasing. It is therefore necessary to conduct an integrated system study of all aspects of government price intervention. This analysis can be based on mathematical modeling. Some models for this analysis are presented below. Consider the aggregate dynamic model (1)-(4). Assume that the price levelp is determined not only by the relationship of supply and demand (2), but also by the previously described process of price increase following the increase of industry costs, as well as the change of the quantity of money in circulation. The latter process is described by Cagan's equation [7]:

~n(~) =,~e(p,M)+r,

(8)

413

where M is the quantity of money; E(p, M) is the inflationary expectation determined by the given price level p and the given quantity of money M; c~, -/ are the model parameters; P2 is the price level determined by the quantity of money and the inflationary expectation (the "inflationary" price). The price level in this model is thus no longer determined by equality (2). Instead we have the relationships p = max (Pl, P', P2), p ~ = m (S - R),

(9)

and P2 is obtained from (8). Here Pl is the price component determined by the imbalance of demand and supply;/~ is the cost level that grows at a constant rate/z during the structuralhyperinflationarycrisis. In Eq. (8) we often take t

E(M,p)

s

= r P ' ( v ) Otv~dv

tj_ p(v)

,, ,

where r is the buildup period of inflationary expectations; 0(v) is some predefined weighting function. If we assume that the parameter ce of Eq. (8) also depends on t, then without loss of generality we may take t

f o(v)jv = 1.

I--T

Analysis of the statistical data for Ukraine in 1992-1993 has shown that r is practically zero. This is so because prices were mainly increased by administrative means: it was impossible to predict the time and the magnitude of price increases by analyzing the statistical data, and the economic agents behaved accordingly. In view of the above, Eq. (8) takes the form

= a - - +p

7.

Comparison of the Ukrainian values of a and 3, with the corresponding values for hyperinflations in countries with a developed market economy in the 1920s-1950s [10-12] has shown that for the 1993 hyperinflation in Ukraine the unit impact of inflationary expectation c~ was an order of magnitude lower, while the effect of emissions 3' was 20%-40% higher. This supports the conjecture [13] that production mechanisms predominate in inflationary processes in the transition economy of CIS countries. Given our assumptions about inflationary expectations, we can estimate the effect of the increase in the quantity of money up to some level M at time t = t0. First assume that M is so large that the emission factor dominates price increases, i.e., for t _> to we have p = P2. Then Eq. (10) takes the form In (M / P2) = a p '2 / P'Z + ?,

P2(to) = P (to)

or

cty'-y+7=lnM,

Y(to)--y 0,

where

y - - l n p 2, y~ = l n p ( t o ) .

414

Hence P2(t) = exp ((In P(to) - In M + 7) e - a

t(t - to) + in M - y).

(11)

The function p2(t) is plotted in Fig. 1. Let us now determine for what values of M there indeed exists an interval [to, tl] where A

p2(/)

=

max CoI (t), p (t), P2(t)).

(12)

For the particular case which is quite typical of the late stages of a structural hyperinflationary crisis, when/3(t) > pl(t) for t > t 0, this problem can be solved analytically. From (9), (11), and (12) we obtain exp ((In P(to) - In M + y) e -a-'(t-to) + + In M - y) ) p (to) ea(t-to). The last inequality is solvable if M ~>M = exp (In p (to) + a,u + ),).

(13)

In general, to solve this problem, we can determine the price dynamics p(t) by solving numerically the system (1), (3), (4) and setting p(t) = max (Pl(t),/5(t)), where pl(t) and p(t) are determined from (9). Then successively reducing M we calculate p2(t) from (11) and find the minimum M = M when the condition p2(t) _>_p(t) still holds for some interval [to, tl]. Thus, if the quantity of money is allowed to exceed M, this will produce an additional increase in the level of inflation, beyond that explained by other factors. If the quantity of money does not exceed M, the inflation is determined by other factors considered above. The proposed model has been applied to make some calculations based on the data for the Ukraine economy in 19921993. Table 1 presents the results and the optimal quantity of money 2~. We see that, starting from the fall of 1992, the increase of production costs became the determining inflationary factor, while the supply of goods and services in 1993 exceeded the cash-paying demand approximately by 20 billion rubles in constant 1990 prices, which is more than 25 % of GDP. This is confirmed by the severe non-payment crisis that developed starting from the fall of 1993. We should also note that the real quantity of money sometimes exceeded M, which also intensified the inflationary processes. This increased emission can be explained by the attempt of the government to correct the deteriorating financial situation of the enterprises associated with growing arrears. Let us analyze the effectiveness of this strategy. To this end, we will estimate the value of M/p, i.e., the real quantity of money after a certain time interval At following the emission at time to. If M < ~r, then the increase of the quantity of money does not affect the price increases, and the ratio M/p increases with the increase of M. If M >/kr, then p(t) = p2(t). For sufficiently large At, e a

t u _-- 0 and P2(to + At) = e x p 0 n M - 7).

Hence M/p -~ e-V = const, i.e., the real quantity of money is independent of M. Thus, money emission increasing the value of M above the optimal level ~r produces only a short-term reduction of the shortage of money. Then, as the prices increase, the real quantity of money again drops to the same level as before the emission. The budget deficit is another important inflationary factor. Note that the effect of the government budget on prices in a transition economy is very complex and multifaceted. It includes the imbalance of supply and demand caused by budgetary reaUocation of producer and consumer incomes, the effect of taxes on production costs, and the consequences of emissions intended to cover the budget deficit. It is difficult to allow for all these factors in a relatively simple analytical model. We accordingly propos e a simplified simulation model for analyzing the consolidated state budget, which is based on the following assumptions.

415

1. We consider a system of n material production industries plus a nonproductive sector, m consumer groups, and the government budget. 2. The revenues of the government budget derive from tax receipts from the industries, the income tax paid by consumers, fixed payments from industries and consumers, and other sources. 3. The model considers three types of taxes on industries: a) value added tax charged at a rate q(1), which is possibly differentiated by industry; b) tax on profit charged at a basic rate q(2), which also may be differentiated by industry; c) excise taxes on some industry products, which constitute a fraction q(3) of the f'mal price. 4. The actual budget revenue from these taxes is proportional to the volume of sales of the industries in current prices. 5. The revenue from income tax on consumers is proportional to the nominal income of consumers with proportionality coefficient q(4), which is differentiated by consumer groups. 6. Budget revenue from fixed payments and other sources is assumed given. 7. The main budget expenditures include the following: a) subsidies to industries; b) indexed and unindexed payments to consumers; c) other expenditures. The expenditures of the first group are proportional to the production volume of the industries eligible for subsidies. Payments to consumers are indexed in proportion to the weighted price index calculated from data on the volume of sales of industry products in current and constant prices. Other expenditures are assumed given. 8. The model is based on the pricing mechanism (9). 9. Three types of product prices are considered: a) fixed prices, when products are sold at a given (constant) price, and the difference between industry costs and sales revenues is made up from the budget; b) controlled prices, when the budget compensates part of industry costs through subsidies; c) free prices, when no subsidies are paid. We denote the set of industries with fixed prices by f)t, the set of industries with controlled prices by f~2, and the set of industries with free prices by f13. 10. The time in the model is discrete with an increment At in the interval [0, 7]. Model inputs: aij is the direct input in constant prices of industry i product consumed to produce a unit of industry j product (i, j = 1. . . . . n); qj is the share of labor costs in the price of industry j product (j = 1 . . . . . n); c)j is the standard profit margin in the price of industry j product (j = 1 . . . . . n); qj+ is the share of other value added components in the price of industry j product (j = 1 . . . . . n); qj(1) is the rate of value added tax for industry j (j = 1 . . . . . n); q..(2) is the rate of tax on profit for industry j (j = 1 .... n)" qj(3) is the share of excise taxes in the price of industryj product (j = 1 . . . . . n); xj(t) is the predicted output of industry j product at time t E [0, T] in constant prices; this quantity may be viewed as the upper bound on the sales volume produced by the available assets and capacities (j = 1 . . . . . n); Bj(t) is the production cost per unit industry j product at time t, which does not depend directly on internal prices (j = 1 . . . . . n, t E [0,7]); B~(t) is the excess profit per unit output of industryj at time t (j E 9 2 t2 f]3, t E [0; T]); V~(t) are the subsidies per unit output of industry j at time t; H(t) is the budget revenue from fixed payments at time t; H(t) is the budget revenue from other sources at time t; ~.(t) is the fixed price of industry j product at time t (j E ill, t E [0; 7]); gj is the proportion of industry j product used for consumption (j = 1 . . . . . n); fljk is the proportion of industryj product in the bundle of goods and services used by consumers of group k (j = 1, .... n , k = 1 . . . . . m); Q(kl)(t) is the amount of indexed payments from the budget to consumers of group k at time t in constant prices (k = 1 . . . . . m, t E [0,7]); Q~2)(t) is the amount of unindexed payments from the budget to consumers of group k at time t in constant prices (k = 1 . . . . . m, t E [0, T]); G(t) are other budget expenditures at time t; cjg is the share of group k consumers in the labor costs of industry j; qk(4) is the income tax rate for group k consumers; Dk(0) are the money balances for group k consumers (k = 1 . . . . . m); M(t) is the predicted quantity of money at time t assuming zero budget deficit in the time interval [0, T]; 416

Model variables: Py(O is the relative

price (measured in relation to the base price) of industry j product at time t (] ~ f2z U fi3, t

[o;-TI);

~j(t) is the price component determined by production costs; Yy(O is the industryj product in constant prices used for consumption (j = zj(t) is the sales volume of industry j product at time t in constant prices; FIj(O is the income of industry j at time t;

1 . . . . . n, t ~ [0, 7]);

IIj(t) is the income earned by consumers of all groups from work in industry j at time t; /~ is the weighted average price index of goods and services;

~ (t) is the cash-paying demand of group k consumers for industry j product (j =

1 . . . . . n, k = 1. . . . . m); is the quantity of money at time t (allowing for emission to cover the budget deficit); D~(t) are the money balances of group k consumers at time t (k = ] . . . . . m, t ~ [0, T]); A~ and B~ respectively are the budget revenue and expenditure at time t. Before starting the simulation, we apply the procedure of [4] to calculate the value added percentage qj and the price influence coefficient aii from the formulas

M(t)

nil= l - q ~ We also calculate the elements a/j of the inverse of the matrix (E - - A), A = {a/y}, E is the identity matrix. Then we do the following for each time instant t = 0, At, 2At, . . . . 1. Calculate the relative prices of the industry products:

~ ( t + At) = ~

+

"aqpt(t) + ~ "aiyPi(t)+ Bl(t + At) +

1-q~)

where

{v6(t+At), if j~r vj(t+~t)--- o, if /eft3, p~q + a t ) = max ( g ( t + ~ 0 , e x r ~ 0 ~ pl~t) - In M (t) + ~,) e - ~ - ' ~ +

+ tQM(t)- ~,)), j E ~ U n 3. The last equality is an analog of (9), (11). 2. Calculate the subsidies needed to sustain fixed prices:

"~/t + ~0 = ~ ~j~#) + '~ ~jpr t~q ~e~u~ +

8/t + ~0 +

1 _ q)a) '

417

3. Calculate the volume of each industry product used for consumption: n

Yi(t + At) = (xi(t + At) - 2 aij xj(t + At)) gi; i = 1, n, j=l

and also the cash-paying demand of consumers: S k(t + At) = pj(t+ Dk(t) ~/k At) ; j f l , n ,

k f l, m.

4. Determine the sales volume of industry products:

zi(t+At)--~jffil "aij rain

k=l

S~(t+At),yl(t+At)

/

)

+~/(t+At) , i = l , n ,

where gj(t + At) are the uses of product for purposes other than consumption and production. 5. Calculate the weighted price index 2 pj{t + At) zj(t + At) + 2 pj(t + At) zl(t + At)

;'(t + At) j e g

je~u~ tl

~, zl(t + at) /=1 6. Determine the industry income and the profits received by consumers: Ilj(t + At) = pj(t + At) zl(t + At) - ( 2 "aq'Pl(t) + 2 "aiJPl(t) + B/(t + At) + ki ~ g i E ~u%

+

1 - - q ~ ) ( 1 - q/Q))

1 -qIQ )

t)/ wj(t + At) - ,,j(t + A j xj(t + At), j E ~ u ~3,

rl,(t + at) = ~ z~t + at)~,(t + at), j e a I ,

7. Calculate the consumer money balances: tl

Dk(t + At) = D~(t) + ~ r

+ At) + ;
1=1 s

..

s~(t + Ao

.. s~(t+at) - ~. p1(t + at) ,,.i. S ~(t + at), r~(t + "O ,.

418

|"

8. Determine the budget revenues: a) from value added tax:

h 0 )(t + At) = 2 q ~1) qj-~l~t + At) Zl(t + At) + 2 q 01.)qpl( t + A,) zl(t + AO; j~ i~u~ b) from tax on industry profits:

rl h (2)(t + At) -- E q~2)~l
h(3)(t+ At)

mE q~3)~1~t+ At) z](l + Al)'4" E q~3)pj(l+ Al) rj(l + A0; j~

j~u~

d) from income tax on consumers:

cyk ~:(t+At) + "p (t+A/) Q ~1)(/+At) + Q ~2)(t+At) .

h (4)(, +At) = 2 q ~4)

9. Calculate the budget revenues:

4 B ~ + At) = X~ h (0(t + At) + H (t + At) + H (t + at). l=l 10. Determine the expenditure on subsidies to industries:

~(t + "0 = ~, -ff:ft+ ,,.t).~? + ,,.t). J~

gush

11. Calculate the total budget expenditure:

m :%

+ : ' 0 -- KCt + : ' 0 + Y~ (~(~ +,"0 Q ~)(t + ' 0 + Q ~:~)(t +,',t)) + o ( t +AO.

k---I 12. Determine the change of quantity of money:

M (t + At) = M (t) + ( ~ (t + ,xt) - ~ (t)) + (~ ~ + :'0 - B ~ + At)). The values of the model variables at time t = 0 are determined as follows. The values of Dk(0), k = 1, m, p](O), j a2 u f13, ~ ( o ) , j ~ ~1, are assumed given. The values ofyi(0), ~(0), l's are calculated from the formulas

yj(0) = xi(0) -

aiA(0) gi, i = 1, n,

]=1 s~(o) = n~(o)/~/k ~1
nl
~Eq

1+

!2)(1" -

qz

l_q~)

I

)~

"a 1('1

ie~u~

Wi(O)- v/.(O))xj(O), j ~ ~2 U ~3"

The other model variables are calculated from the previously given formulas setting t + At = O.

419

Simulations based on this model suggest the possibility of yet another inflationary scenario, which we call "structuralbudgetary inflation." In this scenario, we identify a group of industries with above-average rates of price increase (compared to the entire system). These are the industries involved in the previously described scenario of structural hyperinflationary crisis. The determining factor of price increases for these industries is the growth of production costs, which drives the individual price dynamics. The price growth rates in the other industries are roughly the same, because they are all attributable to the consequences of budget deficit related emission. Simulation results [14] have also demonstrated the low effectiveness of the ,'price freeze" policy in the high-cost industries driving the structural hyperinflationary crisis [4]. The inflationary influence of large money emissions that are needed to pay the subsidies are commensurate in this case with the consequences of cost increases in these industries under conditions of "free" pricing. Our study leads to the following conclusions. 1. Anti-inflationary policy in the transition period should be developed allowing for the effect of inflationary processes both inside and outside the monetary sphere. The effect of purely monetarist measures is fairly limited, and must be combined with deep structural changes in the economy, implemented in the form of goal-directed technological government programs. 2. An optimal quantity of money exists for each period in a transition economy. If this optimal quantity is exceeded, the inflation rate is increased by an additional amount. If the quantity of money is less than optimal, the shortage of money is exacerbated and the economic decline is intensified. 3. By exceeding the optimal quantity of money we eliminate the money shortage only for a limited time, because the real quantity of money (i.e., adjusted for price increases) will not exceed the optimal quantity. 4. Development of an effective government budget, together with optimization of the volume of emission, is one of the main mechanisms for government intervention in prices in a transition economy. The budget should not only be balanced, but it should also allow for the effect of tax rates on prices and sales volumes, positive and negative consequences of subsidies to various industries, and forecasts of budget implementation dynamics. This requires simulation models that will enable us to test the consequences of alternative budgets.

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