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A Monetary Model of a Shortage Economy

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1993
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During the transition from a centrally planned economy to a market-oriented one, many countries have experienced a loss of macroeconomic control.1 To provide a theoretical explanation of this phenomenon, this paper develops a simple monetary model that illustrates how a centrally planned economy functions and how both macroeconomic stability and instability can materialize under a rigid planning system. It also shows that inherent structural imbalances and an irrational price system can frustrate structural reform. In the presence of soft budget constraints on enterprises, price reform that benefits some sectors at the expense of others may translate into wage pressures, which may squeeze enterprise profits and lead to persistent budget deficits and high inflation.

The organization of the production and distribution of goods and services in a centrally planned economy has been extensively documented (Chow (1985),Kornai (1992), and IMF and others (1991)). One important feature of such an economy is low efficiency. To have the government plan, coordinate, and monitor the economic activities of a large number of enterprises requires enormous amounts of information. It implies unrealistic moral and ethical self-discipline on the part of workers and management and is difficult to implement.

A second important feature of a centrally planned economy is the inability of central planners to adjust prices, wages, and production flexibly enough to maintain equilibrium. This inability creates constant tension between supply and demand and results in a chronic shortage of some consumer goods. Because this study examines the relationships between key macroeconomic variables, such as the money supply, the budget deficit, and inflation, it largely ignores efficiency issues and focuses on the imbalances between aggregate supply and aggregate demand and on price and wage policies.

The paper uses a cash-in-advance model with two perishable consumption goods and four types of agents: households, firms, the government, and a central bank. In the model, the government owns all firms and decides what quantity of productive resources should be allocated to each of the two sectors. In particular, it decides how much labor is to be devoted to the production of each good. The government determines the wages of the labor and the prices of the two goods in the model. Since the prices are rigidly fixed and resource allocation to each sector is considered arbitrary, the supply of goods does not necessarily reflect consumer preferences (and thus consumer demand). Consequently, the goods market does not necessarily clear under administrative prices—one good may possibly be in excess supply and the other in excess demand.

In the model, individuals are required to supply a fixed amount of labor in each period. The rest of their time can be spent freely on leisure or black market activity. The existence of deficit goods (those in excess demand) implies that economic agents will seek shortage rents, which are allocated through two main channels. One channel is rationing, in which rents are directly transferred to households. The second channel is random distribution to shoppers; more specifically, goods are randomly distributed to government-owned shops, which sell them to shoppers on a first-come, first-serve basis. The analysis in this paper assumes that the government uses the second channel.2 Thus, an individual can spend time shopping for the deficit good and resell it in the black market at a profit. In equilibrium, the payoff to such an activity must equal the marginal utility of leisure.

Also in the model, firms have no control over the employment of labor, the wages of workers, or the prices of their products. In addition, they rely on the government to balance their books. If a firm makes a profit, the government taxes it away; if a loss is incurred, the government covers the entire loss through subsidies. This is the notion of soft budget constraints posited by Kornai (1986). The government, in turn, relies on its banker—the central bank—to finance its budget. If total tax revenue does not cover total spending, the shortfall is financed by printing money. In the unlikely case that the government runs a budget surplus, the surplus would be turned over to the central bank and the total money in circulation would decrease.

This paper first shows that in a classic centrally planned economy, as described above, if the aggregate wage level is moderate, a steady-state equilibrium exists in which the government budget is balanced, money supply and prices are stable, and there is no monetary overhang.3 In other words, despite the tension between aggregate demand and aggregate supply under an administrative price structure and the existence of deficit and surplus goods, macroeconomic stability can be achieved and sustained in a rigidly planned economy.4 Although black markets divert resources away from productive activity, they do bridge imbalances in the economy and help it to reach equilibrium. Perhaps, then, there has been too much emphasis on dis equilibrium in rigid centrally planned economies, such as China and the former Soviet Union. The model in this paper will provide a reasonable description of the relatively stable macroeconomic conditions in China before 1978 and the former Soviet Union before 1985 (McKinnon (1991) and IMF and others (1991)).

If, however, the wage level is too high and the imbalance between aggregate supply and aggregate demand is too large, the system becomes unsustainable. There exists either no equilibrium or an equilibrium in which economywide shortages will eventually emerge.

This paper then turns to discuss wage and price reforms in a centrally planned economy. In a traditional planned economy, some firms are profitable, and their profits are used by the government to subsidize the unprofitable firms. Since resources are allocated largely administratively and prices are irrational, the line between profitable and unprofitable firms is arbitrary. Nevertheless, the efficiency of enterprises differs and the government’s redistribution of the profits among firms creates tension. Thus, when economic decisions are decentralized during reform, many profitable firms find themselves under pressure to increase wages.

This paper considers two types of wage reform. The first allows firms to retain a fixed percentage of their profits to be used as wage increases. The second type has the government retain rigid wage control but allows some percentage of the profits to be shared by workers as bonuses. The first type of wage reform leads to a continuous squeeze of total profits from profitable firms and a steady decline in tax revenues. Since the government does not reduce its financial obligations to unprofitable firms, the budget deficit worsens, and the deficit-induced printing of money may lead to an economywide shortage, plunging the economy into crisis. The second reform proposal is sustainable, however. Even though the initial loosening of financial control has an expansionary effect and aggravates the shortage, it does not lead to continuous budget deficits, and thus money printing, and from a macroeconomic perspective it can be sustained. However, with production and prices still rigidly controlled by the government, both types of reform tend to worsen shortages and reduce household welfare.

Finally, the paper examines price reform with and without wage control. The analysis shows that price liberalization with rigid wage control leads to a temporary surge in inflation, but it also improves household welfare by eliminating shortages and by freeing resources from nonproductive black market activity. However, owing to adjustments in relative prices, price liberalization tends to benefit some firms at the expense of others, putting pressure on profitable firms to loosen wage control, especially when a price surge follows liberalization. If the government cannot reduce the pressure and accommodate workers’ demands, it risks rapid inflation, even hyperinflation.

This study shows the dilemma facing governments of the reforming centrally planned economies. To the extent that the old wage and price structures are irrational and impede efficiency, wages and prices must be liberalized. However, for most firms that remain in the hands of the state, price liberalization and the decentralization of financial decisions may cause a loss of macroeconomic control and destabilize the economy. The ultimate solution seems to lie in changing the incentive and control system through privatization.

I. Basic Model

This section presents a simple general equilibrium monetary model of a centrally planned economy in which there are two perishable consumption goods, x and y, and four types of agents: households, firms, the government, and a central bank. It is assumed that the government owns all firms, fixes wages and prices, and determines how much labor each firm employs. The model forms the basic building block of the subsequent analysis.

Pattern of Financial Flows

Figure 1 describes the basic patterns of financial flows in a centrally planned economy. Given the figure, consider that at the beginning of a period, t, firms hire labor to produce the two types of nonstorable consumer goods (which type depends on the specific firm). Firms do not pay workers until the end of period t. During period t, firms turn out products that are sold in state shops at prices fixed by the government. Individuals use the money accumulated in the previous period, Mt1,to purchase goods available in the market. The revenue from the sales is used to pay the wage bill at the end of period t. For an individual firm, if revenues exceed the total wage payment, it makes a profit; if revenues fall short of the total wage bill, it incurs a loss.

The government taxes away all firm profits, using them to compensate for the losses of the unprofitable firms. If the government’s tax revenue from enterprise profits is less than its subsidies to unprofitable firms, it turns to the central bank to finance the deficit. If the government has a budget surplus, the surplus money is turned over to the central bank.

Figure 1.Financial Flows

Since the government controls production and prices, imbalances between supply and demand are likely to occur. As mentioned earlier, the shortage rents implied by deficit goods (those in excess demand) are channeled through either rationing or random distribution, with the government in this model adopting the latter approach. The arrow from household to household in Figure 1 indicates financial flows arising from black market activity.

Household Behavior

Individual households derive utility from leisure and from the consumption of goods x and y. Assume that households have the following utility function:

where β is the discount rate, ht is leisure, and xt and yt are average household consumption of goods x and y in period t. (In the following analysis, all quantity variables are in average household terms, unless otherwise specified.)

The only asset in the economy is cash, and there is no capital market to facilitate borrowing and lending. Consumers are subject to cash inadvance constraints. Let ptx and pty be the shadow prices of goods x and y in the black market. Noting that consumers queue to purchase goods at lower prices at state shops (thus earning shortage rent), it follows that

where Nt is the unused cash balance in period t,Mt-1 is the cash balance held by individuals at the end of time period t-1, qt is the time spent queuing, and Rt is the rate of return from queuing. It is also assumed that unused money balances earn zero interest and that the money balances in the initial period t = 0, M-1 are given.

By assuming that the shortage rent earned from queuing can be spent immediately, it is assumed that black market transactions are “frictionless” since no money is demanded in the black market. Alternatively, it could be assumed that shortage rent earned in period t can be spent only in period t + 1.5 This friction creates a transaction demand for money in the black market. In steady state, however, these two cases have identical implications for consumption. In the following analysis, the frictionless case is used for simplicity. Important differences with the friction case are noted, however.

In every period, each representative household is required to supply a fixed amount of labor and will earn wage wt both of which are determined by the government. In addition, each household allocates its nonwork time between two activities—leisure and queuing (ht and qt). Let nonwork time be assigned a value of 1. Thus,

The money balances held by each household at the beginning of period t + 1 are the wage earnings in period tplus the unused cash balances from the previous period:

At t = 0, for given money balances M-1, each individual household tries to maximize its utility (equation (1)) subject to its budget constraints (equations (2)—(4)). Taking the prices of both goods and the rate of return to queuing as given, solving the maximization problem yields each household’s demand for leisure and the demand for goods xt and yt.

Firm Behavior

There are two types of firms in the economy: one producing good x and the other producing good y. Labor is the only input and is rigidly controlled by the government to achieve certain production targets, say X for good x, and Y for good y. The government fixes the wages and prices of both goods. With official prices denoted Px and yx, and the wage costs for the universe of firms j (j = x, y) denoted by wtj,the profits of the two firms are

If πtjis negative, the firms incur losses.

Government Behavior

In a classic socialist economy, all firms are owned by the government. If a firm makes a profit, it does not belong to the firm; rather, the government taxes away most of it in the form of turnover taxes. At the same time, enterprises have soft budget constraints. If a firm incurs a loss, the government covers the loss by providing subsidies.6 Assuming that profit taxes are the only source of tax revenue and that the only expenditure by the government is its subsidies to loss-making firms, the budget deficit, Dt, is

As illustrated in Figure 1, if the government budget is in deficit (Dt > 0), the deficit would be financed by the central bank through money printing. For a given Dt, the net money printing in period t is

Equilibrium

In a competitive dynamic economy, an equilibrium is usually defined as a sequence of prices that clears all markets in all time periods. In a centrally planned economy, such a definition does not apply. Since the government fixes prices and wages, the market for goods does not necessarily clear. In the model above, for given wages (wt), if in a certain time period the demand for good j under the official price exceeds its supply, black market activity would drive the shadow price above the official price until the market for good j cleared. If, however, the demand for good j under the official price is below its supply, the official price would prevail. In this case, the official price is regarded as an “equilibrium” price since it can be maintained by the government without other administrative means. Thus, a dynamic equilibrium is defined as a sequence of prices(ptxpx,ptypy)that satisfies the following condition: if ptj>pj(j=x,y) for some period t, the demand for good j must be equal to the supply of good j.

II. Central Planning System

Using the basic framework of the previous section, the relationships between key macroeconomic variables, such as the money supply, the budget deficit, and wage and pricing policies, can be examined. As shown later, at a moderate wage level (relative to the official price of goods), the economy converges to a steady-state equilibrium in which one good is a deficit good and the other a surplus good. (For the deficit good, black market transactions bridge the imbalances between demand and supply that occur under the official price.) In the steady-state equilibrium, the government budget is balanced, and the money supply is constant. With rigid central planning, therefore, macroeconomic stability can be achieved. The aggregate money balances are absorbed through official transactions, through black market transactions, or through both. There is no involuntary money hoarding.

For simplicity, it is assumed that under a rigid planning system the government fixes the prices of both goods at I. The wages in x- and y- producing firms are set at wt and wy. That is,

Under such assumptions, the wage income in one period for an average household is w=wx+wy.The utility maximization problem of a household can be rewritten:

subject to

whereNt0;

Equation (10) is a combination of equations (2) and (3). Let Jt be the value function for period t, with J only a function of the initial cash balances Mt-1; that is, Jt=J(Mt1)..7 It follows from the principle of optimality that

To characterize the dynamic equilibrium of the economy, the subsequent analysis is divided into two parts. First, the analysis focuses on one period. Recall that in every period tthe resources available to an individual household, Mt1+Rt,are decomposed into two components: the household’s consumption of goods and leisure (measured in terms of shadow prices, htRt+ptxxt+ptyyt) and the unused cash balances, Nt. Noting that the income from black market transactions equals the total shortage rent,8

Substituting equation (13) into equation (2), it follows that

In other words, Mt1Ntis the amount of money an average household spends in state shops.

If one knows the amount of Mt1Ntfor a period t, then the equilibrium prices for the two goods, ptx and pty,the wage rate in the black market transaction. Rt, the demand for leisure, ht and the demand for consumption goods, xt, and yt, are all determined in that particular time period.

More specifically, taking ptx,pty,and Rt as given, each individual household maximizes its utility u=u(ht,xt,yt)subject to the following budget constraint:

whereIt=Mt1Nt. Since there are three “choice” variables, ht, xt and yt, solving the maximization yields three first-order conditions. These three first-order conditions, together with the constraints expressed in equations (3) and (13) and the two market-clearing conditions for goodsx and y, uniquely determine the variables ht,qt,xt,yt,ptx,pty, and Rt.9

The shadow prices of goods x and y are a function of the cash balances spent in state shops. It Under moderate restrictions on preferences, it can be shown that the prices are nondecreasing in It: the more an average household spends, the higher the prices of goods x and y. In the rest of the analysis, the following proposition is assumed to hold:

PROPOSITION 1: Letptx=px(It)andpty=py(It). Then,dpx/dIt0anddpy/dIt0,with at least one strictly positive.

To complete the characterization of the dynamic equilibrium, the intertemporal consumption and saving decisions of households are considered. For given initial cash balances M-1 and wage rate w, each household’s savings (Nt) must be determined from time t = 0 to infinity.

If Nt is determined, Mt1Nt is known for all t. In this way, the equilibrium prices for every time period (and for the whole equilibrium path) are determined.

Before proceeding, some discussion of the aggregate wage level set by the government is necessary. Under central planning, the average output per household valued at state prices is X + Y in every period. The wage paid out to each household is w. If w>X+Y,firms’ revenues never cover their wage bills. Consequently, the government must continuously turn to printing money to cover the losses. In the frictionless case, there is no demand for money in black market transactions. Yet, the official market transactions cannot absorb all the cash balances of households. No equilibrium exists.10

If there is a cash-in-advance constraint on black market transactions, the black market will absorb part of the cash balances held by households, and equilibrium does exist. In the long run, however, as the money supply keeps growing, the supply of goods runs short, and black market prices for goods continue to rise. As shortages grow more acute, individual households spend more time queuing and their welfare continuously worsens (Barra and Grossman (1974), Bennett and Phelps (1988), and Osband (1991)).

If w=X+Yinitially, before all goods are sold in state shops at official prices (that is, there are surplus goods), the revenues of firms do not cover their wage bills, and the government has to print money to bail them out. Over time, as households’ money balances grow, the demand for goods at official prices grows until all goods are in shortage.11 Similar to the case of w>X+Y,with no friction in the black market, no equilibrium exists.

If there is a transaction demand for money in the black market, an equilibrium may exist. The main difference is that the money supply may not grow without bounds. The reason for this is that once all the goods are in shortage. the sale revenue of products at official prices is X + Y, which exactly equals the wage payment w. At that point, the government’s budget is balanced and there is no increase in the money supply. The economy reaches a steady-state equilibrium.

The above cases indicate that, under the assumption that wX+Y,all goods ultimately go into short supply, and the situation becomes explosive. The extreme disequilibrium in the former Soviet Union in late 1991—when real wages grew beyond the government’s control, at much higher rates than labor productivity, and when the shortages became more acute and widespread—is one prominent example. However, one normally observes more stable economic conditions in a centrally planned economy. More important, the assumption violates the fundamental planning philosophy in a classic socialist economy, which states that aggregate demand and aggregate supply must be balanced. In the rest of this section, the analysis is restricted to the case in which government has perfect control over wages, and w<X+Y.12

PROPOSITION 2: Suppose that an equilibrium exists. M1w,thenN0 = 0.

Proof Suppose thatI0<M1,andN0=M1I0>0. Then, the cash balances available for a representative household to spend in period t = 1 are N0+w>M1.In this analysis, a household would spend no more than I0 in period t = 1, meaning I1I0. Otherwise, goods prices in period t = 1 would be higher (Proposition 1). A rational household could increase spending in period t = 0 by a small amount but decrease its spending in period t = 1 by the same amount to raise its utility level. Apply the same argument to periods t = 2,3,4,..., to conclude that the spending level decreases over time. In other words, an average household would accumulate cash balances without bounds. This conclusion is inconsistent with utility maximization, since an individual household could increase consumption, and thus its utility level, by reducing cash balances.

Proposition 2 says that in period t = 0, if the initial cash balances are smaller than the permanent wage earnings w, a household would simply spend all of its cash balances and save nothing.

PROPOSITION 3: Suppose that an equilibrium exists. If M1>w,thenT>0exists, such that Nt>Nt+1,for0tT, and Nt = 0, for t > T.

Proof. Note that in each period t, household consumption of leisure and consumer goods is a function of spending, Mt1Nt. Substituting these variables into equation (12) and differentiating both sides of the equation yield the following equations (Levhari and Srinivasan (1969) and Schechtman and Escudero (1977)):

The first equation says that the marginal utility of initial cash balances in period t equals the marginal utility of spending an extra unit of cash on goods consumption, provided that the entire consumption and saving plan is optimal. The second equation says that if savings are positive (Nt > 0), the marginal utility of cash balances in the present period must equal the marginal utility of cash balances in the next period, discounted by a factor β.

Suppose that no integer T exists such that Nt = 0 for t > T. It follows from Proposition 2 that savings must be positive in every period (Nt > 0), for all t.13 Hence,

Noting that dJ(M0)/dM0>0 and β < 1, it follows that

Following the proof of Proposition 2, it is known that in each period t the spending in state shops, Mt1Nt,must be as high as one period’s wage earnings, w. Obviously, the marginal utility that can be derived from an extra unit of spending has an upper bound, a contradiction of equation (18).

Let T be the smallest integer that satisfies the following: Nt = 0 for t > T. Thus, Nt > 0 for tT. Since savings are strictly positive up to period T and β < 1, the marginal utility of consumption increases until period T, which implies that real consumption and savings decrease until period T. That is, Nt>Nt+1 for tT.

Proposition 3 says that if the initial cash balance exceeds average wage income per period, households would run down excessive money balances, M1w.After that, households would simply spend their entire wage earnings from the previous period, plus the black market rent earned by queuing every period. Combining Propositions 2 and 3, it has been shown that if an equilibrium exists, it converges to a steady state.

For simplicity, it is now assumed that the initial cash balances do not exceed w.14

PROPOSITION 4: Suppose that w < X = Y and M-1 ≥ w. Then, a steady-state equilibrium exists, and the economy converges to if in one period. In the steady state, at least one good is a surplus good.15

Proof. Let Nt = 0 for t ≥ 0. Then, I0=M1, and It = w, for t ≥ 1. It can be readily checked that [px(It),py(It)], for t ≥ 0, is an equilibrium. Starting from period t = 1, the equilibrium coincides with the steady-state equilibrium [px(w),py(w)].It is also clear that in the steady-state equilibrium, at least one good is a surplus good. Otherwise, both goods would sell out in state shops at prices px=py=1,bringing in revenue X + Y. Since an average household’s spending in state shops is only w, this is a contradiction.

The above analysis has shown that at a moderate wage level, w<X+y, the economy converges to a steady-state equilibrium in which at least one good is a surplus good. In the steady state, firms of type j make a profit of

Noting that Nt = 0, it follows from equation (14) that

Hence, in the steady state, the government’s tax revenue exactly covers its expenditure and there is no money printing, ΔM = 0. Intuitively, if initial household money balances are higher than wage income, w, households will initially dissave (Proposition 3) and their spending at state shops will exceed w. In other words, the overall revenues of firms exceed total wage payments; firms make a net profit. The profit is also the government’s surplus, which it turns over to the central bank. Over time, as the “excessive” balances of households dissipate, the profits of firms fall to zero and the government budget surplus disappears.

If, on the other hand, initial household money balances are below wage income, total household spending at state shops is below firms’ total wage payments. The net profit of all firms is negative and the government runs a budget deficit, implying an injection of money into the economy. As household money balances rise, however, the demand for goods at official prices increases and eventually reaches a level equal to wage income. At that point, the sale revenues of firms exactly cover their wage payments and the government budget is balanced.

The steady-state money supply is the total wage payment that firms make to individual households, M = w. The entire money stock is absorbed by transactions in the official markets, and there is no monetary overhang. In the case of a cash-in-advance constraint in the black market, the steady-state money supply would be the wage payments plus rents earned through black market transactions, M=w+qR,which is absorbed by official transactions, w, and black market activity, qR. Again, there are no involuntary money holdings (or “forced” savings).

Thus, under a rigid central planning system, like the one described in the model, the economy converges to a steady-state equilibrium that exhibits macroeconomic stability. In the steady state, the government budget is balanced and the money supply and prices (both official and black market) are stable. Although rigid planning may create tension between demand and supply, the black market bridges the imbalances. The analysis suggests that the notions of “monetary overhang” or “forced savings” are incompatible with an equilibrium model. As long as there are surplus goods and black markets, no involuntary money holdings occur in a shortage economy.16 Households hold money either for (official) transactions, savings, or black market activities.

III. Wage Reform Under Price Control

In the 1970s and 1980s, many centrally planned economies embarked on reforms aimed at liberalizing prices and decentralizing the financial decisions and wage policies of enterprises. The results have not been entirely successful. This section examines how a reforming economy, in its rush to decentralize decisionmaking, may upset the preexisting system, and with it the economy’s macroeconomic equilibrium.

To make the analysis in this section more focused, the only reform considered is wage reform, leaving the study of price reform for later. Specifically, two types of wage reform are examined: the first allows profitable firms to retain a fixed percentage of their profits as funds for wage increases; the second allows profitable firms to share profits with workers (in some kind of bonus scheme).17

Profit-Based Wage Increase

Under the first wage reform, upward wage pressure continuously squeezes firms’ profits. If a fraction of state firms are fundamentally insolvent and require continuous subsidies from the state, the profit squeezing leads to a steady deterioration of the government’s budget, the need for money printing, and eventually widespread shortage in the economy.

Suppose that type-x firms are profitable(πx>0)and that the government allows these firms to retain a fraction, δ, of their profits to be used to increase workers’ wages. For notational simplicity, assume that the economy has been in a steady-state equilibrium up through period t = —1 and that the government begins its wage reform in period t= 0. An average household’s wage income in period t is

where 0 < δ < 1 and t ≥ 0, and where wtx is the wage rate in type-x firms and πtxis the profit of type-x firms in period t (calculated using the wage rate in period t— 1). Thus,

where t ≥ 0 and w1x=wx.. Note that, as long as the demand for consumption good x (x,) increases with income, the profits of type-x firms are always positive, and the wage income of an average household increases over time.

From the assumption, type-y firms are loss makers. However, if as household incomes rise the demand for good y becomes sufficiently high and its sales at state shops exceed wage payments in type-y firms (wy) then firms of type y are fundamentally solvent. In that case, the post-reform economy converges to a steady-state equilibrium in which the profit (or loss) of all firms is zero, and the money supply is constant. Thus, similar to the pre-reform steady-state equilibrium, the economy exhibits macroeconomic stability and there is no monetary overhang.

To verify the above claim, note that starting from the old steady state, money balances are equal to households’ income, M1=w0. Let Nt = 0 for t ≥ 0; then I0=M1 and It=wt1, for all t ≥ 1, and it can be readily checked that [px(It),py(It)]is an equilibrium. Also note that It is increasing but bound from above because profits of type-x firms converge to zero. It is therefore easy to see that [px(It),py(It)]converges to a steady- state equilibrium in which all firms make zero profits.

Suppose that either Y<wy or yt<wy, for t ≥ 0, is true, then firms of type y are fundamentally insolvent, since the sale revenues at official prices never cover wage costs. Under the first wage reform, the profits of type-x firms are continuously squeezed and eventually fall to zero. Hence, in the long run, the government resorts to money printing to finance its subsidies to type-y firms, and the money supply grows without bound. If black market transactions are frictionless and there is no demand for money, similar to the case in which w>X+Y, the money injected by the government cannot be absorbed in the economy and no equilibrium exists.

If, however, there is demand for money in black market transactions, the black market will absorb part of the money in circulation and an equilibrium may exist. For instance, if there is a cash-in-advance constraint on black market transactions, and if Nt = 0, for t ≥ 0, then I0=M1 and It=wt1+qt1Rt1.Thus, [px(It),py(It)] is in equilibrium. In equilibrium, each household simply spends all the cash balances it accumulates in the previous period at state shops or in the black market, or both. With the money supply (or household demand) growing without bound, all goods eventually go into shortage. Moreover, as the shortage grows more acute, productive efforts are diverted to nonproductive black market activity, leading to a continuous worsening of household welfare.

Profit-Based Bonuses

Since wages are rigid downward, the problem with the profit-based wage increase examined in the preceding section is that the upward wage pressure on profitable firms continuously squeezes their profits and thereby drains the tax base on which the government relies to finance its subsidies to loss-making firms. This section examines a second popular wage reform policy, which strictly controls wages but allows profitable firms to distribute a fixed percentage of their profits to workers as bonuses. It is shown that if the percentage is not too high, the pre-reform macroeconomic stability can be maintained.

Suppose that the government allows the profitable type-x firms to distribute a fixed proportion. ρ, of their profits to workers as bonuses. Again, assume that the economy has been in a steady-state equilibrium up through period t = —1 and that the government initiates wage reform in period t = 0. Let wtx be the wage rate in type-x firms. Then,

The wage income of an average household in period t is wt=wtx+wy, for t ≥ 0. Assuming that a household’s demand for good x (xt) increases with income, it follows that wt increases over time and converges to some constant W. Let π=xwxbe the profit of a type-x firm before reform. Since households do not spend the entire increase in their income on good x, one can show that W<w+π[ρ/(1ρ)].

Recalling that w<X+Y, if ρ is small enough, the steady-state wage, W. is smaller than X + Y. It follows from the earlier analysis that an equilibrium exists. In equilibrium, each household simply spends all cash balances accumulated in the previous period. As an average household’s income wt converges to W, the equilibrium converges to a steady-state equilibrium. In the steady state, at least one good is in surplus, the government budget is balanced, and the money supply is constant.

Thus, the reform proposal is sustainable from a macroeconomic perspective. However, household welfare falls because higher incomes exacerbate the shortages and divert more efforts into nonproductive black market activity.

IV. Price Reform

The analysis of wage reform has indicated that, with the government maintaining rigid control over production and prices, financial reforms that give enterprises discretion over wages may disrupt the stable pre- reform macroeconomic equilibrium. As mentioned, the lack of financial discipline on the part of enterprises tends to raise workers’ wages, exacerbating the shortages and inducing households to shift efforts to nonproductive black market activities.

This section examines the macroeconomic implications of price liberalization, particularly two types of price reform. The first liberalizes all prices while rigid control over wages is maintained. The second liberalizes all prices but allows for some wage flexibility to compensate for possible price jumps. The analysis shows that if the government controls wages, price liberalization would eliminate unproductive black market transactions and improve households’ welfare. If wage control is politically implausible, especially at a time of rising prices and rising profits, the government must control its subsidies to loss-making firms. Otherwise, the economy may plunge into rapid inflation, even hyperinflation.

Price Reform with Rigid Wage Control

Assume that the economy has been in a steady-state equilibrium up through period t = —1 and that in period t= 0 the government liberalizes all prices but maintains rigid control over wages. Letting Ptj(j=x,y)denote the price of good j, an average household faces the following budget constraint:

where Mt1=w+Nt1,for t ≥ 0, is the nominal money balance accumulated in period t - 1 andM1=w.Maximizing equation (8), subject to equation (24) and ht ≥ 1, yields an individual household’s demand for goods x and y and savings Nt.

With all prices freely determined through the markets, the definition of equilibrium must be modified. A dynamic equilibrium of the economy is defined to be a sequence of prices [Ptx,Pty]that clears goods markets in every time period t ≥ 0.

Since price liberalization eliminates black market activity, each household would spend all of its free time on leisure; ht = 1. Allowing It=Mt1Nt,Itis an average household’s expenditure on goods x and y in period t. Similar to the two-step analysis in the second section, taking It,Ptx,and Ptyas given and solving the following maximization problem yield a household’s demand for goods x and y,

subject to

Suppose that Ptxand Ptyare the market-clearing prices in period t. Then, Ptxand Pty are a function of household spending in period t, It:

Clearly, [Ptx(w),Pty(w)] for t = ≥ 0 is a dynamic equilibrium of the economy.

Thus, if the initial money balance is the same as the permanent wage earning, which is also the desired level of spending, the moment the government liberalizes prices there is a one-time change in prices, after which the economy reaches a steady-state equilibrium. The new steady- state prices could be higher or lower, depending on whether the goods are in surplus or in deficit. If a good is in shortage, the new market- clearing price would be higher than the official price and lower than the black market price. If a good is in surplus, the new price tends to be lower than the official price. Therefore, if one uses black market prices in calculating a price index, the post-reform price level tends to be lower than the pre-reform level (Cochrane and Ickes (1991)).

The above case is extreme in that black market transactions are assumed to be frictionless and the initial money balances are assumed to be equal to the permanent desired level of spending. Under the more realistic assumption that there is friction in the black market, and black market transactions absorb a fraction of the aggregate money balances, the initial money balances will be higher than the permanent desired spending level. A release of the “excessive-money balances would trigger a price jump. For instance, if there is a cash-in-advance constraint in black market transactions, the initial money balance is M1=w+R.After price liberalization, the long-run average spending is w. Similar to the reasoning in Proposition 3, the “excess” money balance R would be dissipated in finite periods. Immediately after prices are liberalized, prices jump upward and then come down gradually until they reach their long-run levels (Lin and Osband (1992)).

Finally, it is noteworthy that, whether or not price liberalization leads to inflation, if the official prices differ from the equilibrium market prices, households’ utility improves unambiguously. The post-reform utility level for each household is u(1,X,Y)in one period, while the pre-reform utility level is u(ht,Xt,yt)in period t, where ht1,xtX,ytY,with at least one inequality strictly held.

Price Reform Without Rigid Wage Control

So far, households have been assumed identical, and the government has been assumed to control wages during price liberalization. In practice, however, the government is generally under pressure to loosen financial control. First, price liberalization leads to increases in the prices of deficit goods and in the profits of some firms. For these profitable firms, there is pressure to increase wages, especially when prices have surged owing to price reform. Second, noting that the government owns all firms and that soft budget constraints are still in place, even for the unprofitable firms, there is pressure to increase wages, both to catch up with the wage increase in profitable firms and to compensate for price increases. If the government cannot impose wage discipline, price reform may lead to rapid inflation.

For simplicity, assume that there are no excessive money balances before the government liberalizes prices in period t = 0. That is, M1=w.18 It follows from the above analysis that if the government maintains rigid wage control, price liberalization will result in a one-time price change and the economy will jump to its new steady-state equilibrium[Px(w),Py(w)]in one period. In the steady state, the sum of profits from type-x and type-y firms is zero,

Suppose that πx>0and that the government allows firms of type x to retain a fraction. δ, of their profits for wage increases. Consequently, the price level rises and the wage gap between the two types of firms widens. For simplicity, assume that the government compensates workers in type-y firms by raising their wages by a fraction, γ, of the increase in type-x firms:

where Δw denotes the change in w. Hence, the wage income of an average household in period t is

where the profit of type-x firms is

Anticipating that nominal wages will grow over time, rational households spend all of their money balances in every time period. Let λ he the share of household income spent on good x. Ifλ(1+γ)>1, it can be shown that the profits of type-x firms are growing exponentially as time goes to infinity. The reason is that the revenue increase that arises from the rise in household income more than compensates for the increase in wages,

In fact, one can calculate the growth rate to be λ[δ(1+γ)1].The resulting budget deficit to he financed by money printing is

which also grows at an exponential rate, δ[λ(1+γ)1].

In our discrete-time cash-in-advance model, the velocity of money is constant. With the budget deficit and the money supply growing at a rate of δ[λ(1+γ)1],the long-run inflation rate converges to this rate, which could be high but not explosive. In a more realistic model—in which the velocity of money depends on inflation—relying on money printing to finance the growing budget deficit, as in equation (33), may trap the economy in a high-inflation equilibrium, or lead to hyperinflation (Bruno and Fischer (1990)).

λ(1+γ)1,then the profits of type-x firms either stay constant or converge to zero. If they stay constant, the money supply and the price level would grow without bound, but at rates converging to zero. If profits converge to zero, both the money supply and the price level would stabilize in the long run.

V. Concluding Remarks

The modeling of disequilibrium in the centrally planned economies has attracted much attention in recent years. This paper has used the theories of optimizing behavior to explain how centrally planned economies could have demonstrated apparent stability for many years, with little evidence of serious macroeconomic imbalances, but only recently have shown such macroeconomic turbulence.

The model developed in this paper can describe both stable and unstable equilibria in a centrally planned economy. It identifies the mechanisms that ensure stability, provided that some goods are in surplus, and shows why these mechanisms are not operative if both goods are in shortage. More specifically, the paper shows that if an initial imbalance between aggregate supply and aggregate demand is small enough, it is self-correcting; if it is large enough, the system is unstable. The self- correcting mechanisms result from revenues of state-owned enterprises entering the government budget constraint and from black market prices of shortage goods adjusting to shift demand between deficit and sur- plus goods, so that revenues from profitable firms eventually cover the subsidies to loss-making firms.

The paper also shows that price reforms may benefit some firms at the expense of others and that, without hardening enterprise budget constraints, price or wage liberalization may lead to persistent budget deficits and inflation. In addition, the paper shows how “monetary overhang” cannot exist where there are black markets (see Grossman (1982) and Hartwig (1983)).

The methodology of the paper is similar to the growing literature of non-Walrasian general equilibrium macroeconomics, which emphasizes the need for microeconomic foundations (Barro and Grossman (1974), Muellbauer and Portes (1978), and Osband (1992)). This paper’s characterization of a centrally planned economy seems consistent with the empirical work by Fortes and his colleagues, which rejects the hypothesis of sustained repressed inflation in Soviet-type economies since the mid 1950s (Portes (1974) and Portes and Winter (1980)). This paper is also consistent with Portes and others (1987), which argues that some regularities existed and some endogenous mechanisms were at work in adjusting toward equilibria in the planning processes. However, these authors also point to central planners’ adjustments of announced plans and actual supply to reduce excess demand as an instrument, instead of as the self-correcting mechanism identified in this paper.

REFERENCES

Shoukang Lin is an Economist in the Central Asian Department. He was an economist in the Research Department when this work was completed. He received his doctorate from Brown University and taught at York University before joining the IMF. The author would like to thank Eduardo Borensztein. Timothy Lane, Kent Osband, Tian–Ye Wang, Peter Wickham, and an anonymous referee for helpful discussions and comments. He also thanks Catherine Fleck for editorial assistance.

For instance, during 1985–89, the budget of the government of the Soviet Union deteriorated rapidly and budget deficits rose from about 2 percent to 9–10 percent of GNP. These deficits eventually contributed to the economic crisis in 1990. In China, owing to a dramatic decrease in revenues from enterprises (from around 17.1 percent of GNP in 1979–81 to 5 percent of GNP in 1989), government revenues fell steadily throughout the 1980s. Although the Chinese government managed to reduce expenditures, and budget deficits widened only slightly, it experienced increasing difficulty in financing these deficits. Moreover, the trend of rising subsidies to poorly performing state–owned enterprises remains a potential source of macroeconomic instability. For further discussions, see Blejer and Szapary (1989),IMF and others (1991). Khor (1991), McKinnon (1991), and Bell and Kochhar (1992).

Both methods have been observed, with the first being more popular. However, to the extent that the first channel is essentially equivalent to an increase in the wage rate and that both channels coexist, the assumption would not affect the final conclusion.

There are various definitions of “monetary overhang” (see Cottarelli and Blejer (1991)). In this paper, a monetary overhang is defined as household money balances minus voluntary demand for money.

This sustainability is from a purely economic perspective. It does not imply political sustainability.

Hypothetically, one can imagine a case in which there is a large variety of the same consumer good. Each household can queue for only a few varieties of the good at official prices. Since households would rather have a more diversified consumption package, they will resell the goods in the black market to make a profit and use the money to purchase other varieties. Assume that consumers must have cash in advance to purchase goods in the black market; profits in the current period can be spent only in the next period. In that case, the household budget constraint becomes Nt+ptxxt+ptyytMt1, where Mt1=wt1+qt1Rt1+Nt1.

For instance, in China, the government spent almost one–fifth of its 1991 budget on subsidies to loss–making firms.

In general, J should be a function of real variables only. In this model, the government fixes prices of consumer goods in official markets. A different initial nominal money balance implies a different degree of shortage and thus of black market activity, which has a real impact on household welfare.

If the demand for even one good at the official price exceeds the supply of that good, the economy faces a shortage and there are shortage rents to be sought. To model how the shortage rents are dissipated, this paper follows the approach in Osband (1991). Assuming that good x is in shortage, and that the shadow price of x, Px, is higher than its official price, p=1(px>1),then households can queue to buy good x at the official price and resell it in the black market at a profit. Let R be the marginal utility of leisure measured in currency units; q’ the queuing time for shopper j;Q-j the total queuing time of all shoppers other than j; and N the total number of households in the economy. With a total NX units of good x for sale in official markets, a shopper chooses qj to maximize NX(px1)qjqj+qjRqj, which is the expected shortage rent minus costs. For a large enough N, competition assures that in equilibrium. RNqj=NX(px1), or Rqj=X(px1).That is, all shortage rents are dissipated, If both goods x and y are in shortage, then, in equilibrium, equation (13) holds.

Owing to the rigid control of prices, if demand at official prices does not exceed supply, the market is considered “cleared.” As an illustration, assume that I = 2.5. X –= 1, Y =2, and the utility functionu(h,x,y)=Inh+Inx+Iny.By solving the problem, one can uniquely determine h=3/4,q=1/4,x=1,y=1.5,px=1.5,py=1,and R = ¼. Obviously, good x is in shortage, and good y is in surplus.

In this kind of hypothetical situation, disequilibrium could be characterized as an emerging monetary overhang or “forced” saving.

Here, it is implicitly assumed that as income rises, household demand for goods x and y eventually exceeds their supply. Otherwise, the analysis is identical to the case of w>X+Y.

Assuming that w<X+Ymeans that the aggregate wage level is less than the aggregate output measured at official prices. Considering some products are not sellable, or do not enter the household utility function (such as excessive military goods), the assumption is not as restrictive as it appears.

According to Proposition 2, if a T > 0 exists, such that NT = 0, then Nt = 0 for all tT.

The results hold for any initial cash balances, M-1.

It is clear that as long as the per–household wage level is not too low and the official prices are not market–clearing prices, at least one good will be in shortage.

This result contrasts with the considerable discussion about disequilibrium and “monetary overhang” (or “repressed inflation") in a centrally planned economy (Nuti (1986)). The findings here are consistent with Cottarelli and Blejer (1991), who find little evidence of monetary overhang in the former Soviet Union between 1964 and 1985.

For a discussion of various wage control proposals, see Lane (1992).

If there are “excessive” money balances at the time of price liberalization, the qualitative nature of the analysis would change. The release of the excessive money balances may initially speed up inflation, but its effect on long–run inflation is minimal.

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