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, $M_{t-1},$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.

Financial Flows

Citation: IMF Staff Papers 1993, 001; 10.5089/9781451947137.024.A005

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Financial Flows

Citation: IMF Staff Papers 1993, 001; 10.5089/9781451947137.024.A005

• Download Figure
• Download figure as PowerPoint slide

Financial Flows

Citation: IMF Staff Papers 1993, 001; 10.5089/9781451947137.024.A005

• Download Figure
• Download figure as PowerPoint slide

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, h_t is leisure, and x_t and y_t 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 $p_t^x$ and $p_t^y$ 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 N_t is the unused cash balance in period t, M_t-1 is the cash balance held by individuals at the end of time period t-1, q_t is the time spent queuing, and R_t 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 w_t both of which are determined by the government. In addition, each household allocates its nonwork time between two activities—leisure and queuing (h_t and q_t). 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 x_t and y_t.

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 P^x and y^x, and the wage costs for the universe of firms j (j = x, y) denoted by $w_t^j,$the profits of the two firms are

If ${\pi }_t^j$is 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, D_t, is

As illustrated in Figure 1, if the government budget is in deficit (D_t > 0), the deficit would be financed by the central bank through money printing. For a given D_t, 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 (w_t), 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$(p_t^x\ge p^x,p_t^y\ge p^y)$that satisfies the following condition: if $p_t^j>p^j(j=x,y)$ for some period t, the demand for good j must be equal to the supply of good j.

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$({\pi }^x>0)$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 $w_t^x$ is the wage rate in type-x firms and ${\pi }_t^x$is the profit of type-x firms in period t (calculated using the wage rate in period t— 1). Thus,

where t ≥ 0 and $w_{-1}^x=w^x\mathrm{.}$. 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 (w^y) 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, $M_{-1}=w_0\mathrm{.}$ Let N_t = 0 for t ≥ 0; then $I_0=M_{-1}$ and $I_t=w_{t-1},$ for all t ≥ 1, and it can be readily checked that $[p^x\left(I_t\right),p^y\left(I_t\right)]$is an equilibrium. Also note that I_t is increasing but bound from above because profits of type-x firms converge to zero. It is therefore easy to see that $\left[p^x\left(I_t\right),p^y\left(I_t\right)\right]$converges to a steady- state equilibrium in which all firms make zero profits.

Suppose that either $Y<w^y$ or $y_t<w^y,$ 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 N_t = 0, for t ≥ 0, then $I_0=M_{-1}$ and $I_t=w_{t-1}+q_{t-1}{R}_{t-1}\mathrm{.}$Thus, $\left[p^x\left(I_t\right),p^y\left(I_t\right)\right]$ 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 $w_t^x$ be the wage rate in type-x firms. Then,

The wage income of an average household in period t is $w_t=w_t^x+w^y,$ for t ≥ 0. Assuming that a household’s demand for good x (x_t) increases with income, it follows that w_t increases over time and converges to some constant W. Let $\pi =x-w^x$be 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 $W<w+\pi [\rho /(1-\rho )]\mathrm{.}$

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 w_t 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.

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 $P_t^j(j=x,y)$denote the price of good j, an average household faces the following budget constraint:

where $M_{t-1}=w+N_{t-1},$for t ≥ 0, is the nominal money balance accumulated in period t - 1 and$M_{-1}=w\mathrm{.}$Maximizing equation (8), subject to equation (24) and h_t ≥ 1, yields an individual household’s demand for goods x and y and savings N_t.

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 $[P_t^x,P_t^y]$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; h_t = 1. Allowing $I_t=M_{t-1}-N_t,I_t$is an average household’s expenditure on goods x and y in period t. Similar to the two-step analysis in the second section, taking $I_t,P_t^x,$and $P_t^y$as given and solving the following maximization problem yield a household’s demand for goods x and y,

subject to

Suppose that $P_t^x$and $P_t^y$are the market-clearing prices in period t. Then, $P_t^x$and $P_t^y$ are a function of household spending in period t, I_t:

Clearly, $[P_t^x\left(w\right),P_t^y\left(w\right)]$ 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 $M_{-1}=w+R\mathrm{.}$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 $u(h_t,X_t,y_t)$in period t, where $h_t\le 1,x_t\le X,y_t\le Y,$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, $M_{-1}=w\mathrm{.}$^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$[P^x\left(w\right),P^y\left(w\right)]$in one period. In the steady state, the sum of profits from type-x and type-y firms is zero,

Suppose that ${\pi }^x>0$and 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. If$\lambda (1+\gamma )>1,$ 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 $\lambda [\delta (1+\gamma )-1]\mathrm{.}$The resulting budget deficit to he financed by money printing is

which also grows at an exponential rate, $\delta [\lambda (1+\gamma )-1]\mathrm{.}$

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 $\delta [\lambda (1+\gamma )-1],$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)).

$\lambda (1+\gamma )\le 1,$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.