Publications   On the Stability

Excerpts from

Michael Manove

On Decentralized Pricing, Monopoly Power and Inflation in Socialist Economic Systems


It is my intention here to explore the inflationary potential of producer-set prices in a socialist centrally-planned economic system. One of the main variables of this analysis will be the degree of monopoly power that is present. While the connection between monopoly and inflation is firmly established in the minds of most laymen, a substantial group of economists deny any significant causal relationship. They argue that only an increase in the degree of monopoly power could cause prices to increase, and even then the price-increase would be a one­time occurrence, not a sustained inflation. In this paper I dispute this position......

I will argue my case in the context of an extremely simple hypothetical economic framework. ….

The Basic Model

In the basic model, … there is no economic growth. Only one variety of consumer good … and there is one in­dustry …. producing that good. …. There may be other industries producing capital goods, intermediate goods, and public consumption goods, but all of these goods are either allocated by a non-price mechanism or sold at prices fixed centrally.

The labor force in the entire economy is of constant size L, and there is no un­employment. The wage rate wt is uniform and is set centrally each production period. There is a one-period lag between wage-rate determination and the disbursement of wages based on those rates. Household money incomes in period t are given by

(1)            Yt  =  Lw t-1

…. workers desire a certain customary or target real wage  l. … Each period, the planners set a new wage that is a geometric average between … l at current prices and the previous wage. The money wage in period t is given by

(2)                    wt =  (pt l)a w t-1a-1

where pt denotes the current price of consumer goods and  0 < a < 1 is the parameter of adjustment. ….

All income received by households is immediately spent on consumer goods. There is no personal saving or dissaving. The industry demand curve for consumer goods in period t, then, is given by

(3)            Qt  =  Yt /pt

where Qt is the total quantity of the consumer good demanded.

The Behavior of Firms

 The consumer good industry is composed of n firms, with identical production and cost functions. Before the beginning of each production period, each firm sets a tentative price and output target with the intention of maximizing profits. Each firm has access to the production plans of all of the other firms …. By the time the production periods begins, every firm must be “satisfied” with its price and production plan, i.e. a  Nash equilibrium must be reached.

…. We make two assumptions: First, at any given planned price, each firm evaluates the … demand for its output to be the industry demand at that price minus the total planned output of all the other firms. Secondly, the price and quantity planned by each firm must be profit maximiz­ing ….each firm will set a price that equates the … demand for its output with its planned production target. …..because every firm perceives the same total of production targets and the same industry demand curve. every firm will set the same price.

Suppose that total industry-wide planned production of consumer goods in year t turns out to be Qt. and that the planned output for each firm is qt = Qt/n. … The industry demand curve, (3), implies that the … demand for the output of each firm is given by

(4)             qt  =  Yt / pt –  (n-1) Qt /n

or, solving for p,

(5)                         pt  = Yt /[(n-1) Qt /n + qt ]

The individual-firm total revenue function R(q) is given by

(6)                         R(qt )  =   Yt pt  /[ (n-1) Qt /n + qt ]

so that marginal revenue is given by
(7)                   R’(qt ) =  [Yt (n-1) Qt /n  ]/[(n-1) Qt /n + qt ]2

On the cost side, the firms have identical fixed-proportions production func­tions. The consumer good is measured in units such that the coefficient of direct labor input per unit of the consumer good is one. Firms may require other in­puts (intermediate goods and capital) in fixed proportions to the labor they use, and the price charged by the state for these other inputs is proportional to the wage rate over time. Consequently, the marginal cost of producing the con­sumer good in period t is constant and is given by

(8)        C’(qt ) =  (1 + v) w t-1

where v is the unit cost of the non-labor inputs expressed in labor-time. All social-overhead costs and the costs of public consumption goods provided by the state are included in v.

 If qt is to be the profit maximizing level of output, we must have C’(qt) = R’(qt ) so that by (7) and (8)

(9)        (1 + v) w t-1  =  [Yt (n-1) Qt /n  ]/[(n-1) Qt /n + qt ]2

and substituting Qt/n for qt yields

 (10)     (1 + v) w t-1  =  [(n-1)/n] L /(1 + v)   

Substituting the right-hand side of (1) for Yt and solving for Qt yields

(11)       Qt   =  [(n-1)/n] L/(1 + v)

so that

(12)       qt   =  [(n-1)/n2] L/(1 + v)   

Substituting (3) into (10) and solving for pt yields

(13)       pt  =  [n /(n – 1)] (1 + v) w t-1 

This then is an equilibrium solution. By setting quantity and price as in (12) and (13) each firm would be maximizing sure profits given the behavior of the other firms. …


  Substituting the value of pt into the right-hand side of (2) yields

(14)                             wt  =  {[n /(n – 1)] (1 + v) l}a w t-1 

Since, by (13),  pt is a constant times w t , we have also that

(15)          pt  =  {[n /(n – 1)] (1 + v) l}a p t-1 

Thus, the rate of inflation for both wages and consumer goods is

(16)           r  =  {[n /(n – 1)] (1 + v) l}a – 1

In attempting to interpret (16) it is helpful to consider the relationship between  l , the target real wage, and the average productivity of labor, which we denote by g. Since the total cost, expressed in labor time, of producing a unit of the consumer good is 1 + v, it follows that

(17)                  g  =   1/(1 + v)

Substituting (17) into (16) yields

(18)                  r  =  {[n /(n – 1)] l/ g }a – 1

and we see that the degree of market power as measured by n, and the ratio of the target real wage to the productivity of labor, l/ g, emerge as the key factors in determining the rate of inflation.

The Role of Money

In market economies and free market sectors of planned economies, money is not the source of buying-power. Buying-power is generated primarily by income and wealth arising from productive activity. But whenever money is the medium of exchange, as it is in the consumer good sector of most socialist economies, money must be present if buying-power is to be effective. If the stock of money is insufficient to act as a medium of exchange for transactions indicated by real factors, some of those transactions will not be completed. … Thus, monetarists can argue that where prices are flexible, the supply of money can be used as a policy tool to control price levels and inflation, without creating any long term effect on the nature of the real economy.

It is not my intention to dispute this view. …. I would suggest that monetary authorities would be prone (or directed) to “finance” an inflation by creating in every period a money supply sufficient to meet transactions demand at current prices. The rate of inflation indicated in the previous sections would then prevail.

A Concluding Remark

We have created a model of a hypothetical socialist economy with centrally set prices in the producers’ goods industries and centrally set wages, but with pro­ducers of the consumer good free to determine both their price and output levels. If there are a small number of firms in the consumer good industry, an attempt by the authorities to set a wage that approaches the average produc­tivity of labor will result in inflation. What is the underlying cause of this pheno­menon? The answer lies in the fact that in firms with monopoly power which maximize profits, the wage rate paid must be less than the value of the marginal product — and thus less than the value of the average product in the case of constant cost. Any prolonged attempt by a government to end this exploitation of labor by setting higher wage rates, will not change the real wage. but instead will be counteracted by inflation. The existence of monopoly power must result in exploitative real wages unless monopolistic behavior itself can be curtailed.






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