MARXISM 4

 

MARXIAN POLITICAL ECONOMY

 

 

 

Equilibrium Prices in the Capitalist Economy

 

 

down up  To salvage the labor theory of value and to make his theory of price compatible with the observed fact that the rates of profit do not vary inversely with capital/labor ratio, Marx devised the theory of transformation of value into 'prices of production'. According to this theory labor-value ceases to be a general equilibrium price in the capitalist economy and it is in this role replaced by 'production price' determined as cost plus average profit. Note that Marx--and after him all the Marxists--never used the term ‘general equilibrium’ but as the following explanations shows, that was what he meant. The argument goes as follows: Competition makes capitalist to withdraw their capital from less profitable industries - such as corn in our example - and put it into more profitable ones - such as cloth. As a result supply of corn would decrease creating excess demand for corn, and supply of cloth would increase creating an excess supply of cloth. Due to excess demand for corn the price of corn would rise pulling the profit rate up. Simultaneously the excess supply of cloth would cause decline of its price and profits. The process continues until all lines of production are equally profitable, so that no capitalist has an incentive to reallocate his capital. This is the state of general equilibrium in the capitalist market economy. The general equilibrium prices which were called by Marx 'prices of production' deviate permanently from labor-values nevertheless the labor theory of value is still presumed to hold, because prices of production are only 'transformations' of labor values.

 

down up  According to this theory of Marx, the essence - appearance becomes a three tier relation: market price is the most surface disguise of value; in the next tier is the 'production price' which is the essence of market price but itself a 'form of appearance' of the ultimate essence namely the labor-value which is hidden in the third tier under the surface. This amounts to the claim that the capitalist 'relations of production' are particularly deceitful. Marxists say that you were mistaken if you thought that the discovery of general equilibrium price unearthed the true essence guiding the fleeting movements of market prices. The general equilibrium price fooled you to believe that profits were generated by capital but the only true source of profits was the surplus value resulting from exploitation of labor.

Marx insisted that labor value still ruled market even if the 'prices of production' deviated permanently from labor values. He maintained that deviations of prices of production from labor-values represented only a redistribution of the surplus value among capitalists and thus did not affect the more crucial fact of an unequal distribution of value between workers and capitalists as social classes. Those capitalists who were selling bellow value were giving up the part of their surplus value to the less lucky capitalists who operated in capital intensive industries and whose workers produced less surplus value per unit of capital. The aggregate value of all commodities and also its division into three components: the aggregate c, v and s remained unchanged. Total profits after redistribution were still equal to total surplus value created by workers. Marx concluded that the theory of exploitation is valid.

 

down up   Let us use our example to see, how the production prices are formed and whether the claim about the mere redistribution of surplus value is true. Suppose that the total output of corn is 600 pounds and the total output of cloth is 200 pounds, then it must hold for the totals

Aggregates at labor-value prices

 

corn

cloth

total

quantity

600

200

 

cost of material (c)

1000

300

1300

cost of labor (v)

300

200

500

total cost (c+v)

1300

500

1800

surplus value (s)

300

200

500

value (c+v+s)

1600

700

2300

profit rate 
s/(c+v) %

23

40

27.8

Aggregates at 'prices of production'

 

corn

cloth

total

quantity

600

200

 

cost of material (c)

1000

300

1300

cost of labor (v)

300 

200

500

total cost (c+v)

1300

500

1800

profits (z )

361.1

138.9

500

output at prod. prices

1661.1

638.9

2300

profi rate 
 z/(c+v)%

27.8

27.8

27.8

We see that the aggregate material cost is 1300, wage cost 500 and total cost 1800. The aggregate surplus value of 500 added to the aggregate wages gives national income (aggregate "live labor") of 1000. The aggregate labor-value of all goods (the so called "Gross Social Product" or Gross Value of Output) is 2300. The average rate of profit is 500/1800 = .2778 or 27.78 per cent. Marx's solution is to move 61.11 hours of surplus value from cloth to corn so that the rate of profit in cloth industry is reduced from 40% to 27.78% and the rate of profit in the production of corn is increased from 23% to 27.78%

Production prices (per unit of output) are 2.77 for corn and 3.2 for cloth. They were obtained as follows 2.77 = 1661.1/600 and 3.2 = 638.9/200. According to this solution the production price of corn is 2.77, i.e. about 4 per cent above the labor-value of 2.67, while the production price of corn at 3.2 is about 9% below its labor value of 3.5. This solution of Marx's has the claimed property that all the aggregates (last column) at production prices and at labor-values are the same. In particular the aggregate 'newly created value' or national income remains 1000, the aggregate Gross Social Product remains 2300 and the aggregate profits are equal to aggregate surplus value (500). However this solution is wrong. The prices of goods changed but neither the cost of material nor the subsistence wages were changed although both depend on prices of the same two goods.

 

down   The right solution to the 'transformation problem' of Marx was derived by many economists among whom Pierro Sraffa is probably the best known. What we need is to solve the following three simultaneous equations for equilibrium prices:
 

where p1 and p2 are production prices of corn and cloth respectively, and r is the rate of profit

up

p1 = (.2 p1 + .47 p2 )(1 + r)

p2 = (.5 p1 + .33 p2 )(1 + r)

600 p1 + 200 p2 = 2300.

The first two equations give prices as cost plus profit mark-up. The profit rate r is one of the three unknowns that must be obtained by solving equations (6), (7) and (8) simultaneously. The coefficients .2 and .47 of the first equations are obtained in the following way: To produce 1 pound of corn .2 pounds of corn is needed as input of which .1 pound is used as material input directly in the production process and another .1 pound is used to feed workers that are producing corn. The last figure results from the fact that 1 hour of work is needed to produce a pound of corn and the subsistence consumption of corn per one hour of work is .1 pound. Similarly to produce one pound of corn .47 yards of cloth is needed of which .4 yards as material inputs and .07 yards as the subsistence consumption for the workers producing corn. Again the last figure results from multiplying 1 hour of work per one pound of corn by .07 yards of cloth per one hour of work. The coefficients .5 and .33 of the second equation are obtained in the parallel way.

The first two equations (6) and (7) determine the relative prices p1/ p2 and the profit rate r. The third equation (8) is needed to fix the level of prices. We have chosen it in such a way that the aggregate gross value of output (GSP) at production prices and at labor-values will be the same. Alternatively one can choose this equation to maintain the aggregate value added (national income) unchanged or aggregate profits equal to aggregate surplus value. Note that the choice of the third equation has bearing neither on relative prices nor on the rate of profit. It represents just a choice of the 'numeraire'.

To solve simultaneously equations (6), (7) and (8)  is not a trivial matter. One has to use a relatively complex iterative algorithm, which would be difficult to apply without a computer. In our case the solution is
 

p1 = 2.75

p2= 3.26

r = 32.57 %

 

 

down up   Comparing this result with Marx's solution we see some although not very large difference in prices, however the rate of profit is considerably higher: 32.6 instead of 27.7 per cent. The higher profit rate is caused primarily by lower subsistence wage at production prices. Remember that at labor values the subsistence wage (the value of labor power) per 10 hour working day was 5 hours. At production prices we have

subsistence wage = 2.75 + (.67).26 = 4.92

 

 


When we evaluate output at prices (9) we also get aggregates
quite different than those resulting from Marx's solution:
 

Economic Aggregates

at labor-value

at production price

Cost of Material

1300

1242.81

Wage Cost

500

492.06

Profits

500

565.13

National Income

1000

1057.19

Gross Social Product

2300

2300.00

 

 

We can clearly see that the transition to production prices cannot be regarded as a simple redistribution of surplus value from one line of production to the other. Although the gross value of output at production prices was made equal to the labor-value of output the other aggregates changed. National income at production prices is larger than the aggregate 'live labor', aggregate profits are larger than aggregate surplus value, wage cost and material cost are smaller than those evaluated at labor-values.

down up   Marxist concept of  ‘production price’ corresponds approximately to the concept of general equilibrium price in modern economics. If solved properly as shown above it is compatible with the contemporary non—Marxist economic theory. The difference is, however, in interpretation. Contemporary economists see the theory of general equilibrium prices as a complete and self sufficient explanation of price formation in the market economy under perfect competitions. Not only that it needs no support from the labor— theory of value it is incompatible with it. Notice that when solving equations (6), (7) and (8) for prices we did not need to know labor values of the two products. Similarly solving equations for the equilibrium rate of profit r did not require knowledge of surplus value and its relation to total cost evaluated at labor-value prices. In fact the equilibrium rate of profit was quite distinct from the ‘average rate of profit’ obtained from labor-value calculations.

Modern economics reject labor theory of value as a first crude attempt to explain price formation which was not supported by facts. Marxists, on the other hand maintain, that even if the general equilibrium ‘production prices’ deviate permanently from labor—values they are still only ‘transformed form of appearance’ of labor—values. But this claim rests on mathematically incorrect solution to the ‘transformation problem’ by Marx. When the mathematically correct solution is used then the basic Marxist tenet that the profits are merely redistributed ‘surplus value’ cannot be upheld.

 

down  up  There is, of course, also a more basic criticism. Labor—theory of value starts from an unsubstantiated axiom that only labor creates ‘value’. In fact not all the labor but only the so called productive labor is supposed to create value. It follows from this axiom that all the national product is produced just by ‘productive’ workers and that any consumption of nonproductive’ workers comes from the ‘surplus value’ which is an unpaid work of ‘productive’ workers. But ‘nonproductive’ workers may provide labor services  as. ‘va1uable’ as those of   productive  workers. Modern economic theory interprets value as utility or welfare of population and not as cumulated expense of a single productive factor. In a competitive market any labor service that is capable to earn positive payment must contribute to the overall welfare and it is in this sense productive. What Marxists see as an one way flow of value from ‘productive’ to ‘nonproductive’ workers may be an exchange of equally valuable services.

Similarly modern economics consider not just one but all the factors of production to be productive. So that labor creates only part of the total value of product, the other parts being created by capital, land and other factors of production. Each factor contributes proportionally to its marginal product.up

 

 

 

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