Optimal Planning with Consumer Feedback: A Simulation of a Socialist Economy

ABSTRACT

Mathematical optimization can be used to increase the effectiveness of economic planning in socialist economies. Cockshott and Cottrell [Towards a New Socialism, Spokesman: 1993] have proposed a model of socialism in which optimal planning is made responsive to consumer demand. A point of contention has been the emphasis on labor values in their model. The use of labor values could mean that the environmental impact of production is insufficiently reflected in planning targets. This paper discusses how alternative values (opportunity cost valuations, OCs) can be calculated using linear optimization and presents a computer simulation of a socialist economy based on these values. An agent-based consumer model was developed to model the behavior of consumers. An alternative version of the simulation based on labor values is used for comparison. It is found that in specific circumstances the use of OCs does indeed result in a stronger emphasis on more environmentally friendly production than the labor value model. Relevant literature on optimal planning, distribution under socialism and valuation will be reviewed, followed by a presentation of the simulation and a discussion of some of its results for a series of small test economies.

KEYWORDS:

• Socialism
• planning
• valuation

JEL CODES:

• B51
• P21
• P22

Acknowledgments

I thank the three anonymous reviewers for their comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 TNS stands for Towards a New Socialism, the name of their book.

2 The model does not currently allow for economies of scale, but since multiple methods are allowed, different scales of production could be modeled through distinct production methods. The reason that the current model is nonetheless inadequate for representing economies of scale is that there is nothing that would prevent a large scale production method from being used at a very low intensity. Preventing this would require some additional constraint that is not currently included in the model or shifting to a model where the intensities at which production methods are used are discrete.

3 It is also in principle possible for one method to produce several different outputs, as is the case in industries that have some by-product, though this has not been studied for the present paper.

4 This can be seen as a flow of resources for the time period covered by the plan.

5 The unit of the objective function, just as the unit of opportunity cost in Section 2.1.3, is simply the unit in which the Objective Product is measured, i.e., pieces, tons, kilogram, liters,…. Changing from tons to kg would increase the value of the objective function by a factor of 1000. This is not a problem, but shows that one has to be consistent in the use of units.

6 The simulation always uses the strict inequality operator instead due to a limitation in one of the computer scripts used. This makes little difference.

7 The unit of all OC values is given by the unit of the objective product, e.g., tons of corn. However, the unit we might ascribe to the values has no impact on how the algorithm operates and can thus be safely ignored.

8 It would also be possible to use a mathematical model based on price-dependent demand functions. However, demand for a product should be responsive not just to the price of that particular product, but to that of competing products as well. This would require multi-variate demand functions. It would also have to be made sure that overall spending does not exceed the combined budget of consumers. Both of these are achieved in the agent-based model but may prove more difficult in a model based on demand functions.

9 A proportional controller is any feedback control system in which a controlled variable is adjusted in proportion to the difference between the observed and desired state of a system.

10 The chance of the shift being in the same direction every time by chance alone is ${0.5}^5\approx 3.1\text{\%}$. Since this is less than $5\text{\%}$ the results are statistically significant. No further formal statistical analysis of any of the results was deemed necessary, as results were very consistent and any randomness in outcomes must be purely attributed to the consumer model and not the deterministic planning algorithm. It is the latter, however, that is of primary interest and the consumer model is merely used as a replacement for real consumers.

11 W. P. Cockshott and Cottrell (1993) have found that plan optimizations with lp_solve are of order $n^3$, but also proposes a more efficient algorithm with which an optimal production plan for an economy with 200 million products can be calculated in 22 min. However, if one optimization has to be carried out to value each product, this will still take much too long.

Additional information

Funding

This work was supported with a scholarship from the Rosa Luxemburg Foundation.