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In a centrally planned economy, the main risk to a manager wishing to keep his job is that of receiving an unimplementable plan for next year.
The company manager does not have a profit motive, as all profit belongs to the state. He is interested solely in keeping his job, which (as we assume) is conditional on implementing the plan. The plan (plan constraint) separates out the production situations which are acceptable to the firm's directly superior economic centre from the set of technically implementable production situations.
However, the supreme master in a communist country is not the economic centre, but the political centre (politburo), which is facing (unsuccessfully, as we now know) the threat of total defeat in economic competition with the West.
The economic centre therefore fulfils the political directive, which (since the 1960s) is primarily to boost production efficiency. However, the economic centre is caught between a rock and a hard place — political pressure from above and evasive manoeuvres by firms from below. Moreover, the firm is in a position of total information superiority vis-a-vis the centre. The only way the centre can produce a balanced and more efficient plan is by means of the "index planning method”. This is simple. The status quo (which, of course, is materially balanced) is directly incorporated into the plan for the next period in such a way that either all outputs are multiplied by an index slightly above unity or all inputs are multiplied by an index slightly below unity
Company managers knew all this in advance. Anyone who foolishly revealed his production possibilities by exceeding the previous year's plan would end up with the more difficult — and perhaps impossible — economic problem of fulfilling the plan next year. In the interests of their own survival (in the post of manager) company managers therefore had to set aside reserves (the bigger the better) in order to gain room to implement tougher indexed plans in future years. Moreover, producing well below capacity is less difficult for managers than balancing close to the production-possibility frontier (production function), especially in conditions of uncertainty and general scarcity (shortages of replacement parts, scarcity of for eign exchange to pay for raw materials imports, frequent supply shortfalls, etc.).
So, it wasn't just that producers were not interested in maximizing their profits. It was that they were interested in the exact opposite—in producing as inefficiently as possible and protecting themselves against a tougher future plan by creating the largest possible reserve against it.
In the original 1980s for mulation of the homo se assecurans model, the reserve r in production situation (where y is the output volume and is the vector of input volumes) is defined as the difference between the firm's production capacity (the value of the production function at point) and output volume y, i.e.
The behaviour of a communist producer was modelled as the maximization of this reserve on the set of feasible production situations, i.e. the constrained maximization problem:
This model therefore assumes that the utility of the firm is given exclusively by the amount of the reserve, i.e. by the difference between the technically achievable and the actually implemented level of output. The following figure illustrates such utility isoquants for the case of a single input x. The arrow in the figure indicates the direction of increasing utility:
Figure 34: Isoquants of a homo se assecurans producer maximizing its absolute reserve against the plan
It is noteworthy that the criterion of a homo se assecurans producer does not explicitly contain prices. In a centrally planned economy, prices are merely a "language" for for mulating the plan constraint.
In Figure 35, which again illustrates the situation for a single [aggregate) input, the production function and the plan function are indicated by unbroken lines and the utility (absolute reserve) isoquants by dotted lines. The tangents to the production and plan functions are drawn with dashed lines. The producer tries to "descend” to the lowest possible isoquant that still allows it to fulfil the plan, i.e. to point E* with the maximum margin relative to the extinction zone, which for a homo se assecurans agent is the set of points (production situations) above the production function line f(x). The producer's optimal production situation is point E = [x, g(x)], where x* is the sole input volume at which the tangents to the two functions f(x), g(x) have the same slope:
Figure 35: The optimal production situation for a producer maximizing its absolute reserve against the technological maximum
As we explained above, the following assumptions are economically well interpretable:
• strict concavity of
• strict convexity of
• differentiability of and
• a non-empty intersectionof the set of technically feasible production situations T and the set of production situations feasible under the plan P,
• location of the optimal production situation on the plot of the plan function.
As the sum of the strictly concave functions , , the absolute reserve, which, given the final assumption, we can write as , is necessarily strictly concave. This means that the problem of maximization of the absolute reserve on the intersection of the technically feasible set and the set feasible under the plan has a unique solution.
The optimal solution (the producer's optimum) is therefore production situation , where is the input vector for which the marginal product and the partial derivative of the plan function are equal for all inputs:
As the optimum necessarily lies on the plot of , we can express the largest possible absolute reserve with input volume as
For the single-input case (n = 1), the absolute reserve function under the a for ementioned assumptions is unimodal and has a unique maximum , as illustrated in Figure 36:
Figure 36: The maximum absolute reserve against the plan versus input volume: the producer's optimum at point x