Chapter Ƕ: Ļe Debate about the Efficiency of a Socialist Economy ȆȄhouseholds and the common marginal technical rates of substitution for
firms.
Ļe point of the discussion so far is that a socialist planning board
could formulate a set of optimum conditions and translate these condi-
tions into mathematical equations. If the planning board knew in com-
plete detail the preferences of all people as workers and as consumers,
if it knew the production functions of all productive processes, if it had
detailed information on the stocks of all resources, and if it could decide on
some scheme of income distribution, then—conceivably—it could deter-
mine the amounts of each and every sort of good and service which
“should” be allocated to each and every use. If the planning board were
omniscient, then—as Hayek remarks—the solution of the community’s
economic problem would be a matter of pure logic (HayekȀȈȃȇ, p.ȆȆ).
For the board would embody its omniscience in mathematical equations.
As Barone showed, there would be as many equations as unknowns. Ļe
equations are to be solved simultaneously, and the solution would be deter-
minate.
Writers before the time of Mises’s famous article—notably Wieser,
Pareto, and Cassel, as well as Barone—had used the concept of equi-
librium determination through simultaneous equations as an expository
device. But some socialist writers have envisaged the solution of simulta-
neous equations as the actual method of socialist resource allocation (for
instance, Carl Landauer, and—at one time—H.D. Dickinson).
On this approach, the comments of Lionel Robbins are most perti-
nent. I quote from Robbins,Ļe Great Depression(ȀȈȂȃ, pp.ȀȄǿ–ȀȄȀ).
On paper we can conceive this problem to be solved by a series of math-
ematical calculations. We can imagine tables to be drawn up expressing
the consumers’ demands for all the different commodities at all conceiv-
able prices. And we can conceive technical information giving us the
productivity, in terms of each of the different commodities, which could
be produced by each of the various possible combinations of the factors
of production. On such a basis a system of simultaneous equations could
be constructed whose solution would show the equilibrium distribution
of factors and the equilibrium production of commodities.
But in practice this solution is quite unworkable. It would necessitate the
drawing up of millions of equations on the basis of millions of statisti-
cal tables based on many more millions of individual computations. By
the time the equations were solved, the information on which they were
based would have became obsolete and they would need to be calculated