In addition to that, material balance sheets (6) serve also to determine the allocation of intermediate goods (plan of material-technical supplies), which can be represented by the following matrix
Q = Aq^
is a matrix with a typical element Qij representing the planned allocation of the intermediate product i for the production of product j;
is a diagonal matrix made up of the vector of production targets q.
When setting output targets, planners must inspect "balance sheets of labor" to take into account labor constraints
Gq £ l
is a matrix of planned labor requirements per unit of output, whose typical element Lij epresents the quantity of rth kind of labor needed to produce one unit of product i
is a vector of available labor of the individual kinds.
Balance sheets of labor help to allocate the labor force:
L = Gq^
is a matrix the typical element Lrj of which represents the quantity of rth kind of labor allocated to the production of product j.
Planners also have to take into account capacity constraints in order to be able to allocate investment in such a way that the capital stock of each industry is sufficient to produce the planned output. They use "balance sheets of fixed capital" (basic funds) for this purpose.
Bq < K + J - R
Ju = i
is a matrix of planned technological capital-output norms
is a matrix representing the allocation of the existing capital stock in the previous year
is a matrix of the allocation of investment goods
is a matrix of planned scrappage of the old capital stock
is a unit or "summation" vector u' = (1, 1,.....l)
is the vector of supply of investment goods from the equation (6)
Planners also fix prices, wage rates, profit margins and "turnover tax" margins in such a way that the following price equations hold:
p'= p'A + w'G + d' + z'
p' = p' + v'
is a vector of "wholesale" or producer prices
is a vector of "retail" or consumer prices
is a vector of wage rates for different kinds of labor
is a vector of depreciation
is a vector of profit margins
is a vector of 'turnover tax' margins.
If planners were successful in "balancing" the plan, then equations (6) to (13) would guarantee that equilibrium between supply and demand for intermediate and investment goods was achieved; however, no such equilibrium would be guaranteed for consumer goods. In the absence of rationing, planners can influence the demand for consumer goods only indirectly by manipulating the disposable incomes of the population and retail prices. In this way, they could try to achieve equilibrium on the consumer goods market
c = cD (YD, p)
is a vector of supply of consumer goods, from eq. (6)
is a vector of demand functions for consumer goods
is the disposable income of the population
is a vector of retail prices.
The above system of equations (6) to (14) can guarantee general equilibrium between supply and demand for both producer (i. e. intermediate and investment) and consumer goods, providing that planners
(a) know the right form of the demand functions cD (YD, p),
(b) are able to solve the equations simultaneously, and
(c) the plans are perfectly fulfilled.
It is clear that direct simultaneous solution of the planning equations would be an enormously difficult task. To facilitate the planning process, planners usually try to establish first the overall balance between macroeconomic aggregates such as gross social product (GSP), national income (NI), aggregate consumption, investment, etc.
For that purpose, they use aggregate balance sheets of which we shall here discuss only two, namely the balance sheet of the creation, distribution, redistribution, and final use of the gross social product and national income, and the balance sheet of money incomes and expenditures of the population.
The balance sheet of gross social product and national income can be obtained by aggregating the system of partial material balance sheets. It can be described by the following identities:
Creation of GSP:
P = p'q + v'c
is gross social product (GSP)
|p', q, V', C|
are vectors defined in eq. (6), (12) and (13).
The first term on the right-hand side is the gross value of output at producer prices, while the second term is the aggregate volume of turnover tax which is assumed to be charged on consumer goods only
Creation of NI:
Y = P - p'Aq - D
is national income created
is aggregate volume of depreciation.
Apparently national income created (sometimes called also net material product) is equal to GSP minus aggregate material costs (or aggregate value of intermediate goods) and minus depreciation.
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