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Sekerka - Kyn - Hejl:  Price Systems Computable from Input-Output Coefficients

 

9. Empirical calculations

 

Tables 1 and 2 present price indices Pi calculated according to eqs. (41) and (42) for various values of  m*,n*, and r*. The calculations were based on an input-output table for the Czechoslovak economy for the year 1966 aggregated to 13 branches. This table was prepared by updating the statistical input-output table for 1962 to production and price conditions valid in 1966. 

 

TABLE 1.

F-two-channel-prices 

Value
 prices
Produ-
ction 
prices
F-
income 
prices

r*

0.00 0.05 0.10 0.15 0.20 0.228 0.25 0.30 0.35 0.40 0.42

m*

2.711 2.277 1.878 1.511 1.175 1.000 0.868 0.588 0.334 0.105 0.021
1  Electric. 

144.78

161.04  175.27  187.54  197.95 202.97 206.55 213.40 218.54  221.99 222.91
2 Coal and oil  176.74 177.45 177.30 176.33 174.59 173.29 172.09 168.88 164.97  160.38 158.36
3 Metallurgy  152.12 156.47 160.13 163.11  165.43 166.43 167.08 168.07 168.39  168.03

167.70

4 Chemicals 167.77 169.45 170.73 171.60  172.06 172.12 172.11 171.74 170.93  169.66 169.03
5 Engineering  176.18 172.02 167.92 163.87  159.85 157.61 155.84 151.80 147.72  143.56 141.86
6 Cons. goods 176.05 169.23 162.65 156.28  150.10

145.73

144.11 138.28 132.60  127.06

124.88

7 Building mat. 186.60 181.96 177.20 172.31  167.27 164.39 162.08 156.72 151.17  145.41

143.05

8 Food industr. 122.93 128.89 134.73 140.48  146.14 149.28 151.74 157.29 162.79  168.27 170.45
9 Other indust. 109.09 140.45 168.57 193.60  215.68 226.79 234.95 251.52 265.47  276.89 280.77
10 Construct.  185.82 171.76 158.38 145.64  133.50 126.96 121.92 110.87 100.32  90.25

86.36

11 Agr.,forest.  98.63 107.68 116.37 124.72 132.76 137.13 140.52 148.02 155.28  162.33 165.09
12 Services  170.95 159.70 148.91 138.55 128.57 123.17 118.97 109.71 100.78  92.16 88.80
13 Foreign tr. 162.96 160.07 157.17 154.23  151.24 149.55 146.20 145.08 141.87  138.57 137.21

 

Table 1 contains F-two-channel prices, calculated as follows. In eq. (41) we set n* = 0, and varied r* from 0 to 0.05, 0.10, etc. We calculated m* from eq. (42). The price vectors in table 1 include three special cases: value prices (r* = 0 and m* = 2.71); production prices (m* = 1 and r* = 0.228); and F-income prices (to be more exact, ‘nearly F-income prices’ with parameters r* = 0.42 and m* = 0.021).
 

At first glance it may seem very strange to permit the values of m* to fall below unity. However, this case has a reasonable economic interpretation. Multiplying matrix C by m* < 1 lowers real consumption of workers proportionally in all branches. Thus, the dependence of  r* on m* can be interpreted as dependence of the rate of profit on the level of real wages. A similar approach is taken in SRAFFA (1963). Another possible interpretation is to assume that part of personal consumption is subsidized from the state budget; (1 - m*) is then something like a negative turnover tax rate.
 

The changes in price relations in table 1 show that the growth of the value of r* from 0 to 42 per cent is associated with a rise in prices in some branches and a drop in others. The direction of price change depends on the complex capital-output and complex labor-output ratios in a given branch.
 

 

Table 2 contains N-two-channel prices, calculated from (41), with  r* = 0 and various values of n*. The value of m* was determined by eq. (42). Among the price vectors in table 2 there are two special cases: value prices (n* = 0; m* = 2.71) and cost prices (n* = m* - 1 = 0.02862). The lower limit of the range of n* is not covered, and hence N-income prices were not calculated.

On the basis of the calculated F-two-channel prices, we derive a diagram of the function m* = f(r*), where n* = 0. This diagram is shown as fig. 1. Fig. 2 is a diagram of the function m* = g(n*), where r* = 0, derived for an N-two-channel price system. Figs. 1 and 2 clearly show the limits that must be respected in the choice of parameters n*, m* and r*. These limits depend on the sequence in which the parameters are chosen. First, we choose r* arbitrarily from the interval [0; 1/lb] and designate the chosen value as r*Given r*, the value of f(r*) can be found, where f is the function represented in fig. 1. Parameter m* can be chosen arbitrarily within the limits [0; f(r*)]. The value of n* is then uniquely determined and n* ³ 0. Alternatively, we can choose parameters in a different sequence. For instance, we can choose m* arbitrarily in the interval [0;1/la] and n* in the interval   [0;g-1(m*)]  where g is the function represented in fig. 2. The value of r* is then uniquely defined.

 



 

Fig. 1.

 

Fig. 2.

 

 

 

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