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Cost and price indices
Emgkeering
Costs and Boducfiotr
kkorronrics
5 (1980)
3- 6
Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
COST AND PRICE INDICES
Index numbers (or indices) provide a convenient method of rzpfesenting cost and price levels at different times. If the prices of a product at times t, and t2 are P, and P7 respectively, then the index number is given by: I,=
x I,
+ 1
where I, is the index number at time I,. Any time may be selected as the starting point, or base, for a series of numbers and the index for that time, f,,, is taken as 100. If the price at the base time is P,, then the indices WrJuld be: x I,=
$
100
and
x 100
ities like lubber when annual averages are used. When a composite index for a group of products is considered, the complications of “weighting” arise. As a simple example consider an index for costs of materials for reinforced concrete structures where the amounts of steel reinforcement are 1% and 5% respectively of the cross-sectional area of concrete. The following comparison is based on U.K. costs in 1974 and 1978 for concrete of & 9.10 and g 23.70 per cubic metre and for steel reinforcing rod of & 132.50 and & 182.30 per tonne respectively: IL’74 Cost< Weighting
1978 Custs
Concrete (m5) 1% Reinforcement (78.8 Kg.)
d 9.10 k IO.44
0.466 0.534
f 23.70 6: 14.37
Totals
6 19.54
1.ooo
& 38.07
Index
100
Concrete (m3) 5% Reinforcement (394 Kg.) Totals
E 9.10 & 52.21
0.148 0.852
E 23.70 f. 71.83
E 61.31
1.000
E 95.53
Index
100
195
0
As long as a single product is being considered and it can be specified accurately and has a single price at any given time, there are few problems in compiling a series of indices which reflects accurately any price changes. It may be inconvenient however to maintain such a series on a daily basis and some other time period, such as a month or a year, may be selected instead. Tbis means that average prices in these peripds have to be used and the indices then fail to show day-to-day price variations. An example of these is shown by the price of gold on the London market in January 1980. The market closing prices ranged from $567.50 on 2nd January to $835 per ounce on the 18th. This range of $267.50 is about 40% of theaverage v&le of $672.60 for the month. Similar variatiol!s occur with other metals such as copper and tin and with commod0167-188x/80/0000-0000/$02.25
156
In passing it is worth looking at an altrrnative method for calculating the 1978 overall indices, The individual indices are 260 for COW Crete and 138 for steel, with 1974 = 100. Multiplying these individual indices by their respective weightings, i.e. the proportion which their individual costs bear to the t:>tal costs in I 97 4 gives: For 1% Reinforcement 121+74=195 For 5% Reinforcement 38+ 118 = iS6
(260 x 0.466) + (138 X 0.534) = 1?60 x 0.148) + ( 138 X 0.852) =
This example illustrates two points. The first is the importance of the relative importance of the component costs in the total base cost.
@ 1980 Elsevier Scientific Publishing Company
therefore in these articles to aid the prospective user by giving a series of indices which are reasonably well defined. The base price or cost for each series will be shown so as to facilitate comparisons between various countries and it will be left to the user to adapt and combine them in the manner best suited to his particular purpose. It is hoped they will be applicable to assessments of operating and capital costs. The data given in the Appendix relate to average hourly: earni!lgs in four branches of industry as defined by the ISIC [ 11, industrial chemicals, iron and steel, manufacture of machinery and construction in seven countries. The actual average hourly earnings at the base date, together with the U.S.dollar equivalent at that time, are shown, but it must be remembered that the relationship between curCommodity Price Index Code No. rencies is constantly changing. Yhe figures refer Metals and Metal Products 10 257.6 to national averages and there an: regional varialron and Steel 101 282.9 tions in many countries. Steel Mill Praducts 101: 277.3 Finished Steel Products 10:s 02 It must be stressed that the data do not rep276.4 IO13 0246 Plates, Carbon, A-36 311.8 resent labour costs. Labour costs for any work, 1013 0279 Mechanical Tubing, Stainless, Seamless 170.4 whether it be for the erection of a major inThe Code No. !O cbmposite index is derived dustrial complex or for the manufacture of a from several 3-figure codes, including 10 1, small piece ol’ equipment, are the product of which in turn is derived from several 4-figure the average hourly cost and the number of codes including 1013, and so on. Code 1013.02 hours taken. The average hourly cost is the sum comprises 50 items, 8 of which refer to stainof the average hourly earnings, i.e. paid to the less steel products based on 1967 = 1010(others employee, and the supplementary costs per were added later) with indices ranging from ho+r incurred by the employer on behalf of, or 170.4 as above to 230.4 for Bars, Stainless, to haintain, the employee. These suppleType 303. It will ble obvious that the composite mentary costs can be further sub-divided. First index for 10 13 02 overstates the rises in prices there are the costs which the employer is of stainless steel products and understates’those obliged by law or agreement to meet, such as r”orother steel products. his’contributions to pensions, holiday and vacaFrom the foregoing it will be clear that if tion pay, insurances and the like. These costs, changes in the cost or price of a product are to expressed as a percentage of ave.rage hourly be properly reflected by indices, then the inearnings, are fairly constant within a country dices should apply as far as is practicable/, to but differ conbiderably between countries. Data that product both as regards the constituents for the EEC countries are pubiished in Eurostat contained. therein and their relative weights. [2 1, and are tabulated in Table 1. There are UnfortunaGely while it is sometimes difficult to other supplementary costs which apply particobtain published indices, especially foreign ones, ularly on large capital works such as for the it is even r.nore difficult to discover the bases provisioin of camps and transportation within used in their compilation. It will be the aim sites whic,h can affect the overall cost per hour
&ormally composite indices are kept up-to-date by adjusting them only for changes in the component indices, but weightings can also alter. For a complete plant, for instance, these a’fterations can arise from changes in design, in size, and in construction methods to mention only some of the reasons. The second pojnt illustrated above is that changes in composite indices give no indication of changes in the indices for the individual components. Examples of the variations between individual and composite indices can be seen in pub,tications such as “Producer Prices and Price Indexes” issued by the U.S department of LaPor, Bureau of Labor Statistics. The following extract gives figures for June 1979 with all indtoes based on 1967 = 100.
TABLE 1 Ratio of total hourly labour costs to avtmge hourly k’.x-~ngs for
manual workers (b.wd on data pnblibed in Errrc/*~rz’i 21)
-.
country
Industry
1969
1972
1975
Belgium
Industrial chemicals Iron & steel Mech. engineering Construction
1.57
1.63
1.56 1.68
1.64 1.87
1.74 1.71 1.73 2.01
Denmark
Chemicals Mech. & elect. cngineeting Construction
n.a. n.a. n.8.
n.a. n.a. n.a.
1.22 1.21 n.a.
France
Industrial chemicals Iron & steel Mechanical engineering Construction
1.65
1.64
1.66 1.74
1.66 1.71
1.88 1.98 1.76 1.71
Jndustrial cherr.icals Iron & steel Mechanical engineering Construction
1.58
1.58
1.50 1.46
!.59 1.53
1.91
1.91
2.03 1.83
1.96 1.84
1.58
1.59
1.68 1.65
1.69 1.76
Germany
Itall
Industrial chemicals Iron & steel Mechanical engineering Construction
Nethcrlands Industrial chemicals Iron & steel Mechanical engineering Construction UK.
Chemicals Iron & steel Mechanical enginecring Construction
n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. -~ _ -...---
1.69 1.76 1.67 1.53 2.02 2.10 2.06 1.87 n.a. n.a. n.a. n.a. 1.39
the man-hocll.2 required to perform a gi\b:u task) efficiency of mznJgement, delay,; in dclia/ery uf materials cxtcnt 01’jnechanisation and automation, weather, e:c. and their effects vary with the country, industry and locale considered. It will be noted that the indices, which are based on data published by the I.L.O. [3 j and the various national statistical offices, are oased 011 earnings in October for years up to 1977 rrild in 4rril and October thereafter, except for Demnark where the third and first quarters arc used. Many countries publish monthly figures for wages and/or earnings in broad terms. e.g. for all manufacturing, and confine the more detailed breakdown for individual sectors of industry to one (;i two specific periods each year. However it w;juld be logical in compiling a price index on the lines suggested by Cran [al to use the October earnings indices in conjunction with steel indices even earlier in the year to give a price index as at the following January. If a manufacturer sets the irice of his product at the delivery date, he will have incurred the materials and wages costs at some earlier ddtes, and the time gap will range from weeks to months depending on the product.
1.29
1.29 1.25
REFERENCES
n.a., non-available.
1 International
Standard Industrial Classification -- we
“Uptired Nutiotrs - Statistical PaQWS, Series hf, NO. 4, rev. 2.
to the employer and these will be discussed later. Returning now to the element of time in labour costs, there are many factors affecting the tatal number of hours required. These include productivity (using this as a measure of
(New York 1968). published by Statistical Office of lhc European Communities, Luxembourg. 3 1978 Year Book oj’Lrrbotrr Statistics, published by the International Labour Organization. 4 “‘ran, j., 1976. “Cost indices,” l:‘ugineeritg atrd Process (:‘taaomics, 1 ( I, March); l3--23.
2 Eur,mu,
35112 38213 5
351 371 382 5
351 371 382 5
351 371 382 5
351 37 382 5
35 l/2 371 382 5
Demnark (3rd X 1st X 3rd quarters )
France
German Fed. Rep.
Italy
Netherlands
U.K.
47 50 50 49
51 50 51 51 56 58 58 54
58 56 58 57
51 53 50 52
70
59
42 41 39 43
69 73
5s 52 60 57
62
52 52 54 55
60 65
51 46 53 51
56
47 47 48 48
64 63 63 61
66 63 67 68
61 62 57 58
77
76 75
65 61 67 63
70
60 60 61 60
71 74 73 75
74 71 73 77
66 66 64 63
80 81 81 84
71 69 73 74
69 70 76
73 70 70 68
79 84 83 84
87 81 83 87
83 82 82 78
88 89 90 93
82 79 83 85
82 82 87
81 78 81 80
1969 1970 1971 1972 1573 Oct. Oct. Oct. Oct. Oct.
Pound 1.17 1.16 1.10 1.04
Guilder 10.60 10.73 9.47 9.70
Lire 1486 1542 1325 1255
D.M. 11.02 10.05 9.89 10.00
F.Fr. 12.02 11.71 11.04 10.08
Kr. 26.63 27.92 29.17
B.Fr. 157.25 171.89 133.94 130.07
Local currency
1974-Oct.
2.74 2.71 2.57 2.43
3.93 3.98 3.51 3.60
2.25 2.34 2.01 1.90
4.16 3.80 3.73 3.78
2.54 2.48 2.33 2.13
4.36 4.56 4.77
4.01 4.38 3.42 3.32
Equivalent U s. $
___-
._- -
128 130 126 128
115 109 112 114
122 124 124 125
1.06 105 108 104
114 121 115 115
115 119 114
118 108 114 116
140 147 140 143
123 120 120 123
135 144 149 170
115 113 114 110
129 136 135 137
129 131 129
131 122 125 132
150 158 155 157
134 130 130 135
163
124 120 123 117
145 152 153 154
143 142 144
147 132 137 146
171 175 168 165
138 134 134 139
176
125 123 126 120
154 161 162 160
156
152 137 142 150
___
174 184 177 175
141 137 137 143
185
127 126 129 124
165 172 173 171
163
196 140 145 !SJ
_-
1975 1976 1977 1918 Oct. Oct. Oct. -Apr. Oct.
226 200 209 209
148 144 144 150
146 141 141 148 196 195 194 188
230
128 133 135 134
190 191 198 192
168 151 156 167
Oct.
206
129 134 134 125
177 180 184 180
165
lb2
163 146 152
-- -.
Apr.
1979 L___.---
‘Internal Standard Industrial Classification: 351 Manufacture of industrial r:lemicals; 352 Manufacture of other chemicals; 37 Basic metal industries; 371 Iron & steel basic industries; 382 Manufacture of machinery, except electrical; 383 Manufacture of electrical machinery; 5 Construction.
351 371 382 5
Belgium
IS1@
lndiccs o:‘averagchour!y omiugs of adult manual workers in scloctod industries. Oct. 1974 = 100 [Based on data published by International Labour Office, Geneva.] ---..__ -__p---)-~ -
_--_
-
Costs and Boducfiotr
kkorronrics
5 (1980)
3- 6
Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
COST AND PRICE INDICES
Index numbers (or indices) provide a convenient method of rzpfesenting cost and price levels at different times. If the prices of a product at times t, and t2 are P, and P7 respectively, then the index number is given by: I,=
x I,
+ 1
where I, is the index number at time I,. Any time may be selected as the starting point, or base, for a series of numbers and the index for that time, f,,, is taken as 100. If the price at the base time is P,, then the indices WrJuld be: x I,=
$
100
and
x 100
ities like lubber when annual averages are used. When a composite index for a group of products is considered, the complications of “weighting” arise. As a simple example consider an index for costs of materials for reinforced concrete structures where the amounts of steel reinforcement are 1% and 5% respectively of the cross-sectional area of concrete. The following comparison is based on U.K. costs in 1974 and 1978 for concrete of & 9.10 and g 23.70 per cubic metre and for steel reinforcing rod of & 132.50 and & 182.30 per tonne respectively: IL’74 Cost< Weighting
1978 Custs
Concrete (m5) 1% Reinforcement (78.8 Kg.)
d 9.10 k IO.44
0.466 0.534
f 23.70 6: 14.37
Totals
6 19.54
1.ooo
& 38.07
Index
100
Concrete (m3) 5% Reinforcement (394 Kg.) Totals
E 9.10 & 52.21
0.148 0.852
E 23.70 f. 71.83
E 61.31
1.000
E 95.53
Index
100
195
0
As long as a single product is being considered and it can be specified accurately and has a single price at any given time, there are few problems in compiling a series of indices which reflects accurately any price changes. It may be inconvenient however to maintain such a series on a daily basis and some other time period, such as a month or a year, may be selected instead. Tbis means that average prices in these peripds have to be used and the indices then fail to show day-to-day price variations. An example of these is shown by the price of gold on the London market in January 1980. The market closing prices ranged from $567.50 on 2nd January to $835 per ounce on the 18th. This range of $267.50 is about 40% of theaverage v&le of $672.60 for the month. Similar variatiol!s occur with other metals such as copper and tin and with commod0167-188x/80/0000-0000/$02.25
156
In passing it is worth looking at an altrrnative method for calculating the 1978 overall indices, The individual indices are 260 for COW Crete and 138 for steel, with 1974 = 100. Multiplying these individual indices by their respective weightings, i.e. the proportion which their individual costs bear to the t:>tal costs in I 97 4 gives: For 1% Reinforcement 121+74=195 For 5% Reinforcement 38+ 118 = iS6
(260 x 0.466) + (138 X 0.534) = 1?60 x 0.148) + ( 138 X 0.852) =
This example illustrates two points. The first is the importance of the relative importance of the component costs in the total base cost.
@ 1980 Elsevier Scientific Publishing Company
therefore in these articles to aid the prospective user by giving a series of indices which are reasonably well defined. The base price or cost for each series will be shown so as to facilitate comparisons between various countries and it will be left to the user to adapt and combine them in the manner best suited to his particular purpose. It is hoped they will be applicable to assessments of operating and capital costs. The data given in the Appendix relate to average hourly: earni!lgs in four branches of industry as defined by the ISIC [ 11, industrial chemicals, iron and steel, manufacture of machinery and construction in seven countries. The actual average hourly earnings at the base date, together with the U.S.dollar equivalent at that time, are shown, but it must be remembered that the relationship between curCommodity Price Index Code No. rencies is constantly changing. Yhe figures refer Metals and Metal Products 10 257.6 to national averages and there an: regional varialron and Steel 101 282.9 tions in many countries. Steel Mill Praducts 101: 277.3 Finished Steel Products 10:s 02 It must be stressed that the data do not rep276.4 IO13 0246 Plates, Carbon, A-36 311.8 resent labour costs. Labour costs for any work, 1013 0279 Mechanical Tubing, Stainless, Seamless 170.4 whether it be for the erection of a major inThe Code No. !O cbmposite index is derived dustrial complex or for the manufacture of a from several 3-figure codes, including 10 1, small piece ol’ equipment, are the product of which in turn is derived from several 4-figure the average hourly cost and the number of codes including 1013, and so on. Code 1013.02 hours taken. The average hourly cost is the sum comprises 50 items, 8 of which refer to stainof the average hourly earnings, i.e. paid to the less steel products based on 1967 = 1010(others employee, and the supplementary costs per were added later) with indices ranging from ho+r incurred by the employer on behalf of, or 170.4 as above to 230.4 for Bars, Stainless, to haintain, the employee. These suppleType 303. It will ble obvious that the composite mentary costs can be further sub-divided. First index for 10 13 02 overstates the rises in prices there are the costs which the employer is of stainless steel products and understates’those obliged by law or agreement to meet, such as r”orother steel products. his’contributions to pensions, holiday and vacaFrom the foregoing it will be clear that if tion pay, insurances and the like. These costs, changes in the cost or price of a product are to expressed as a percentage of ave.rage hourly be properly reflected by indices, then the inearnings, are fairly constant within a country dices should apply as far as is practicable/, to but differ conbiderably between countries. Data that product both as regards the constituents for the EEC countries are pubiished in Eurostat contained. therein and their relative weights. [2 1, and are tabulated in Table 1. There are UnfortunaGely while it is sometimes difficult to other supplementary costs which apply particobtain published indices, especially foreign ones, ularly on large capital works such as for the it is even r.nore difficult to discover the bases provisioin of camps and transportation within used in their compilation. It will be the aim sites whic,h can affect the overall cost per hour
&ormally composite indices are kept up-to-date by adjusting them only for changes in the component indices, but weightings can also alter. For a complete plant, for instance, these a’fterations can arise from changes in design, in size, and in construction methods to mention only some of the reasons. The second pojnt illustrated above is that changes in composite indices give no indication of changes in the indices for the individual components. Examples of the variations between individual and composite indices can be seen in pub,tications such as “Producer Prices and Price Indexes” issued by the U.S department of LaPor, Bureau of Labor Statistics. The following extract gives figures for June 1979 with all indtoes based on 1967 = 100.
TABLE 1 Ratio of total hourly labour costs to avtmge hourly k’.x-~ngs for
manual workers (b.wd on data pnblibed in Errrc/*~rz’i 21)
-.
country
Industry
1969
1972
1975
Belgium
Industrial chemicals Iron & steel Mech. engineering Construction
1.57
1.63
1.56 1.68
1.64 1.87
1.74 1.71 1.73 2.01
Denmark
Chemicals Mech. & elect. cngineeting Construction
n.a. n.a. n.8.
n.a. n.a. n.a.
1.22 1.21 n.a.
France
Industrial chemicals Iron & steel Mechanical engineering Construction
1.65
1.64
1.66 1.74
1.66 1.71
1.88 1.98 1.76 1.71
Jndustrial cherr.icals Iron & steel Mechanical engineering Construction
1.58
1.58
1.50 1.46
!.59 1.53
1.91
1.91
2.03 1.83
1.96 1.84
1.58
1.59
1.68 1.65
1.69 1.76
Germany
Itall
Industrial chemicals Iron & steel Mechanical engineering Construction
Nethcrlands Industrial chemicals Iron & steel Mechanical engineering Construction UK.
Chemicals Iron & steel Mechanical enginecring Construction
n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. -~ _ -...---
1.69 1.76 1.67 1.53 2.02 2.10 2.06 1.87 n.a. n.a. n.a. n.a. 1.39
the man-hocll.2 required to perform a gi\b:u task) efficiency of mznJgement, delay,; in dclia/ery uf materials cxtcnt 01’jnechanisation and automation, weather, e:c. and their effects vary with the country, industry and locale considered. It will be noted that the indices, which are based on data published by the I.L.O. [3 j and the various national statistical offices, are oased 011 earnings in October for years up to 1977 rrild in 4rril and October thereafter, except for Demnark where the third and first quarters arc used. Many countries publish monthly figures for wages and/or earnings in broad terms. e.g. for all manufacturing, and confine the more detailed breakdown for individual sectors of industry to one (;i two specific periods each year. However it w;juld be logical in compiling a price index on the lines suggested by Cran [al to use the October earnings indices in conjunction with steel indices even earlier in the year to give a price index as at the following January. If a manufacturer sets the irice of his product at the delivery date, he will have incurred the materials and wages costs at some earlier ddtes, and the time gap will range from weeks to months depending on the product.
1.29
1.29 1.25
REFERENCES
n.a., non-available.
1 International
Standard Industrial Classification -- we
“Uptired Nutiotrs - Statistical PaQWS, Series hf, NO. 4, rev. 2.
to the employer and these will be discussed later. Returning now to the element of time in labour costs, there are many factors affecting the tatal number of hours required. These include productivity (using this as a measure of
(New York 1968). published by Statistical Office of lhc European Communities, Luxembourg. 3 1978 Year Book oj’Lrrbotrr Statistics, published by the International Labour Organization. 4 “‘ran, j., 1976. “Cost indices,” l:‘ugineeritg atrd Process (:‘taaomics, 1 ( I, March); l3--23.
2 Eur,mu,
35112 38213 5
351 371 382 5
351 371 382 5
351 371 382 5
351 37 382 5
35 l/2 371 382 5
Demnark (3rd X 1st X 3rd quarters )
France
German Fed. Rep.
Italy
Netherlands
U.K.
47 50 50 49
51 50 51 51 56 58 58 54
58 56 58 57
51 53 50 52
70
59
42 41 39 43
69 73
5s 52 60 57
62
52 52 54 55
60 65
51 46 53 51
56
47 47 48 48
64 63 63 61
66 63 67 68
61 62 57 58
77
76 75
65 61 67 63
70
60 60 61 60
71 74 73 75
74 71 73 77
66 66 64 63
80 81 81 84
71 69 73 74
69 70 76
73 70 70 68
79 84 83 84
87 81 83 87
83 82 82 78
88 89 90 93
82 79 83 85
82 82 87
81 78 81 80
1969 1970 1971 1972 1573 Oct. Oct. Oct. Oct. Oct.
Pound 1.17 1.16 1.10 1.04
Guilder 10.60 10.73 9.47 9.70
Lire 1486 1542 1325 1255
D.M. 11.02 10.05 9.89 10.00
F.Fr. 12.02 11.71 11.04 10.08
Kr. 26.63 27.92 29.17
B.Fr. 157.25 171.89 133.94 130.07
Local currency
1974-Oct.
2.74 2.71 2.57 2.43
3.93 3.98 3.51 3.60
2.25 2.34 2.01 1.90
4.16 3.80 3.73 3.78
2.54 2.48 2.33 2.13
4.36 4.56 4.77
4.01 4.38 3.42 3.32
Equivalent U s. $
___-
._- -
128 130 126 128
115 109 112 114
122 124 124 125
1.06 105 108 104
114 121 115 115
115 119 114
118 108 114 116
140 147 140 143
123 120 120 123
135 144 149 170
115 113 114 110
129 136 135 137
129 131 129
131 122 125 132
150 158 155 157
134 130 130 135
163
124 120 123 117
145 152 153 154
143 142 144
147 132 137 146
171 175 168 165
138 134 134 139
176
125 123 126 120
154 161 162 160
156
152 137 142 150
___
174 184 177 175
141 137 137 143
185
127 126 129 124
165 172 173 171
163
196 140 145 !SJ
_-
1975 1976 1977 1918 Oct. Oct. Oct. -Apr. Oct.
226 200 209 209
148 144 144 150
146 141 141 148 196 195 194 188
230
128 133 135 134
190 191 198 192
168 151 156 167
Oct.
206
129 134 134 125
177 180 184 180
165
lb2
163 146 152
-- -.
Apr.
1979 L___.---
‘Internal Standard Industrial Classification: 351 Manufacture of industrial r:lemicals; 352 Manufacture of other chemicals; 37 Basic metal industries; 371 Iron & steel basic industries; 382 Manufacture of machinery, except electrical; 383 Manufacture of electrical machinery; 5 Construction.
351 371 382 5
Belgium
IS1@
lndiccs o:‘averagchour!y omiugs of adult manual workers in scloctod industries. Oct. 1974 = 100 [Based on data published by International Labour Office, Geneva.] ---..__ -__p---)-~ -
_--_
-