73 1 It is unfortunate that more recent statistics is not always available, but it serves to illustrate the general trends. Requests for copies should be addressed to: EPJ Kleynhans, School of Economics, Risk Management and internationalTrade, PU for CHE, Private Bag X6001, Potchefstroom, 2520. A MICROECONOMIC ANALYSIS OF PRODUCTIVITY IN THE MANUFACTURING INDUSTRY OF NORTH WEST EPJ KLEYNHANS School of Economics, Risk Management and InternationalTrade, Potchefstroom University for Christian Higher Education ABSTRACT This article studies the productivity in the manufacturing industry of the NorthWest Province. Estimates of the Cobb-Douglas production function for the province’s manufacturing industry are utilised and then applied to the industry’s cost structure to determine whether the factors of production are optimally allocated. It was found that the levels of labour productivity are continuously declining. Higher gains in output could have been achieved if expenditure on production factors were optimally allocated.What the optimal allocations should have been are then determined in monetary terms. Finally the paper accepts that the manufacturing industry is estimating market demand fairly accurately without stockpiling of supplies.The paper then determines what the level of optimisation of the capital and labour input base in the manufacturing industry should have been andwhat the extent of savings could be if production factors are optimally allocated in the NorthWest Province’s manufacturing industry. OPSOMMING Die produktiwiteit van die vervaardigingsnywerheid in die Noordwes Provinsie word in hierdie artikel bestu- deer.’n Cobb-Douglas produksiefunksie word vir die vervaardingsnywerheid van die provinsie geskat. Die resul- tate word dan op die nywerheid se kostestrukture toegepas om te bepaal of die produksiefaktore optimaal geallokeer is. Daar is gevind dat daar ’n kontinue afname in arbeidsproduktiwiteit bestaan. Hoe« r winste in uitset is moontlik indien besteding aan produksiefaktore optimaal toegewys word.Wat die optimale allokasie moes wees word dan bepaal. Laastens word aanvaar dat die vervaardigingsnywerheid markvraag redelik akkuraat voorspel sonder ophoping van voorrade. Daar word dan bepaal wat die vlak van optimalisasie van die kapitaal en arbeidsbasis in dievervaar- digingsnywerheid behoort te wees en hoeveel die besparings kan wees indien produksiefaktore optimaal geallo- keer word in die vervaardigingsnywerheid van Noordwes Provinsie. The optimal level of the labour and capital input base in the manufacturing industry of the NorthWest Province is investi- gated in this study. It determines whether the industry was functioning at the optimal level, how much the deviation is costing the industry and how much could be gained when the input combination is recti¢ed. Van Zyl & Kleynhans suggested a unique way of determining productivity through the evaluation of the input combination of the factors of production in the issue of theJournal of Indus- trial Psychology of May 1995.This paper aims to investigate that technique by applying it to the manufacturing industry of the NorthWest Province.The excellence of this method lies in the fact that it expresses productivity or the loss thereof and the possible gains of higher productivity in monetary terms. As the ¢ndings are expressed in rand and cent planners can use them directly in their development strategies. With the elimination of protective tari¡s and the globalisation of the South African economy, optimal levels have to be striven for to survive increasing international competition. Future competitiveness is critically dependent on a higher level of cost e⁄ciency and especially on a more productive labour and capital input. Manufacturing in the province is important as a provider of employment and foreign revenue and it contributes towards the balance of payments and technological advancement. Manufacturing demands locally provided raw and interme- diate materials and helps to alleviate of poverty in the region. It is therefore important to be able to measure and quantify the extent of the perceived lackof productivity.The Cobb-Douglas e⁄ciency criterion provides a straightforward instrument for this purpose.The ¢ndings should help industry, labour unions and other interest groups to comprehend the full implications of the low levels of productivity in the industry. This article will commence with an overview of the economy of the NorthWest Province and its manufacturing industry in particular.Then the theoretical concept of the e⁄ciency crite- rion will be explained. Next a production function for manu- facturing in the province will be estimated, which will provide the elasticities and other variables to estimate the op- timal input ratios and e⁄ciency criteria, based on historical achievements. Thereafter the optimal utilisation of the total cost outlay will be determined and lastly the optimal factor allocation warranted by the market demand will be deter- mined. In each case the optimal input combination of the fac- tors of production will be determined, the losses that occurred with the unproductive input combinations and possible gains in monetary terms.The paper concludes by evaluating the me- rits of the method applied, and suggestions will be formulated that could enhance manufacturing in the province. THE ECONOMY OF THE NORTH WEST PROVINCE The NorthWest Province embraces 9.7 per cent of SouthAfri- ca’s soil and houses 8.6 per cent of the population.The popula- tion grows at a rate of 2.9 per cent and the region’s GGP grows annually at only 1.2 per cent (1980-1991), which implies that the per capita income is declining (Erasmus,1998:81-82)1. The province provides 5.7 per cent of South Africa’s GDP (1996). Manufacturing is contributing 10.35 per cent and it is growing at an annual rate of 4.01per cent, which is the second best of all the provinces (Erasmus,1998:81-82). SAJournal of Industrial Psychology, 2002, 28(1),73-77 SATydskrif vir Bedryfsielkunde, 2002, 28(1),73-77 2 Being competitive indicates an ability to design, produce and market goods and services that are more appealing, of better quality and/or less expensive than those of competing suppliers (ITRISA, 2001:9). The unemployment rate is 36.6 per cent (1994), which is four per cent above the national average (Schneider, 1998:85). In 1991 only 48.9 per cent of the extended labour force was formally employed.The low employment levels contribute to the high level of poverty in NorthWest (DBSA,1995:79). The NorthWest Province experienced employment growth of 0.55 per cent annually, between 1980 and 1991. The best em- ployment growth rates were in ¢nance, insurance & real estate, which grew by 4.42 per cent and manufacturing, where em- ployment was growing at 2.66 per cent. These employment growth rates are still much less than their increase in produc- tion. This implies that jobless growth occurred in the North West. The only sectors in North West, which experienced negative employment growth were agriculture, mining & quarrying (DBSA,1995:117). The underdeveloped state of the NorthWest’s manufacturing is not only evident in its relatively low contribution of twelve per cent to provincial GGP relative to 32 per cent in Gauteng (1998), but in the fact that the whole manufacturing sector is dominated by only three industrial sectors. Fabricated metals (51%), non-metallic minerals (21%) and food and beverage products (18%) are responsible for 90 per cent of theprovince’s manufacturing output. Manufacturing is spatiallyconcentrated with more than 80 per cent of the ¢rms located in the Klerksdorp-Potchefstroom and Rustenburg-Brits districts, in close proximity to Gauteng and the Platinum SDI. The three dominating industries in North West are all low technology medium-wage and resource-intensive products. The types of industry whichwould bene¢t from SouthAfrica’s trade liberalisation and the GEAR strategy, like textiles and electronics, are absent from the province (Kleynhans, Naude¤ & Suleman,1998:46). Similar trends emerge when looking at the value added and capital/labour ratios. In NorthWest, only 60 per cent of manu- facturing ¢rms can be classi¢ed as high value added industries. In Gauteng it is 76 per cent. This suggests that technology is not as advanced in North West, and more importantly from an investment point of view, that pro¢ts are not as high as in Gauteng or other provinces (IDC,1998a:75). North West has a low degree of competitiveness2. This does not bode well for attempts to encourage investment - especial- ly FDI. Competitiveness is one of the fundamental determi- nants of investment and of decision by industrialists regarding location (Kleynhans et al.1998:47). North West has the lowest R & D expenditure per person annually (R55 000 in real terms) compared to all other provin- ces (IDC,1998a:75). In terms of R & D to GGP, it ranks ¢ve out of nine. However, the province boasts two universities (at Potchefstroom and Ma¢keng) with signi¢cant R&D ex- pertise and potential. North West Province in particular has a low degree of inter- nationalisation, and currently exports only 8.4 per cent of the manufacturing output. The province also does not have the same exposure to international tourism as most other provin- ces do. The province does, however, have much merit in its favour.The advantages to investors in the NorthWest Province are the accessibility of water, electricity and labour.Water elec- tricity, rent, labour, telephone, transport and airfreight is rela- tively less-expensive than is the case in the rest of the country. The province has a supply of supplier networks, support ser- vices, fresh produce, skilled and unskilled labour, infrastruc- ture, internet & cell phones, roads and aviation. The rail network comprises critical linkages in the national and regional networks. These are the North-South line (Harare- Johannesburg-CapeTown), the East-West line (Maputo-Rus- tenburg-Gaborone-Windhoek-Walvis Bay) and the Central corridor (Botswana-Zimbabwe-Zambia). The airports at Pilansberg and Ma¢keng are an important hub in the regional air network, especially as far as tourism is con- cerned. Ma¢keng International Airport has amongst the highest ratings and designing standards in Southern Africa. The meat processing industry has backward and forward link- age potential in such areas as feed production, animal science and breeding, feedlot development, and animal by-products for the fertiliser industry.The NorthWest Province has a com- parative advantage in this sector due to the extensive livestock production across the province, particularly in the Vryburg region, which has some of the most favourable conditions for cattle farming in the world, especially in terms of the absence of disease (Kleynhans et al.1998:48). Other signi¢cant industries are grain milling, edible oils and soaps (where the province can provide the potential investor ample access to raw materials), chemical products and the basic metal industry. An investigation by the Industrial Develop- ment Corporation in 1997 has found that North West has a comparative manufacturing advantage in the basic metal, food processing and chemicals industries; it was rated the top prov- ince in each of these industries (See Naude¤ ,1997:26 & Service group,1997:25). Given positive expected prospects for platinum, agro-indus- tries and tourism in years to come, North West is set to ex- perience a phase of growth and development. The province has already succeeded in turning the negative economic growth rates of the 1980s into high positive growth rates dur- ing the 1990s. Economic growth is expected to reach between ¢ve and six per cent per annum in future (IDC,1998b:15). Current real GGP per capita averages around R4 385 per an- num but is still characterised by high inequalities, especially between rural and urban areas (Erasmus,1998:81-82). Human development in the NorthWest Province shows severe spatial disparities. The infant mortality rate per 1 000 of the popula- tion is 43.3, which is nearly the same as the national average of 41.8 per cent (Schneider,1998:85), but for some disadvantaged sections of the population, the infant mortality rates are up to seven times higher (DBSA,1995:79). Life expectancy in North West is 64.1 years, which is about one year longer than the national average. The province has only 4.5 hospital beds per 1000 of the population,0.7 less than the South African average; and the dependency rate in the province is about average at 1.6 (Naude¤ ,1998a:85). The province has a Human Development Index (HDI) of only 0.543 (1993) compared to the national average of 0.64 (WEFA, 1996:41-45). This HDI is an improvement since 1980 when it was only 0.482 (Naude¤ ,1998b:66).The Gini coe⁄cient is about average at 0.6 in the NorthWest Province (Whiteford,1995:21), but it still indicates inequality in the distribution of income and a huge challenge to economists and the authorities in the province. Among the population in the province 41.3 per cent live below the absolute poverty line and the poverty situation is even more acute in the rural areas (Naude¤ ,1998b:61 & DBSA, 1995a:79). The structure and context in which manufacturing operates in the NorthWest Province’s economy was sketched above. In the following section the theoretical concept of the e⁄ciency cri- terion will be explained to demonstrate how this study was done. THE EFFICIENCYCRITERION The theoretically purist and most widely used production function is the Cobb-Douglas function (Van Zyl1995:6) which PRODUCTIVITY IN THE MANUFACTURING INDUSTRY74 * Appreciation is expressed to Prof. Dr. JHP van Heerden for his assistance in estimating the production function; and assistant PJ Fourie for his preliminary investigation of the theme. states the relationship of labour (L) and capital (K) to output (Q) as: Q=aK�L�. The level of technology is indicated by ‘‘a’’. Parameter � is the output elasticityof capital and � the out- put elasticity of labour. Parameter � denotes the percentage change in output as a result of a percentage change in labour input, keeping capital constant (Cobb & Douglas, 1928:139- 165). The Cobb-Douglas production function is estimated by converting the function Q ¼ aK�L� to Q = log a þ � log Kþ � log L. By means of linear regression analysis para- meters a, � and � are determined.The marginal products of labour and capital are respectively MPL ¼ �ðQ=LÞ and MPK ¼ �ðQ=KÞ. The optimal cost e⁄cient utilisation of production factors is obtained at the point where the last Rand is spent all factors yields equal marginal products: ; ðMPL=wÞ ¼ ðMPK=rÞ where w is the unit wage cost and r the unit cost of capital. The estimated production function can now be used to determine whether the input combination of an industry is optimal or sub-optimal (Van Zyl & Kleyn- hans,1995:6). WhenMPL=MPK < w=r it is an indicationofover-utilisationof labour, indicating a decline in labour productivity. On the other hand, if MPL=MPK > w=r, capital is over-utilised, indicating a decline in the productivity of the capital goods used and an over- utilisation of labour, ceteris paribus. The marginal rate of technical substitution of labour for capital is: MRTS ¼ MPL=MPK ¼ ð�=�Þ: ðK=LÞ.The optimum input mix of labour and capital is then at the point where w/r ¼ ð�=�Þ: ðK=LÞ or ð�=�Þ: ðK=LÞ �ðw=rÞ ¼ 0. Multiplying by � yields the input e⁄ciency crite- rion � ¼ �ðK=LÞ � �ðw=rÞ ¼ 0: If �ðK=LÞ � �ðw=rÞ < 0 (thus� < 0Þ the industry is experiencingadecline in labour pro- ductivitysince� < 0 impliesthatðMPL=MPKÞ < ðw=rÞ (Mau- rice and Smithson,1985:126-130). The prices of the factors of production can be calculated in va- rious ways.The input price of labour (w) is obtained by divi- ding total salaries and wages by the number of employees.To make the price of wages comparable to the price of capital, the average wages (in R’000) per annum are de£ated by the pro- duction price index. The input price of capital (r) is generally expressed as r ¼ QKði þ �Þ where QK is the unit acquisition cost of the capital stock.The rate of depreciation (�) is calcula- ted as the percentage of total capital depreciation and the real interest rates were obtained by de£ating the long run Escom rate by the PPI. Data for the years 1970 to 1995 were obtained from WEFA, StatsSA and the Quarterly Bulletins of the South African Re- serve Bank. The production function for the manufacturing industry of North West was then estimated as Q ¼ 10:541 K0;548L0;499, with a R2 of 98 (Fourie, 2000:32)*. The output elasticity of labour (�) implies that a ten per cent increase in labour productivity would result in a 4.99 per cent increase in output, ceteris paribus. This indicates that the industry is not very labour intensive.The industry is regarded as labour inten- sive when more is spend on labour than on capital goods in the production process, when � is larger than � and/or the point of production on the isoquant graph is to the right of the point of optimisation ^ employing more labour. As inVan Zyl et al. (1994:5-7) the optimal utilisation of the la- bour component is expressed by the e⁄ciency criteria (�) which is calculated utilising the formula � ¼ �ðK=LÞ� � ðw=rÞ as indicated in the theoretical exposition above. The results for the period 1970-1995 are shown inTable 1. It is evident from the table that � < 0 for most of the 26 produc- tion years, irrespective of the business cycle phases and since 1987 labour was over-utilised in every year. This is an indi- cation of a continuous decline in the level of labour produc- tivity. The next step is to quantify the decline in labour pro- ductivity in terms of cost wastage (in Rand). TABLE 1 EFFICIENCY CRITERIUM (�) Year � Input over-utilisation 1970 -185.243 L 1971 -45.154 L 1972 -57.1995 L 1973 12.47374 K 1974 13.1072 K 1975 20.52269 K 1976 30.88467 K 1977 90.51764 K 1978 -574.411 L 1979 18.11745 K 1980 29.26706 K 1981 322.1764 K 1982 64.90608 K 1983 -52.2772 L 1984 -24.7052 L 1985 -151.745 L 1986 68.55199 K 1987 -197.723 L 1988 -94.1441 L 1989 -720.424 L 1990 -117.068 L 1991 -102.598 L 1992 -54.3686 L 1993 -1300.21 L 1994 -94.753 L 1995 -185.528 L THE OPTIMUM UTILISATION OF THE TOTAL COST OUTLAY The optimal input ratio of labour and capital (z) must be such that K=L ¼ ð�wÞ=ð�rÞ. The optimum allocation of the labour input can be calculated from the optimal input ratio. Thus Lo ¼ ð�rKÞ=ð�wÞ. The optimum allocation of the la- bour input can also be derived from the isocost line for a speci¢c cost outlay C ¼ rK + wL and L ¼ (C - rK)/w. Levels of production where � ¼ 0 are rarely found in practice. Should the calculations show no optimal input allocation, it must be determined whether the calculated � is signi¢cantly di¡erent from 0.This is done by means of a t-test.The calcula- ted t-statistic is t ¼ �=S�. S� is the estimated �’s own stan- dard error and the estimated variance of � can be calculated as: Varð�Þ ¼ ðK=LÞ2Varð�Þ þ ðw=rÞ2Varð�Þ � 2ðK=LÞðw=rÞ Covð�; �Þ. The estimated standard error of � is: S� ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Varð�Þ p .The absolute t-value of � is then calculated. Should it exceed the critical t-value, it can be said that � is signi¢cantly di¡erent from zero (Maurice & Smithson, 1985: 128-130). When evaluating the optimum total cost outlay, it is import- ant to take note of the intensity factor and the factor demand equations, derived from the Cobb-Douglas function. The in- tensity factor is ð�=�Þ; the higher this ratio the more labour intensive the production technique (Koutsoyiannis, 1979:65). When � ¼ 0; �ðK=LÞ � �ðw=rÞ ¼ 0 thus L ¼ Kð�=�Þðr=wÞ. Substituting K and L in the production function the factor de- mand equations are derived in terms of output and relative fac- tor prices Ld ¼ ½Q=Lðr=w:�=�Þ��1=ð�þ�Þ (Heat¢eld,1987:82). The low levels of labour productivity in the industry over the period 1970-1995 had an adverse e¡ect on the output level. From the results (see table 2) it is evident that a better utilisa- tion (input mix) of the cost outlay would have resulted in a higher output level. KLEYNHANS 75 The possible optimal output gain was calculated for every year since 1970. For example,1995: K = R1.484m; L = 57.345; w = 15 608; r = 0,0461; � = -185,578 indicating an over-utilised labour situa- tion with declining productivity. The true K/L ratio employed was K/L = 12.98433, while the optimal ratio should have been: (K/L)0 ratio = z = (�wÞ=ð�r) = 371.825 ^ indicating that the capital to labour input base was sub-optimal. The money spent on the factors of production was: C = rK + wL ;C = R895.13m The optimal input levels of capital and labour should have been: K0 ¼ ð�CÞ=ðr�Þ ¼ R101:82m where � = (� + �) and L0 ¼ ð�rKÞ=ð�wÞ ¼ 27 385 workers. Test: K0/L0 = 371.825 The level of production was calculated as: Q ¼ aK�L� The amount produced in that year was: Qtrue = R3100.272m, but at the point of optimisation Qo = R271.33m could have been produced utilising the same cost outlay. The ine⁄ciency output loss was: Qo - Qtrue = R68.23m, where ‘‘O’’ indicates optimal and ‘‘true’’ the amount that was really occurred in that year. The ine⁄cient labour component is calculated as: Ltrue - Lo = 29 959 excess workers. Table 2 shows the possible output wasted in each year (1987- 1995) and the unproductive labour that was employed at the non-optimal factor allocation and total cost outlay levels. TABLE 2 NON-OPTIMAL UTILISATION OF THE TOTAL COST OUTLAY Year Output loss Unproductive labour (R mil.) (excess workers) 1987 300.3 32223 1988 210.7 34020 1989 658.8 34526 1990 244.9 34997 1991 222.8 34309 1992 146.3 32219 1993 811.9 30919 1994 187.9 30444 1995 268.2 29960 From the table, it is obvious that the calculated output loss as a result of the employment of unproductive labour remained re- latively high over the entire period. OPTIMAL FACTOR ALLOCATION ACCORDING TO MARKET DEMAND Producing a higher output when an alternative optimal input combination is applied at the same cost-outlay would be un- wise. Motor vehicles manufactured in South Africa are, for in- stance, sold within six weeks (Van Zyl & Kleynhans,1995:8) ^ to produce more would be a waste. The assumption in this paper is then also made that manufacturers are already sup- plying what the market currently demands. It is therefore bet- ter to continue manufacturing the same amount of output, but at an optimal input combination of production factors. When an optimal factor allocation at a given labour and capi- tal cost has been determined for a particular cost outlay, it can be used to determine the optimal factor allocation warranted by the market demand. The optimum amount of labour in the industry required to meet market demand can be calculated by the use of the formu- la LD ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi QD=Z�LÞ� p where Z ¼ optimal K=L ¼ ð�wÞ=ð�rÞ: The optimal capital input can be determined by KD =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi QD=ðaLD �Þ� p (Van Zyl & Kleynhans,1995:8-10). Table 3 lists the non-productive labour component per level of market demand and the possible cost gain as a result of better factor utilisation, for eachyear during1978-1995. It can be seen fromTable 3 that the manufacturing industry is burdened by a signi¢cant number of non-productive labourers.These ¢gures are disturbing when compared with the relevant facts. Real wages increased relatively, while the number of non-produc- tive labourers had increased. This is an indication of a con- tinuous decline in labour productivity. TABLE 3 FACTORWASTAGE ACCORDING TO MARKET DEMAND Year Unproductive Possible cost gain labour with less labour employed (R mil. ^ real prices) 1987 61659 146.8146 1988 65093 62.93753 1989 66072 321.6911 1990 66968 199.2662 1991 65651 221.7978 1992 61654 44.95409 1993 59172 6417.455 1994 58254 204.0643 1995 57330 376.2697 SUMMARYAND CONCLUSIONS A) Evaluation of the Method Used The Cobb-Douglas e⁄ciency criteria and in particular its ex- tensions, serve as e¡ective and useful instruments to measure and quantify the extent of a decline in labour productivity in a particular industry. The method is easy and economical to apply. More elaborate methods to obtain more accurate ¢ndings, better production functions and adjusting the ¢gures to include changes in tech- nology do not yield better results (see e.g. Kleynhans,1996:15). The fact that it measures productivity in Rand and Cent ma- kes this method unique. The method gives development managers a useful instrument when planning, as it gives the exact number of unproductive labour units and indicates the value of capital that should optimally be applied and the loss due to unproductivily in speci¢c monetary terms. It also indicates what returns can be gained in Rand and Cent terms. In this regard it is not only an indication of the problem of unproductivity but also suggests part of the solution. The method utilises real values and when real interest rates are negative it is impossible to draw roots when applying it and thus makes this method useless for those years. Alternative in- terest and in£ation rate series might then be employed like the BA rate or CPI, but this will be less accurate. As companies gain tax gains on their levels of depreciation, it is very di⁄cult to determine the true value of depreciation. Companies are also reluctant to release their production ¢gures to others for research purposes. Indexes are, however, more readily available and the same technique could be employed to determine the percentages of unproductive labour and the percentages with which inputs should change and how that will alter produc- tion ¢gures and costs.Within ¢rms this method can, however, be used with ease as well as by investment institutions where ¢rms have to declare their ¢gures to obtain funds. B) Productivity in the NorthWest Province The results of the e⁄ciency criteria measurements do indeed substantiate the view that the continuous decline in labour productivity in the manufacturing industry of NorthWest is one of the more important causes of rising market prices.The key challenge facing all those associated with the industry is the improvement of labour productivity at a time when the overall productivity trend remains under pressure and wages and other costs have been rising at a faster rate than those of the overseas competitors have. The alternative is to employ more capital goods, mechanise, implement robotics and re- trench those unproductive labourers. PRODUCTIVITY IN THE MANUFACTURING INDUSTRY76 The demands of the labour unions have probablycompelled the industry to employ more labour at higher wage levels than would have been the case had management been at liberty to act more rationally. 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