ALLOCATIVE EFFICIENCY OF CAPITAL INVESTMENT: THE CASE OF THE SUDANESE PUBLIC AND PRIVATE MANUFACTURING SECTORS
Fareed Mohmed Ahmed Hassan^*

1. INTRODUCTION

The structure of the manufacturing output in the Sudan is typical of most developing countries. Light consumer goods dominate other industries. Food, beverages and tobacco production accounts for almost 70 per cent of the manufacturing value added and about 62 per cent of the capital investment. Processing of non-food agricultural materials into goods such as textiles and leather provides about 20 per cent of the manufacturing sector employment, but its contribution to value added is much less. Chemicals and non-metallic minerals industries are more capital intensive and contribute about 17 per cent of value added in manufacturing (Industrial Survey, 1981/82).

Manufacturing in the Sudan today is preponderantly in the private sector. Based on the 1981/82 survey carried out by UNIDO, the private sector accounted for 78 per cent of gross output, 69 per cent of gross value added, 53 per cent of gross investment, 68 per cent of wages and salaries and 42 per cent of employment in the manufacturing sector. Yet some 50 large establishments (employing 25 workers or more), most of them concerned with the processing of agricultural materials, are government owned. They accounted for 9 per cent of gross output, 10 per cent of gross value added, 14 per cent of gross investment, 25 per cent of wages and salaries, and 26 per cent of employment in the manufacturing sector.

The contribution of the manufacturing sector to the economy at large accounted for only 6.7 per cent of GDP (Gross Domestic Product), 5 per cent of total labour force,and less than 1 per cent of total exports in 1988/89 (Economic Survey, 1988/89). The limited role of manufacturing has resulted,among other things, from malallocation of resources among the manufacturing activities.

The main objective of this paper is to examine the extent of resource malallocation in both public and private manufacturing sectors. Capital investment distribution, in particular, is analysed in order to get some quantitative measure of existing malallocation and the corresponding welfare effect. The dead-weight loss, defined as the loss in efficiency, measured by the value of output sacrificed due to monopoly practices in both sectors, is also measured. As this is not the kind of analysis one can do with great precision, the best we can hope for is to arrive at the general orders of magnitude that are involved.

The paper is organized as follows. Section 2 offers a theoretical model of optimal resource allocation. Section 3 is concerned with the empirical analysis -- data employed, methodology, and empirical results; it also attempts to provide a consideration of the difficulties involved in operationalizing the theoretical model. An overall evaluation of the empirical results -- in terms of assumptions, methodology, and data employed -- is given in Section 4. Section 5 provides a summary and conclusion.

2. THEORETICAL MODEL OF OPTIMAL RESOURCE ALLOCATION

Let us assume a situation of optimal resource allocation in which all manufacturing firms are operating on their long-run cost curves. These cost curves are so defined as to yield each firm an equal return on its invested capital, and markets are cleared. We never see this ideal situation in the real world, but if long-run costs are in fact close to constant and markets are cleared, we can pick out the places where the resources are misallocated by looking at the rate of return on capital. Those firms which are returning higher than average rates have too few resources; and those yielding lower than average rates have too many resources. How much reallocation of resources it would take to eliminate the observed divergences in the rate of return depends on demand elasticities for the products in question.

Pending a discussion of assumptions and procedure a little later, the assumption of unit elasticity indicates that the amount of excess profits measures the amount of resources that must be called into a firm in order to expand its supply to wipe out the excess (monopoly) profit. That is, monopoly profit is defined as existing in a firm when the average rate of return on invested capital is higher than that earned by all firms. If the elasticity of demand is different from one, say e, then the desired resource transfer is given as follows:

Desired resource transfer = (r-m) * k * e (2.1)

where r= rate of return on capital for the firm in question

m= average (market) rate of return

e= elasticity of demand, and

k= capital investment

Let us suppose that somehow we effected these desired resource transfers. The question then arises: by how much would people be better off? This question was answered by Harberger (1954) for an analogous problem. His formula for calculating the welfare improvement resulting from such reallocation is based on the well-known welfare triangle method (see Hotelling (1938), Spencer (1986), Tullock (1967), among others). In terms of our own notations, the formula is given as:

Welfare gain= 1/2 (r-m)*desired resources transfer (2.2)

The following hypothetical example illustrates the idea discussed above. Suppose the firm in question is earning 15 per cent on a capital of 10 million Sudanese pounds(L.S), whereas the average return on capital is only 10 per cent. Since cost is defined to include normal profit, we therefore build 10 per cent into the cost. This leaves the firm with 1/2 million in excess profit. How much reallocation of resources would it take to expand the firm's supply enough to wipe out excess profit? If the elasticity of demand for the firm's product is unitary, it will take a shift of 1/2 million in resources (see equation 2.1). Applying equation (2.2), the welfare gain resulting from such reallocation is L.S. 12500.

In the following section, the above theoretical model is applied to both private and public manufacturing activities in order to measure the extent of capital malallocation.

3. EMPIRICAL RESULTS

The Industrial Survey of 1981/82,which is the most recent comprehensive survey undertaken in the Sudan, provides data on capital investment, rate of return, gross output, etc. for 47 industries classified according to the International Standard Industrial Classification Codes (ISIC). If we classify these industries by type of ownership, we only get 13 public manufacturing industries and their corresponding private counterparts (see column 2 of Tables 3.1 and 3.2).

The capital investment in thousands of Sudanese pounds and the rate of return as reported in the 1981/82 survey are given against each industry in columns 3 and 4, respectively, of Tables 3.1 and 3.2. The differences among these rates of return, as between industries, give a broad indication of the extent of capital malallocation in the Sudanese private and public manufacturing sectors in the early 1980s. Column 6 of Tables 3.1 and 3.2 shows the amount by which the return (profits) in each industry diverged from what that industry would have obtained if it had earned the average rate of return for all manufacturing industries. Now in order to get an idea of how big a shift of resources it would take to equalize the rates of return in all industries, we have to know something about the elasticities of demand confronting the industries in question. The question then arises: how high are these elasticities? By looking at the list of industries in question -- which contains consumer goods, intermediate goods and few luxuries -- one gets the feeling that the elasticities in question are probably quite low. This presumption is further strengthened by the fact that what we envisage is not the substitution of one industry's product against all other products, but rather the substitution of one aggregate of products (those returning high rates of profit) for another aggregate (those returning low rates of profit). Taking these considerations into account, an elasticity of one is about as high as one can reasonably allow for, though a somewhat higher elasticity would not seriously affect the general tenor of our results.

Once the assumption of unit elasticity is made, we find that to obtain equilibrium we would have to transfer about 33 million Sudanese pounds in resources from low to high profit public manufacturing industries. Hence the malallocation of resources which existed in 13 public industries in 1981/82 could have been eliminated by a net transfer of roughly 7 per cent of resources in the manufacturing sector, or 1/2 per cent of the total resources of the economy (as measured by GDP). For the private sector, the desired resource transfer amounts to 78 million Sudanese pounds constituting 17 per cent of the manufacturing sector resources, or 1 per cent of the resources of the economy at large.

The amount by which consumer welfare would increase if the industry in question either acquired or divested itself of the appropriate amount of resources is given in column 7 of Table 3.1 and Table 3.2. The total improvement in consumer welfare which might come from the 13 public industries amounts to about 19.2 million Sudanese pounds -- about 0.335 per cent of GDP or 0.80 Sudanese pounds per capita. In the private sector, the welfare gain amounts to 22.3 million constituting about 0.389 per cent of GDP and about 0.93 pounds per capita (see Table 3.3).

Pending a discussion of possible biases in the 1981/82 Industrial Survey results a little later (see Section 4), we tentatively conclude that the amount of resource misallocation in the private sector is greater than that of the public sector. The share of the private sector in total welfare loss is 53.8 per cent, whereas that of the public sector is 46.2 percent. It should be noted that the difference between the two sectors, in terms of allocative efficiency of resources as measured by welfare loss, is not great. The difference can partially be attributed to the relatively low rates of return in the public sector, and as Van der Wel (1984) pointed out:

Prices used for transactions within the public sector are often set in such a way that the profit or loss figures of individual public corporations cannot be used as an indicator of their performance. (page 1)

Table 3.1 Calculations of Welfare Loss Estimates in the Sample of 13 Public

Manufacturing Industries in the Sudan (1981/1982)

ISIC CODE	INDUSTRY	CAPITAL INVESTED (In '000 L.S)	RATE OF RETURN ON CAPITAL	DIFFERENCE BETWEEN THE RATE OF RETURN AND THE AVERAGE (MARKET)RATE OF RETURN	AMOUNT BY WHICH RETURN DIVERGES FROM THE AVERAGE	WELFARE LOSS
3113	Canning and Preserving of Fruits and Vegetables	811	-0.492	-0.981	-795,591	390,237
3119	Coca, Chocolate & Sugar Confectionery	278	-1.068	-1.557	-432,846	336,971
3134	Soft Drinks and Carbonate Water	261	-0.115	-0.604	-157,644	47,608
3211	Spinning, Weaving and Finishing Textile	48,511	-0.083	-0.572	-27,542,372	7,877,118
3213	Knitting mills	112	0.679	0.190	21,280	2,023
3231	Tanneries and Leather Finishing	5,279	0.017	-0.472	-2,491,688	588,038
3420	Printing, Publishing and Allied Industries	2,527	1.023	0.741	1,872,507	693,764
3560	Plastic Products not elsewhere classified	5	34.002	33.711	168,555	2,841,079
3692	Cement, Lime and Plaster	1,247	2.103	1.614	2,012,658	1,624,215
3710	Iron and Steel Basic Industries	195	-1.308	-1.797	-350,415	314,849
3822	Agricultural Machinery and Equipment	27	0.259	-0.023	621	7.14
3843	Motor Vehicles Activities	312	5.381	4.892	1,526,304	3,733,340
3901	Jewellery and related articles	725	-0.917	-1.406	-1,019,350	716,603
	Total (L.S)	60,290				19,166,559

Sources: Columns (3), (4) are from 1981/82 Industrial Survey

Columns (5), (6), (7) are calculations by the author

Table 3.2 Calculations of Welfare Loss Estimates in the Sample of 13 Private

Manufacturing Industries in the Sudan (1981/82)

ISIC CODE	INDUSTRY	CAPITAL INVESTED (In '000 L.S)	RATE OF RETURN ON CAPITAL	DIFFERENCE BETWEEN THE RATE OF RETURN AND THE AVERAGE(MARKET)RATE OF RETURN	AMOUNT BY WHICH RETURN DIVERGES FROM THE AVERAGE	WELFARE LOSS
3113	Canning and Preserving of Fruits and Vegetable	2652	0.218	-0.271	-718,692	97,383
3119	Coca, Chocolate & Sugar Confectionery	4005	0.481	-0.008	-32,040	128
3134	Soft Drinks and Carbonate Water	8354	0.136	-0.353	-2,948,962	520,492
3211	Spinning, Weaving and Finishing Textile	121312	-0.102	-0.591	-71,695,392	21,185,988
3213	Knitting mills	770	0.109	-0.380	29,260	556
3231	Tanneries and Leather Finishing	167	0.016	-0.473	-78,991	18,682
3420	Printing, Publishing and Allied Industries	3461	0.026	-0.229	-792,569	90,749
3560	Plastic Products not elsewhere classified	3588	0.289	-0.200	-717,600	71,760
3692	Cement, Lime and Plaster	5420	0.680	0.191	1,035,220	98,864
3710	Iron and Steel Basic Industries	421	0.420	-0.069	-29,049	1,002
3822	Agricultural Machinery and Equipment	279	-0.161	-0.650	-181,350	58,939
3843	Motor Vehicles Activities	241	0.066	-0.423	-101,943	21,561
3901	Jewellery and related articles	1440	0.133	-0.356	-512,640	91,250
	Total (L.S)	152,110				22,312,392

Source: Columns (3), (4) are from 1981/82 Industrial Survey

Columns (5), (6), (7) are calculations by the author

Table 3.3 Comparative Efficiency of the Public and Private Sectors in the Sudan

SECTOR	CAPITAL INVESTED IN MILLIONS OF L.S.		AMOUNT OF MISALLOCATED RESOURCES OF THE ECONOMY IN MILLIONS OF L.S.		THE WELFARE LOSS PER CAPITA IN PIASTERS		THE WELFARE LOSS AS PERCENTAGE OF CAPITAL INVESTED		% CONTRIBUTION OF SECTOR IN TOTAL WELFARE LOSS
	VALUE	%	VALUE	%	VALUE	%	VALUE	%
Public	59.9	28.3	19.2	0.335	80	46.2	59.9	32	46.2
Private	152	71.7	22.3	0.389	93	53.8	152	15	53.8
Total	211.9	100	41.5	0.724	173	100	211.9	47	100

Sources

Figure in column (3) are calculated as follows:

The welfare loss is divided by the GDP 1984 (5730 millions of L.S.) and the result is multiplied by 100

Figures in column (4) are calculated as follows:

The per capita loss is given by dividing the loss in the sector by the total population in the Sudan which was 24 million persons in 1983/84.

4. EVALUATION OF EMPIRICAL RESULTS

Our empirical results are evaluated in terms of assumptions, methodology, and data used. Let us consider the basic assumption of long-run constant costs. First, the investigation period had to be reasonably close to a long-run equilibrium period; that is, no violent shifts in demand or economic structure were to be in process. Unfortunately, our investigation period of early 1980s witnessed the implementation of several structural adjustment programmes [see Ali (1986), Hussien (1985), Hassan (1990)]. Yet the lack of data did not enable us to consider other periods. Furthermore, we did not get rid of short-period variations in the rates of return by, say, averaging the rate for each industry for a five or even ten-year period due to lack of data. Consequently, the one-year period (1981/82) cannot represent for long-run partial equilibrium conditions. Finally, the assumption of constant cost is plausible, but if it is wrong, costs in all probability would tend to be increasing rather than decreasing in the manufacturing sector. Increasing costs would lower our welfare loss estimates since less resources would have to be transferred in order to equalize profit rates.

It would have been appropriate for our purpose to deal with firms directly. Unfortunately, the ISIC system lumps together in particular industries products which are only remote substitutes and which are produced by quite distinct groups of firms, that is,the ISIC industries are in some instances aggregates of sub-industries or firms. That violates our assumption of high substitutability among the products produced by different firms within any industry and relatively low substitutability among the products of different industries. Consequently the use of ISIC in such cases biases our estimates of welfare loss downward. If data were available at the firm level, the extent of the bias would be easily revealed.

Flaws in the industrial survey data tend to overstate our estimate of welfare loss. In particular, the indirect measure of the rate of return on capital is defined in the survey (see page 57) as:

r=(gross value added - wages & depreciation)/capital (4.1)

This indicates an overstatement of the actual rate. As it is evident from the definition of value added given by Miller (see equation 4.2),this proxy is gross of many factors and it might better be termed the `economic surplus'. In an attempt to check the extent of the bias, four public manufacturing industries with high rates of return are excluded. Consequently, the welfare loss drops by about 50 per cent.

Value added= (payments of wages & salaries, interest, profits & rents)

+ (business transfer payments, indirect business taxes & depreciation) (4.2)

In conclusion, we turn to ask what resource malallocations we have measured. We actually have used excess profit as an adequate measure of monopoly due to maldistribution of capital neglecting other factors of production that might be a function of monopoly. In other words, monopoly certainly can yield inefficient use of labour and materials as well as of capital. In effect, this would mean departure from some proper figure for value added, or for profits. In fact, it is hard to quantify with any precision welfare losses due to monopoly for the following reasons. First, monopoly usually includes costs that consumers under truly competitive conditions would not elect to pay for (such as high marketing, advertising and packaging costs). Leibenstein (1966) termed those organizational slacks "X- inefficiency." An interesting test of "X-inefficiency" was conducted by Primeaux (1977). He found that in 49 U.S. cities, there was competition between at least two electronic companies and the costs of those companies that face competition were 11 per cent below those of monopoly supplies. Secondly, monopoly rent-seeking behaviour -- where real resources have to be spent on lobbying, leading to substantial social losses -- should be taken into consideration [see Krueger (1974)]. Thus, our estimates of welfare losses due to capital maldistribution represent lower bounds to the true loss to society because they neglect other losses.

5. SUMMARY AND CONCLUSION

In this paper we have measured the malallocation of resources (as measured by capital) and the corresponding welfare loss which existed in both public and private Sudanese manufacturing sectors in 1981/82. Table 3.3 provides a comparative summary of our empirical results. The results indicate that the elimination of resource maldistribution in 13 public manufacturing industries involves a maximum transfer of 1/2 per cent of GDP and a net gain of 0.335 per cent in consumer welfare, or L.S. 0.80 per capita. On the other hand the maldistribution of capital existing in 13 private industries could have been eliminated by a net transfer of 1 per cent of GDP. The resulting improvement in consumer welfare amounts to 0.389 per cent of GDP, that is, 0.93 Sudanese pounds for every man, woman,and child in the Sudan in 1981/82.

In reaching these estimates we have assumed constant rather than increasing costs in manufacturing industry and have assumed unitary elasticities of demand, which are believed to be high.

On both counts we therefore tend to overstate the welfare loss. Furthermore, we have treated intermediate products in such a way as to overstate the loss. Finally, our analysis is greatly constrained by the rather special character of the industrial survey, namely the use of an indirect rate of return for each industry rather than individual industries, or even better, individual firm profit figures.

If broad generalizations are possible, our results suggest that the share of the private sector in community welfare loss is greater than the public sector. That is, the public sector is economically efficient relative to the private sector.

R E F E R E N C E S

1. Ali, A.A.(1985), "Structural Adjustment Programmes in the Sudan" in Background Papers for ILO/JASPA Mission to Sudan on Employment and Economic Reform, Development Studies and Research Centre, Ithaka Press.

2. Economic Survey (1988/89), Annual Report prepared by the Ministry of Finance and Economic Planning, Khartoum, Sudan.

3. Harberger, A.(1954), "Monopoly and Resource Allocation",The American Economic Review, 44, May 1954, pp.76-87.

4. Hassan, F.M.A. (1990), "Impact of Structural Adjustment Programmes on the Sudanese Economy", University of Khartoum, Unpublished report.

5. Hotelling, H.(1938), "The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates", Econometrica, July 1938, pp.242-69.

6. Hussein, M.N. (1985), "IMF Economics in the Sudan: A Preliminary Evaluation" in Ali, A.A. (ed), Sudan Economy in Disarray, Ithaka Press, 1985.

7. Industrial Survey in The Sudan 1981/82, A Technical Report prepared for the Government of the Sudan by United Nations Industrial Development Organization.

8. Krueger, A. (1974), "The Political Economy of the Rent Seeking Society", The American Economic Review, 64, June 1974, pp.291-303.

9. Leibenstein, H. (1966), "Allocative Efficiency vs X-Efficiency", The American Economic Review, 56,June 1966, pp. 392-415.

10. Miller, N.C. (1938), Macroeconomics, Houghton Mifflin, 1983.

11. Primeaux, W. (1977), "An Assessment of X-Efficiency Gained Through Competition", Review of Economics and Statistics, 59, Feb. 1977, pp.105-108.

12. Spencer, M. (1986), Contemporary Microeconomics, Worth Publishers, Inc. New York.

13. Tullock, G. (1967). "The Welfare Cost of Tariffs, Monopolies and Theft", Western Economic Journal, 5, June 1967, pp.224-232.

14. Van Der Wel, P. (1984), "Transfer Pricing and Surplus Extraction: The Case of The Sudan Sugar Industry", Development Studies and Research Centre, Seminar No.44, University of Khartoum.