`Get Complete Project Material File(s) Now! »`

**The computed output and price elasticities of water**

This sub-section first presents and discusses the output elasticities computed for the combined sectors and for each sector as specified in equation 3.8. It then presents and discusses the price elasticity of the demand for water as specified in equation 3.5. The computed sector specific results and the combined output elasticity of water are presented in column 4 of Table 3.2. Output elasticity measures the degree of responsiveness of changes in the value of output to a unit change in the level of water use.

The results show an industry-wide output elasticity of water of 0.20. This implies that on the average, the value of output increases by 2 percent for every ten percentage increase in the level of water use. Generally, there is not much variation in output elasticity among the various sectors. The metal manufacturing industry, with an output elasticity of 0.56 has the highest value. This is followed by machinery and equipment with an output elasticity of 0.47, while the energy sector has the least output elasticity of 0.07. An output elasticity of 0.22 in the agriculture sector is higher than the combined sectors output elasticity, indicating that for every ten percent increase in level of water use in agriculture, the value of output increases by only about two percent. These results suggest that for every 10 percentage increase in the level of water, the percentage increase in the value of output in the metal manufacturing industry is more than the percentage increase in the value of output in any other sectors and that the energy sector has the least percentage increase in the value of output. The estimated industry-wide output elasticity of water, which is 0.20, is consistent with the findings of Wang and Lall (2002) with an elasticity measure of 0.17 and with sector-specific output elasticities varying from 0.04 to 0.26.

The computed price elasticities are reported in column 6 of Table 3.2. The sectoral price elasticity of the demand for water shows the degree of responsiveness of each sector’s water use to changes in the price of water. The computed figures show that generally, sectoral water demand is price elastic, with elasticity measure of -1.27. From the computed elasticities, it could be seen that the price elasticity of demand for water in the agriculture sector (-0.89) is less than the combined sectors’ price elasticity of demand for water. The computed elasticities also show that when the price of water increases by 10 percent, water use in the agriculture sector decreases by about nine percent, while all the sectors’ water use decreases by about 13 percent. However, individual sectors differ in the degree of their responsiveness to changes in water prices as shown above in column 6 of Table 3. 2. For example, the demand for water is price elastic in the mining (-1.34), energy (-1.42), machinery (-2.03), construction (-1.35), metal manufacturing (-2.44), electricity (-1.38) and beverages and tobacco (-1.46) sectors. Relative to these sectors the demand for water is price inelastic in agriculture (-0.89), leather products and wearing apparel (-0.94), and pulp and paper (-0.87) sectors. In the mining sector for example, mine water can easily be recycled. Therefore, for some increase in the price of freshwater, mines can reduce freshwater intake and treat and recycle the wastewater. These results are also consistent with the findings of Wang and Lall (2002), with an industry-wide price elasticity of the demand for water of -1.03 and sector specific price elasticities ranging from -0.57 in power generation to -1.20 in leather manufacturing.

**Estimated sectoral marginal values of water**

This subsection presents and discusses the computed sectoral marginal values of water specified in equation 3.10.

The computed sectoral marginal values of water are presented in Column 5 of Table 3.2 and graphically illustrated in Figure 1. The marginal value measures the change in the value of output of a given sector, as a result of a unit change in the level of water use in that sector. In this study, the marginal value of water in a given sector shows the increase in the value of output due to a cubic meter increase in water use in that sector. This is an important concept in general production theory. The unit cost of an input (marginal cost) is compared with the unit contribution of that input to output or revenue, which in this study, is the marginal value. If the marginal value is less than the marginal cost, less of that input should be used until the marginal value is equal to the marginal cost. In a multi-input industry, the ratio of the marginal value to the price of the input must be the same for all the inputs and must be equal to unity (Beattie and Taylor, 1993). The combined sectors and the sector-specific marginal values, including agriculture, are presented in column 5 of Table 3.2. The marginal values of water are computed at the mean values of the variables.

**CHAPTER ONE ****INTRODUCTION**

1.1 BACKGROUND

1.2 ALTERNATIVE WATER ALLOCATION MECHANISMS

1.3 WATER ALLOCATION REFORM IN SOUTH AFRICA

1.4 PROBLEM STATEMENT

1.5 THE OBJECTIVES OF THE STUDY

1.6 HYPOTHESES TO BE INVESTIGATED

1.7 OUTLINE OF THE STUDY

1.9 LIMITATIONS OF THE STUDY

**CHAPTER TWO ****ECONOMIC VALUATION OF WATER RESOURCES: AN OVERVIEW OF METHODS AND APPLICATIONS **

2.1 INTRODUCTION

2.2 ESTIMATING THE PRODUCERS’ DEMAND FUNCTIONS FOR WATER

2.3 THE RESIDUAL IMPUTATION METHOD

2.4 VALUE ADDED APPROACH

2.5 ALTERNATIVE COST APPROACH

2.6 OUTLINE OF THE APPLIED METHODS USED IN THIS STUDY

2.7 SUMMARY AND CONCLUSION

**CHAPTER THREE ****MARGINAL PRODUCTIVITY ANALYSIS OF GLOBAL SECTORAL WATER DEMAND**

3.1 INTRODUCTION

3.2 THE EMPIRICAL MODEL AND ESTIMATION PROCEDURE

3.3 DATA SOURCES AND DESCRIPTION OF EXTRACTED DATA

3.4 PRESENTATION AND DISCUSSION OF ESTIMATED RESULTS

3.8 SUMMARY AND CONCLUSIONS

**CHAPTER FOUR ****MARGINAL PRODUCTIVITY ANALYSIS OF SECTORAL WATER DEMAND IN SOUTH AFRICA**

4.1 INTRODUCTION

4.2 MODEL SPECIFICATION, ESTIMATION AND DATA SOURCES

4.3 PRESENTATION AND DISCUSSION OF ESTIMATED RESULTS

4.5 SUMMARY AND CONCLUSIONS

**CHAPTER FIVE ****SECTORAL WATER USE IN SOUTH AFRICA: EQUITY VERSUS EFFICIENCY**

5.1 INTRODUCTION

5.2 THE FEATURES OF THE SOUTH AFRICAN SAM

5.3 THE THEORETICAL FRAMEWORK AND MODELING PROCEDURE

5.4 PRESENTATION AND DISCUSSION OF SIMULATION RESULTS

5.5 SUMMARY AND CONCLUSIONS

**CHAPTER SIX ****A COMPUTABLE GENERAL EQUILIBRIUM APPROACH TO ANALYSE THE HOUSEHOLDS’ WELFARE EFFECTS OF CHANGES IN SECTORAL WATER USE IN SOUTH AFRICA**

6.1 INTRODUCTION

6.2 DATA, THEORETICAL FRAMEWORK AND SIMULATIONS

6.3 PRESENTATION OF SIMULATION RESULTS

6.4: DISCUSSION OF MAIN RESEARCH FINDINGS

6.5 SUMMARY AND CONCLUSIONS

**CHAPTER SEVEN ****GENERAL SUMMARY, CONCLUSIONS AND RECOMMENDATIONS**

7.1 INTRODUCTION

7.2 GENERAL RESEARCH FINDINGS

7.3 POLICY RECOMMENDATIONS

7.4 RESEARCH FINDINGS AND POLICY INSIGHTS

7.5 FUTURE RESEARCH ISSUES

**REFERENCES **