The influence of Road and Rail Freight Rates on the South African Economy - A tax simulation through a Computable General Equilibrium Analysis
J.L. Erero & Jan van Heerden1
Department of Economics, University of Pretoria
This paper is concerned with the road and rail freight rates in the South African Transport Industry. Rates are a difficult subject. There is more frankness about the costing procedures that underlie the rates and about the kind of percentage mark-ups that are involved in different types of movement. A based 1998 “Social Accounting Matrix (SAM)”was constructed and ORANI-JL, a General Equilibrium Model of the South African Economy was developed based on the generic version of the model, ORANI-G, which is designed for expository purposes and for adaptation to other countries. ORANI applied general equilibrium (AGE) model of the Australian economy was preferred because it has been widely used by academics and by economists in the government and private sectors.
Our description of the model's equations and database is closely integrated with an explanation of how the model is solved using the GEMPACK system to discover the influence of the road and rail freight in the South African Economy. The result of modeling impacts of a 5% general tax decrease is presented in this paper. JEL Classifications: C68, D58, L92
Keywords: Simulating, general taxes, freight rates, freight forwarders, rail and road freight, Computable General Equilibrium modeling.
Rates are the most important single factor influencing companies’ decisions on choice of transport mode. In order to study the effects of rates on corporate freight movements, it is necessary to discuss transport operations with numbers of industry. A general study of what the latter require from transport services, similar to that produced by the British Ministry of Transport,2 would be very interesting but impossible in the time available. A number of individual firms was interviewed and we did investigate what their transport needs are, how well they are served and to what extent rate structures affect their freight movements.
The organizations have been drawn from a variety of industries in an attempt to obtain a broad view of the situation. Although some companies based in rural areas are included, there is a strong blast towards the province of Gauteng ones due to the obvious reasons of time and convenience. However, as many of the organizations studied are national distributors, the location of their Head Offices should not influence their transport requirements unduly.
Investigating a number of companies in the same industry would highlight any differences due to location, but would reduce the scope of this research. It has therefore been assumed that companies of similar size in the same industry are influenced by virtually identical factors.
Most of these findings were collected by personal interview of a very unstructured nature. A certain amount of direct questioning was necessary to obtain information on company operations and transport arrangements, but by encouraging company personnel to talk freely on the thinking behind the latter, important factors came to light. The use of a more formal research method, such as a questionnaire, would limit the information received because questions relevant to one company may not be to another and there is little scope for the informant to offer personal views or company philosophy.
The number of cases investigated was also limited by the time available and also by the sometimes prolonged efforts needed to obtain information.
Generally speaking, companies approached were willing to discuss their transport needs, but some shyed away from making specific data public. Unless sufficient background is available, there is little point in publishing findings as others cannot benefit without being able to compare their situation with that of the company under discussion. The industries covered are far from exhaustive, but hopefully cover a reasonable range. There is perhaps a slight bias towards domestic retailing, but this is a very interesting area because of the effects that the trend towards larger stores and fewer companies has had on distribution in general and transport in particular.
It seems likely that freight forwarders will be of increasing importance in transport operations. Their move into the distribution field has relieved several companies of problems in this area, so there is no reason that the trend should not continue. To carry the concept of total distribution to its logical conclusion, the freight forwarders should be able to offer a door-to-door service anywhere in South Africa.
The paper is structured as follows. Section 2 introduces the case study in the context of the paper, followed by the setting up of the model in Section 3. Section 4 contains the treatment of the tax in the model and its simulation. Section 5 discusses results, and Section 6 offers conclusions.
2. CASE OF MOTOR FORD COMPANY IN SOUTH AFRICA 2.1. INTRODUCTION In the majority of cases, rate is the most important single factor influencing companies’ decisions on choice of transport mode. However, there are occasions when other considerations carry more weight, of these, incidence of damage is probably the most important, which road having considerable advantage over rail in the area. In the case of Ford Motor company in South Africa, the mode offering the lowest rates will not necessarily give the lowest total distribution cost because of differences in handling requirements, inventory levels and packaging. Although there are some problems in using total distribution cost, a detailed calculation can only be made with the aid of a computer. Large companies that are able to negotiate rates with the transport industry obtain a considerable advantage over their smaller competitors. Among some companies, Ford South Africa is able to dictate its own terms.
Because of this, companies are very secretive about the rates they pay for transport. Due to the size of the South African market, it is difficult to reap maximum plant economies of scale, so transport become an important area where costs can be pared by large organizations3.
2.2. GOODS’ MOVEMENTS Since Ford is generally a larger user than its suppliers are manufacturers, it has a better bargaining base for transport. It therefore undertakes to arrange all transport of components from suppliers as well as moving nationally manufactured item and completed vehicle. Thus Ford’s goods’ movements fall into two categories: material movements from suppliers and manufacturing plant to the assembly plants and the shipment of built-up vehicles from the latter to customers. The approximate volumes of those movements are shown in Table 1. The small amount of material moved to Eastern Cape province is to supply a reactivation plant, which replaces any parts damaged whilst completed vehicles are in transit from the Eastern Cape.
2.3. METHOD OF TRANSPORT Volume moving by each of road, rail and air are shown in Table 1. An accurate breakdown by mode of goods moving between two provinces is not possible because of fluctuations due to specific requirements.
In general, about 70 rail trucks per day are moved between the manufacturing and assembly plants, but varying amounts are carried by road in Ford’s own vehicles. The latter are also used within other metropolitan areas. In most cases, the company negotiates its rates with the South African Railways or carriers; its only commitment to freight forwarders at present is the moving of between five and eight containers a day between Eastern Cape and Gauteng. Air freight is occasionally used if components are required urgently.
2.4. CHOICE OF MODE Ford’s choice of mode is made on the basis of total distribution cost. For each mode, the company costs the whole physical distribution system from point of manufacture until the goods are loaded ready for line haul.
Table 1: Ford Motor Company- Full year 1998 of Built-up Vehicles
Eastern Cape Plant
Source: Motor Ford SA Figure 1: Freight by destination from the Eastern Cape Plant to Gauteng and other provinces
Quotations are then obtained from railways and road operators and added to the above to obtain total distribution costs for each mode. The cheaper one is then selected. Thus the lower line haul rate is not necessarily the mode chosen. For example, rail is usually cheaper than road for line haul, but may require sufficient extra packaging or handling to erase this advantage.
The regularity of the service is also taken into account, as the more services there are, the smaller the stock that has to be held. With this in mind, Ford also calculates the optimum frequency of service and the quantities required in each order. Into these is also added a safety margin to cover fluctuations in demand and any other unexpected contingencies. Thus the total cost in required inventory becomes very significant in the choice of transport mode.
However, there are certain factors that may over-ride these calculations in decision-making. For example, one advantage of road is that goods may be sent at any size lots. Thus, even though the bulk of plants movements are by rail, considerable volumes also travel by road. Because of the economies of production runs, it is not always possible for the exact part needed to be ready when the train leaves, so road transport has to be used if delivery is urgent. Some seeming anomalies in vehicle shipments can be similarly explained. Although the majority of movements are by rail, road is extensively utilized for the reverse journey. The reason for this is that Ford employ road carriers to move completed vehicles from plants to all provinces of South Africa because they are cheaper than rail, but have to send them on into Gauteng to collect vehicles for back loading. In general, rail is the better mode where back loading is not available, as users do not have to pay for the return of empty wagons.
It is interesting to note that the vast majority of movements within a province are by road, despite the fact that from Ford’s point of view door-to-door delivery of a vehicle with no intermediate handling has obvious advantages.
The choice of mode can be affected by the availability of suitable railway rolling stock. At present, old, open-top wagons are used, but Ford is hoping to persuade the railways to introduce new, enclosed, high-cube wagons, 75 feet long and able to stack three pallets high instead of the present two. Three savings would accrue from this: forklift trucks instead of the present two could do investment flexibility, loading and unloading by forklifts would be quicker; packaging costs would be reduced – there would be less risk of damage with enclosed wagons, particularly as rust caused by rail would be eliminated. Such wagons would initially be used between Eastern Cape and KwaZulu-Natal, but in future, all movements out of Eastern Cape could be rail instead of road and Ford would not have to employ freight forwarder for its Pietermarisburg deliveries. Although road is at present used more than rail, the introduction of such rolling stock could shift the balance considerably.
Regarding the transport costs, when the sums being spent on moving significant volumes are considerable, the company is able to negotiate contracts with the railways and road operators, which would be likely to offer very favorable rates.
2.5. ANALYSIS Theoretically Ford approaches its transport arrangements in a highly scientific way and should be attaining optimal allocation of resources. However, there are several problems in this approach, of which the company is no doubt aware. The most significant of these is the measurement of costs required in the calculation of total distribution cost. It is difficult to understand the concept of a plant closure “costing R8, 000 to R12,000 per minute”, and on a more basic level, exactly what does warehousing, for example, “cost” a company? Although it is probably highly impractical, factors such as alternative uses of funds should be considered. If rail is used, it is likely that larger inventories will be held. As discussed above, this would have been considered in the calculation of total distribution cots, so that by having a larger investment in stocks, savings could be made in distribution costs. However, if the capital so employed could be invested elsewhere at a return high enough to cancel out the transportation cost differential, then suing the more expensive mode of transport would give better allocation of total resources. Such calculations are not being proposed as feasible alternative to the present method because their obvious practical difficulties, but the theory does emphasize that complete reliance on a concept such as total distribution cost is not advisable. There may be circumstances where exogenous factors outweigh the result of theoretical calculations.
Ford is a good example of the power a large company wields in the transport industry. The company is almost able to dictate its own terms, even to the extent of suggesting new types of rolling stock to the railways. It would be one of the few companies that arranges transport from its suppliers, but considerable cost savings can obviously be realized. Such arrangements also allow Ford a greater degree of control over their component manufactures which is necessary in a fast-moving, production line operation which faces huge losses if work is interrupted because of stock shortages.
3. SETTING OF THE MODEL
A CGE model is an economy-wide model that includes feedback between demand, income and production structure, and where all prices adjust until decisions made in production are consistent with decisions made in demand (Naudé & Brixen, 1993a). It considers the economy as a complete system of interdependent components (industries, investors, households, governments, importers and exporters). It explicitly recognizes that economic shocks impacting on any one component can have repercussions throughout the system and that accounting for these repercussions may be essential in assessing the shocks – even on the components upon which they impact initially (Naudé & Brixen, 1993b).
The ORANI-JL adapted from the ORANI-G model is a static computable general equilibrium model of the South African economy based closely on the Australian ORANI-G model4. It is a model of the economy in a single period, designed for comparative static analysis of the effect of the policy changes on the economy in that period. ORANI-JL disaggregates the economy into:
Due to the size of ORANI-JL, a complete description falls outside the scope of the present paper. However, for a more complete description5, see Horidge (1997). Because of our focus on tax issues, some comments on the modelling of taxes in the ORANI-JL may be appropriate.
4. SIMULATING A 5% REDUCTION IN GENERAL TAXES
In order to simulate a tax decrease in the ORANI-G framework we need to investigate and understand the tax equations of the model as well as identify the relevant variable to apply the shock to. For this purpose we revert to the documentation of Mark Horridge, “ORANI-G: A Generic Single-Country Computable General Equilibrium Model”, Centre of Policy Studies and Impact Project, Monash University, Australia, 1997.
Excerpt 23 from the ORANI-G (Horridge, 1999) contains default rules for setting sales-tax rates for producers, investors, households, and government. Sales taxes are treated as ad valorem on basic values, with the sales-tax variables in the linearised model being percentage changes in the powers of the taxes. Each equation allows the changes in the relevant tax rates to be commodity-specific or user-specific. To simulate more complex patterns of tax changes, we would omit or modify these equations.6
We used a short-run closure: capital and land usage in each industry are fixed while labour is everywhere in elastic supply at fixed real wages. Constant real wages in the short-run closure determine employment.
On the national expenditure side, real consumption, real aggregate investment, and real government consumption are fixed. Also it allocates fixed national investment across industries following endogenously determined rates of return (ROR).
Foreign currency prices of imports are naturally exogenous and the exchange rate is fixed as numeraire. Population is also held constant. There are other exogenous variables in this closure such as changes in rate of production tax, technology, price and quantity shift variables.
We shocked the variable f3tax_cs by –5% which allows us to simulate the effects of a 5% reduction in tax rates of households, and the economy-wide effects thereof7.
4.3 MODELLING IMPACTS OF A 5% GENERAL TAX DECREASE
The main mechanism, through which the effect of the tax increase will be transmitted for the purpose of this simulation is the variable that allows a shock to be applied as a uniform % change in powers of taxes on household usage (f3tax_cs). In normal simulations this variable is exogenous, and can therefore be shocked with changing the standard closure. This allows us to simulate the effects of a 5% reduction in tax rates of households, and the economy-wide effects thereof.
The other relevant variable to keep in mind in a simulation like this would be real private consumption expenditure (x3toth), as any gains or losses due to a tax increase / decrease would influence this variable directly. Based on the current closure applied (DPSV shortrun closure) real private consumption expenditure is treated as exogenous for the short run – implying that nominal private consumption expenditure would just adjust with the inflation changes in order to have no real effect.
5. RESULTS INTERPRETATION
It would be informative to obtain a prior expectation of the macroeconomic effects of the road and rail freight rates before examining the simulation results. A stylized model proposed by Adams (2003) is used for this purpose. The stylized model represents a single- country and allows for exogenous changes in the position of foreign demand schedules for exports and foreign supply schedules for imports and allows changes in the global rate of return on capital. This model is representative of a model such as ORANI (Adams, 2003) as described by De Wet (2003).
Decrease in tax on household usage should decrease the cost of skilled and informal sector labour (variable factors of production) if the terms of the trade remain unchanged or decreases. This result also follows from the assumption that real wages are fixed in the short run. Simulation results indicate that the balance of trade is indeed positive. It is therefore clear that the price of the variable factor of production will decrease as a result of the tax reduction.
The decrease in the price ratio between the price of the variable factor of production and that of the fixed factor of production implies that the quantity of the variable factor that is employed will increase.
The increase in the use of variable factors of production will result in an increase in gross domestic product (GDP) at factor costs. The effect of the rise in GDP at market prices on the demand side aggregates is a function of the closure assumptions and the terms of trade. The nominal exchange rate is fixed by assumption, therefore the fall in terms of trade will result in an increase in the trade balance.
The prior expectations are confirmed by the simulations results. Table 2 reflects the actual results from the CGE simulation. As expected, gross domestic product, exports and employment increase. Because skilled labour is fixed by assumption, the increase in employment represents an increase in the use of unskilled and informal sector labour in the production process. The prices of capital, land, and skilled labour fall. The terms of trade decreases, which is the result of a fall in the price of exports. The fall in the terms of trade results in an increase in exports. The increase in exports allows the trade balance to increase. The impacts of this simulation on various macro-economic variables are listed in the table 2.
Table 2: Impact on selected macro-economic variables
Suppose the initial level of GDP is X and the initial growth rate g percent. The new level of GDP without the intervention would have been X(1+g). Assume that in terms of GDP, the CGE result is g. The new level of GDP after the implementation of the Transport restructuring productivity increase is thus X(1+g)(1+g). The new growth rate can then be determined as:
Essentially, the new GDP growth rate is the sum of the initial growth and the change in the growth rate plus their product. In other words, instead of for example GDP growth of say 2.5 percent over a period of 3 years we can now expect GDP growth of
2.5% + (1.4341%) + 2.5% x (1.04341%) = 3.97%.
Intuitively one would expect a positive impact on both GDP and employment, as is the case in the above results (GDP increased by 1.43 % and employment by 2.7%). However, the fact that import volumes decline while consumer products become relatively cheaper and households effectively can spend more while employment increases and general price levels (CPI) decreases, is counter-intuitive. Historical econometric analysis shows that the South African economy is very import intensive, and one would therefore expect imports to increase in the event that consumer. The comment remains that this result is probably due to Armington elasticities in the model’s database that have been set to 2 for all sectors due to lack of data from the first source. These (and other coefficients) in the model need to be calibrated based on existing and further research before this model’s results can be applied in an applied policy environment.
As expected based on the short run closure, there is no change in the real domestic consumption expenditure. One may think of changing this assumption for a simulation relating to tax rates, for such a change would in all probably lead to a change in domestic expenditure in the short term, especially for middle and lower income households. However, we do not analyse such a scenario in this case.
If one assumed for the moment that these current results are plausible, then the tax decrease could have a relatively large impact on GDP and employment.
6. STRUCTURAL SECTORAL RESULTS For the purposes of this analysis the following variables on a 15-sector level of detail are listed in Table 3. There are clear “winners and losers” in this kind of simulation results, and it is not surprising that the industries that are closely linked to the transport industries are the “winners”, while those industries that are not linked to the transport industries are the “losers”.
Table 3: Decrease in general price levels via 5% Tax decrease- Comparative results
Fixed Real Wages-Inflation adjusts
Productivity Impacts through Technology Coefficient
Sector Output or Value Added/GDP
Import Volume Impacts
A reduction in price levels via a five percent reduction in taxes causes the prices to fall in all sectors. With fixed exchange rate as a numeraire, domestically produced goods become cheaper and increase their demand in foreign markets. As expected, imports in most sectors decline excepting agricultural (1.8) and mining (1.6) sectors. In the former sector, the rise can be attributed to factors such as drought, while in the mining sectors the rise in imports results from the fact that mining products are processed overseas and then imported into South Africa. Household demand is mixed across all income categories, being largely positive for services sectors and negative for primary and secondary sectors. The rise in export is largely responsible for increased output, which is made possible by a rise in labor demand.
Fixed Real Wages-Inflation adjusts
Export Volume Impacts
Household demand impacts-Total
Household demand impacts- Low income
Household demand impacts-Middle & High Income
7. CONCLUSION As has been stressed throughout this paper, it is difficult to draw any valid conclusions on rates, simply because we not only do not know what the vast majority of them are, but also they may vary between customers over the same route.
However, when the choice between using company-owned vehicles and outside contractors is being considered, economics are the sole criterion. The only unusual facet of this decision is that it is done in the long-term so that comparisons of internal costs and industry rates are less frequent than normal.
It seems likely that freight forwarders will be of increasing importance in transport operations. Their move into the distribution field has relieved several companies of problems in this area, so there is no reason that the trend should not continue, particularly for companies that require inter-province warehousing facilities.
To carry the concept of total distribution to its logical conclusion, the freight forwarders should be able to offer a door-to-door service anywhere in South Africa. This would require liaison with the railways for inter-province as well as movements within a specific province. Such an arrangement should be beneficial to the railways as well as users, as terminal facilities, handling and so on would be left to the forwarders, so radically reducing the railways’ capital expenditure.
This attempt at modelling the decrease in a general tax rate should be viewed as a cursory investigation only. In order to be in a position to evaluate this question in a more thorough fashion would require more research regarding the specific sensitivities and elasticities of the other economic sectors in this model, as well as household behaviour and alternative closures allowing better understanding of the implications of such a simulation.
The results from the simulations indicate that, over the short run, a tax reduction has positive impact on the GDP, exports and employment. The rise in export is largely responsible for increased output, which is made possible by a rise in labor demand.
APPENDIX: COMMAND FILE
! Command file for ORANIG model, short-run closure
check-on-read elements = warn; ! very often needed
cpu=yes ; ! (Optional) Reports CPU times for various stages
! Variable f3tax_cs # Uniform % change in powers of taxes on household usage #
shock f3tax_cs = -5 ;
Armington PS (1969) The Geographic Pattern of Trade and the Effects of Price Changes, IMF Staff Papers, XVI, July, pp 176-199.
Armington PS (1970) Adjustment of Trade Balances: Some Experiments with a Model of Trade Among Many Countries, IMF Staff Papers, XVII, November, pp 488-523.
Bandara, J S. 1991. Computable General Equilibrium Models for Development
Policy Analysis in LDCs. Journal of Economic Surveys, 5 (1) : 4-27.
Bulmer-Thomas, V. 1982. Input-output analysis in developing countries.
New York : John Wiley & Sons LTD.
Cameron, B. 1968. Input-output analysis and resource allocation. Cambridge :
Cambridge University Press.
Cameron, M, De Jongh, D, Joubert, R, Suleman, A, Horridge, JM & Parmenter, BR,
1994: IDC-GEM simulations for the workshop on economy-wide models of the South
African economy, Development Bank of Southern Africa, 14-16
July 1994, Halfway House.
Cameron, C., de Jongh, D., Joubert, R., Suleman, A., Horridge, J.M. & Parmenter, B.R. (1994): IDC-GEM simulations for the workshop on economy-wide models of the South African economy, Development Bank of Southern Africa, 14-16 July 1994, Halfway House.
Carvalho, Soniya (2003). 2002 Annual Review of Development Effectiveness - Achieving Development Outcomes: The Millennium Challenge. The World Bank. Washington. ISBN 0-8213-5436-1
Chowdhury, A & Kirkpatrick, C.(1994), ‘Development Policy and Planning:
An Introduction to Models and Techniques’, London and New York:Routledge
Horridge, J M, Parmenter, B R and Pearson, K R. 1993. "ORANI-F: A
General Equilibrium Model of the Australian Economy", Economic and Financial
Computing, 3(2) Summer.
Johansen L (1960) A Multisectoral Model of Economic Growth, Amsterdam:North-
Holland, (2nd edition 1974).
King, B. B.(1988), ‘What is SAM?’ in Pyatt, G. and Round, J. I. (ed.), Social
Accounting Matrix: A Basis for Planning, Washington D.C: The World Bank.
Lundberg, D. E., Krishnamoorthy, M., & Stavenga, M. H. (1995).
Tourism economics. New York: John Wiley & Sons.
Naudé, W.A. 1992. A Conceptual Framework for a Computable General Equilibrium
Model based on the 1988 South African SAM. Journal for Studies in Economics &
Naudé, W.A. 1993. Sharpening the Tools: A Comment on the Provisional 1988
Social Accounting Matrix. Development Southern Africa, 10(2).
Naudé, W.A. & Brixen, P. 1993. A Provisional CGE model for South Africa. South
African Journal of Economic & Management Sciences. 10.
Naudé, W.A. & Brixen, P. 1993. On a Computable General Equilibrium Model for
South Africa. South African Journal of Economics. 61(3).
Parmenter BR and Meagher GA (1985) Policy Analysis Using a Computable General
Equilibrium Model: a Review of Experience at the IMPACT Project, Australian
Economic Review, No. 1'85, pp.3-15.
Powell A (1977) The IMPACT Project: an Overview—First Progress Report of the
IMPACT Project, Vol 1,Canberra:Australian Government Publishing Service.
Powell A (1991) A Brief Account of Activities 1988 to 1990, IMPACT Project Report
No. R-08, February, 50pp.
Powell A and Lawson A (1989) A decade of applied general equilibrium modelling for
policy work, pp. 241-290 in Bergman L, Jorgenson D and Zalai E (eds), General
Equilibrium Modeling and Economic Policy Analysis, New York:Blackwell
Pyatt, G., & Round, J. I. (1985). Social accounting matrices for development
planning. In G. Pyatt & J. I. Round (Eds). Social accounting matrices: A basis for
planning (pp. 52-69). Washington, D.C.: The World Bank.
Sen, Huseynin (1996). Unpublished Assessed Article, Bradford University,
Development Project Planning Centre (DPPC), Bradford, UK.
van der Mensbrugghe, D. (1995): Technical description of the World Bank CGE of the
South African economy, Unpublished report OECD, Paris.
van der Merwe, C. & van Seventer, D.E.N. (1995): Towards a system of economic and
social accounting matrices for South Africa, Development Paper 63, Development
Bank of Southern Africa, Halfway House.
Vincent DP (1989) Applied General Equilibrium Modelling in the Australian Industries
Assistance Commission: Perspectives of a Policy Analyst, pp. 291-350 in Bergman L,
Jorgenson D and Zalai E (eds), General Equilibrium Modeling and Economic Policy
Analysis, New York: Blackwell
Black Book - see Dixon, Parmenter, Powell & Wilcoxen (1992).
Green Book (DPSV) - see Dixon, Parmenter,Sutton & Vincent (1982).
Yellow Book - see Dixon, Bowles & Kendrick (1980).
Orange Book - see Dixon, Powell & Parmenter (1979).
A number of working papers may be downloaded from:
1 Mr Erero is PhD student, Department of Economics, University of Pretoria, while Jan van Heerden is Professor and the Head of the Department of Economics at the same institution. Views expressed are those of the authors and do not necessarily reflect those of any institution they may be involved with. All remaining errors are sole responsibility of the authors though.
2 . B.T Bayliss and S.L Edwards, Industrial demand for Transport, Ministry of Transport, London, 1978, p.16.
3 Personal interview with Ford South Africa Ltd
4 The model ORANI-JL was developed by Jean Luc Erero with the help of Dr Mark Horidge from the Centre of Policy Studies (CoPS) at the Monash University, Melbourne, Australia.
5 The main equations of this model are derived from the constrained optimisation of neo-classical production and utility functions. Producers choose inputs to minimise costs of a given output subject to non-increasing returns to scale industry functions. Consumers are assumed to choose their purchases to maximise utility functions subject to budget constraints. Productions factors are paid according to their marginal productivity. The government sector is included and imperfect competition has been introduced via price fixing, rationing and quantitative restrictions. At the equilibrium level these models solutions provide a set of prices that clear all commodity and factor markets and make all individual agents’ optimisations feasible and mutually consistent. The behavioural equations of the model are augmented by sets of equations showing the flows of income in the economy and sets of equations defining an economic equilibrium in each market as where supply equals demand. These equilibria may be reached via adjustments in prices and/or quantities. The present model uses a 1998 Social Accounting Matrix prepared by the author as database.
6 The same problem, that exogenous variables have too many dimensions, sometimes arises when we wish to simulate technical change. Suppose we wished to shock the variable a1 (which varies by commodity, source and industry). It might be simplest to write a new equation, like the equations of Excerpt 28 that related a1l to one or more new vector variables. The modeller is expected to add these equations and variables as required, since their form is experiment-specific.
7 We shocked this model by applying f3tax_cs by –5%. The shock affects all the transport sub-sector.