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The aim of this study is to solve numerically an infinite horizon optimum growth path and investigate the qualities of such a path. To do this, I surveyed the macroeconomic behaviour of the Egyptian economy over a limited period of time (1945-1965). Statistics on population, employment, wages, investment and production for the two main sectors in Egypt were analyzed with the view to establishing the production and consumption patterns in each sector. In both sectors, neo-classical production functions provided the framework for the available time series data on agricultural and industrial production. Under the assumptions of a constant exponential rate of growth of the population and constant rates of depreciation of the capital stocks in the sectors, the dynamic behaviour of the population and the capital stocks was determined. The rate of change of the proportion of labour in the urban sector was assumed to depend on the real wage differential between the two sectors and the size of the urban sector. This behavioural relationship turned out to be quite crucial in the determination of the optimum path. The index of performance chosen was that of a constant elasticity of utility functional. Although the utility function is convex in its main argument (consumption), the convexity of the utility functional subject to the dynamic constraints was difficult to establish through either analytic or numerical methods. Consequently any computed optimum path was provisionally assumed to be a local one. The final optimum path was obtained by repeated computations. The methods used for the main computations are fully explained in a technical chapter and the Appendix. The importance of computation errors and the problem of numerical stability of the solutions are fully explored. The Optimum path was surprising in many aspects: 1. Initial high rates of savings in the agricultural and the urban sectors. 2. The agricultural sector was virtually depleted of all its labour force within the first fourteen years. During this period urban capital reached its peak and agricultural capital its apogee. 3. A reversal of the early trend occured 30 years after the start of the program. This meant that agricultural capital was rebuilt, and labour flowed back into agriculture. 4. The effect of increasing the gross rate of discount was to render the optimization inoperative after 40 years. In the short run, increasing the discount rate reduced slightly the rates of savings in both sectors. The basic model was extended to cover two possible aspects of Government expenditure policies on education and their effects on the rate of unemployment in the urban sector. Labour in agriculture was assumed to be fixed. The net result was to shift the savings burden on to the urban sector where the initial rate was up to 80% of urban output. Part of the urban savings was used to build up agricultural capital. Finally an attempt was made to compare the optimum path with the actual path for the first 20 years of the program. The actual path was found to be closer to the optimum path of the second model than the first.
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