# Economic analysis of the long-term planning investment strategies for the oil surplus funds in Saudi Arabia : an optimal control approach

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This dissertation is mainly concerned with the long- run intertemporal planning strategy problems facing Saudi Arabia in recycling the petro-dollar surpluses. The economy of Saudi Arabia depends on a single, exhaustible natural resource, which is unlikely to last longer than a few decades, as the principle source of an easy single income. The characteristics of the Saudi economy are expressed here first by means of a simple macroeconomic model, and then invoked in the optimization process. More specifically, the methodology in intertemporal planning investment strategies is explicitly demonstrated by using optimal control theory, which is the method of optimization of choice over time, and which focuses on the determination of the optimal expenditure of the oil revenue surpluses in such a way that the economy will maintain its overall economic position in the post-oil era. The objective function is to show what is the maximum stock of domestic non-oil capital that can be accumulated, given the resource's lifetime. In other words, the task is to determine how much the economy should invest internally and how much externally and at which point in time, given the constraints operating for the conversion of the resource wealth into other forms of wealth. Thus the model is mainly designed to solve for the trajectory of non-oil domestic investment. The time paths of all other endogenous variables are determined in relation to this variable, including the time path for overseas investment. The planning model is advanced in two stages. First, a simple macroeconomic model is developed to explain the basic structure and characteristics of the Saudi economy. Second, a dynamic programming technique is applied in order to solve the optimization problem using the Lagrange multipliers within the framework of Kuhn-Tucker conditions. Although the Kuhn-Tucker conditions characterize a solution, they do not provide a constructive method for obtaining a solution. A solution algorithm exists for nonlinear programming problems. An algorithm method based on the "Method of Feasible Direction" is used to compute numerical solutions to the planning model. The problem is treated as one with a finite horizon, working with discrete time, where, at any moment in time, the economic system is assumed to be in some "state" described by the state variables. There are also some variables which can be chosen by policymakers to control the economy. These are referred to as "instruments" or control variables. The control and state variables at any given time determine the state of the system in the next period. We regard the rate of extraction of the oil resource as an exogenous factor in Saudi Arabia (i.e., influenced by external political considerations). The length of the time period in our model covers the period 1971-2000 (inclusive). We choose 1971 as the beginning year of our time span to enable us to compare the solution reached by the algorithm method with those policies actually practiced in Saudi Arabia during the 1970's. It is hypothesized that by the year 2000, the oil revenue in Saudi Arabia will have sufficiently dwindled that the resource will then be regarded as exhausted. However, it is important to note that there is an elemental force of uncertainty surrounding the future. Therefore, we would like to emphasize here that our prime concern is to demonstrate a planning technique for solving the problem of investing such vast amounts of funds as those now produced by Saudi Arabia in a manner consistent with national objectives, and not to forecast the future course of events.