Aspects of risk programming

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Virginia Polytechnic Institute

The purpose of this thesis was to investigate certain aspects of risk programming.

In the computational example, experimental data based on varietal tests were used to obtain estimates of the variances of net revenue of the various crops considered. As was expected, the consideration of risk increased the importance of corn, the crop with the lowest unit level variance, and decreased the importance of tomatoes, a comparatively high risk crop. In the risk program, the total revenue was, of course, decreased, but the expected utility was increased and the standard deviation of the net revenue was substantially decreased. The risk program also requires less capital and labor than the no-risk program.

An opportunity curve was formed by joining several points of tangency between the opportunity line and indifference curve corresponding to utility functions with different values of the risk aversion constant “a”. This opportunity curve represents combinations of net revenue and the variance of net revenue which are available to the entrepreneur. An entrepreneur could choose a point on the curve which to him represents the best combination of net revenue and variance. In doing so, he will effectively be choosing his own risk aversion constant and corresponding optimal program. By this procedure, the difficulty of hypothesising an incorrect risk aversion constant can be avoided.

Computational shortcuts for arriving at optimum programs for various risk aversion constants were developed as were methods for varying the price of a process and the availability of a scarce resource.