Stochastic CVP Analysis with Economic Demand and Cost Functions

The analysis focuses on key concepts associated with the extensive CVP under uncertainty literature which has developed since the seminal contribution by Jaedicke and Robichek (1964). For the most part the previous literature has not incorporated economic functions relating production quantity to price and/or average cost. This model developed herein incorporates a linear demand function and a quadratic average cost function. Explicit solutions are found for five special quantities: (1) the lowest quantity which sets breakeven probability equal to the minimum acceptable level, (2) the quantity which maximizes breakeven probability, (3) the quantity which maximizes a Cobb-Douglas utility function defined on expected profits and breakeven probability, (4) the quantity which maximizes expected profits, and (5) the highest quantity which sets breakeven probability equal to the minimum acceptable level. Comparative statics effects are determined of the various model parameters on the five special quantities. A CVP possibilities graph is developed showing attainable combinations of expected profits and breakeven probability. Possible applications of the model are discussed.