On a Dynamic Model of Revenue Maximizing Firm

To effectively manage a firm means to consider either the profit of the firm or the revenue of the firm. What is better to maximize? According to Baumol, firms aim to maximize their sales revenue rather than their profit. This idea is known as revenue maximization theory. In the present paper we study a dynamics model of a revenue maximizing firm. The model considers that the firm aims to maximize its revenue within a very long time period hence the infinite time horizon is used. The further assumption of the model is that the firm respects a minimum acceptable rate of return on capital. The model is formulated as an optimal control problem on infinite time horizon. Necessary conditions of maximum principle for optimal solution suggest that the rule for maximization revenue of the firm is the equality of the ratio of marginal substitution of labor over capital and the ratio of the wage rate over the discount rate. If the firm is governed by this hypothetical maximization rule it grows endogenously at the rate directly proportional to the return on capital.