The ability of unions to raise the wages of their members above the wages of similar but nonunionized workers is well documented. This paper examines empirically the implications of that wage differential for resource allocation and economic efficiency. This is accomplished by explicitly solving a numerically specified general equilibrium system with and without the wage differential. Comparison of the two solutions yields the desired information. The findings indicate that the wage premium results in adjustments in prices and quantities of factors and commodities that vary widely across industries. These adjustments are found to carry a small deadweight loss, as measured by the Hicksian equivalent variation.

Auditing, Internal controls, Audit judgement, Consensus

Black and Scholes [1] derived the pricing equation for a European put when the stock price follows geometric Brownian motion. For this same case, Merton [5] derived the pricing equation for an American put with infinite time to maturity. Brennan and Schwartz [2], Rubinstein and Cox [7], and Parkinson [6] have developed numerical solutions for the price of an American put. Numerical solutions are expensive and do not provide much intuition. Naturally, an analytic solution would be much preferred; unfortunately, pricing the American put requires solving a formidable and presumably intractable boundary value problem.

This paper begins an investigation into the incentive problems at a firm when the effort of the employer and the employees combines to determine final output. The major conclusion is that optimal reward functions in this circumstance will in general value the performance of a worker relative to that of his peers. The paper thus joins a growing literature associated with the work of Lazear and Rosen on rank-order tournaments.