Accounting Thornton and Moore ^26 used a total audit fee...

Accounting Thornton and Moore $^{26}$ used a total audit fee function as $F(w, y)=p(y) q(w),$ where $p$ is the hourly fee charged by the auditor, $q$ is the number of hours required to perform the audit, $y$ is the auditor quality, and $w$ is a measure of internal controls. Then the authors state that $p^{\prime}(y)>0$ and $q^{\prime}(w)<0 .$ Explain why this is reasonable.

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Key Concepts

Auditor Quality and Hourly Fee

The hourly fee is modeled as an increasing function of auditor quality, meaning that higher quality auditors charge more per hour. This relationship is represented by a positive derivative with respect to quality, reflecting the idea that auditor expertise, reputation, and the expected thoroughness of the audit are valuable attributes that justify a higher fee rate.

Internal Controls and Audit Hours

The number of hours required to complete an audit is modeled as a decreasing function of the strength of internal controls. This is captured by a negative derivative with respect to internal controls, indicating that robust and effective internal controls reduce the amount of work (and time) needed for an audit. This relationship shows that better internal controls enhance efficiency by reducing the scope or complexity of the audit process.

Total Audit Fee Function

This concept involves modeling the total audit fee as the product of two functions: one representing the auditor's hourly charge and the other representing the number of audit hours required. It captures how different elements, such as quality and internal controls, jointly influence the cost of performing an audit. This approach simplifies the complexity of setting audit costs by isolating the effects of quality and efficiency on the overall fee.

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