An Illustration of Optimal Employment

Determination of the optimal input level can be clarified by reconsidering the Tax Advisors, Inc., example, illustrated in Table 7.3. If three CPAs can process 2.4 returns per hour and employing a fourth CPA increases total output per hour to 2.8, then employing a fourth CPA reduces marginal product from MPcpa=3 = 1.4 to MPcpa=4 = 0.4. Employment is in a range of diminishing returns. Nevertheless, a fourth CPA should be hired if expanding employment will increase profits.

For simplicity, assume that CPA time is the only input required to process additional tax returns and that CPAs earn $35 per hour, or roughly $70,000 per year including fringe benefits. If Tax Advisors, Inc., receives $100 in revenue for each tax return prepared by the fourth CPA, a comparison of the price of labor and marginal revenue product for the fourth CPA reveals because

If a fourth CPA is hired, total profits will rise by $5 per hour (= $40 - $35). The additional CPA should be employed.

Because the marginal product for the fifth CPA equals 0.2, MPcpa=5 = 0.2, the marginal revenue product falls to only $20 per hour, or less than the $35-per-hour cost of hiring that person. The firm would incur a $15-per-hour loss by expanding hiring to that level and would, therefore, stop with employment of four CPAs.

This example assumes that CPA time is the only variable input involved in tax-return preparation. In reality, other inputs are apt to be necessary. Additional computer time, office supplies, and clerical support may also be required to increase output. If such were the case, determining the independent contribution or value of CPA input would be more complex. If variable overhead for CPA support staff and supplies equals 50 percent of sales revenue, then the net marginal revenue, or marginal revenue after all variable costs, for CPA time would be only $50 per unit (= 0.5 X MRQ). In this instance, Tax Advisors, Inc., would find that the $20 (= 0.4 X (0.5)($100)) net marginal revenue product generated by the fourth CPA would not offset the necessary $35 per hour cost (wage rate). It would, therefore, employ no more than three CPAs, a level at which MRP = 1.4 X (0.5)($100) = $70 > $35 = PCPA. The firm will employ additional CPAs only so long as their net marginal revenue product equals or exceeds their marginal cost (price of labor).

This explains why, for example, a law firm might hire new associates at annual salaries of $80,000 when it expects them to generate $150,000 per year in gross billings, or 1,500 billable hours at a rate of $100 per hour. If variable costs are $70,000 per associate, only $80,000 is available to cover associate salary expenses. When customers pay $100 per hour for legal services, they are paying for attorney time and expertise plus the support of legal secretaries, law clerks, office staff, supplies, facilities, and so on. By itself, new associate time is worth much less than $100 per hour. The net marginal revenue of new associate attorney time, or CPA time in the preceding Tax Advisors, Inc., example, is the marginal value created after allowing for the variable costs of all other inputs that must be increased to provide service.

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