# which diminishes as l increases, eventually becoming negative. This implies that q reaches a…

which diminishes as l increases, eventually becoming negative. This implies that q reaches a maximum value. Setting MPlequal to 0,

120,000l – 3,000l2 = 0

40l = l^{2}

l = 40

as the point at which q reaches its maximum value. Labor input beyond 40 units per period actually reduces total output. For example, when l = 40, Equation 9.7 shows that q = 32 million flyswatters, whereas when l = 50, production of flyswatters amounts to only 25 million. Average product.To find the average productivity of labor in flyswatter production, we divide q by l, still holding k = 10:

which occurs when l = 30. At this value for labor input, Equation 9.12 shows thatAP_{l}= 900,000, and Equation 9.8 shows that MP_{l}is also 900,000. When AP_{l}is at amaximum, average and marginal productivities of labor are equal.^{3}

Notice the relationship between total output and average productivity that is illustrated by this example. Even though total production of flyswatters is greater with 40 workers (32 million) than with 30 workers (27 million), output per worker is higher in the second case. With 40 workers, each worker produces 800,000 flyswatters per period, whereas with 30 workers each worker produces 900,000. Because capital input (flyswatter presses) is held constant in this definition of productivity, the diminishing marginal productivity of labor eventually results in a declining level of output per worker.

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