Final answer:
The average product for the third worker in a sloth-shaving boutique being 11 sloths suggests positive contributions to total output up to that worker. However, due to diminishing marginal productivity, adding a sixth worker could result in a lower total number of sloths shaved, as the marginal product of additional workers begins to decrease and could even become negative.
Step-by-step explanation:
When analyzing the production data for a sloth-shaving boutique, it's important to understand the concept of marginal product (MP). Marginal product is the additional output produced by the addition of one more worker, which can be calculated by dividing the change in total product by the change in labor (MP = ΔTP/ΔL). Initially, the marginal product may increase as more workers are added due to improved division of labor and specialization.
However, diminishing marginal productivity comes into play as more workers are added beyond a certain point. This phenomenon occurs because each additional worker contributes less to the total output, since the opportunities for efficient specialization become limited and fixed capital remains unchanged. Eventually, adding more workers could even lead to negative returns, where the total output decreases. This is due to workers interfering with each other's productivity, similar to too many barbers in a barber shop bumping elbows.
Based on these principles, if the average product for the third worker is 11 sloths, it means that up to that point, each worker might still be contributing positively to the total output. However, adding a sixth worker could lower the total number of sloths shaved, as the marginal product of additional workers likely decreases due to the law of diminishing marginal productivity.