Final answer:
The Cobb-Douglas production function q = 10L⁰.⁷¹K⁰.₈⁴ exhibits increasing returns to scale, as the sum of the exponents of labor and capital (0.71 + 0.84) is greater than 1, indicating that output increases by a larger percentage than the increase in inputs.
Step-by-step explanation:
When considering the production function q = 10L⁰.⁷¹K⁰.₈⁴, we need to assess returns to scale by adding up the exponents of labor (L) and capital (K). The exponents in the Cobb-Douglas production function represent the output elasticity with respect to each input. In this case, we have 0.71 for labor and 0.84 for capital. Adding these together gives us 0.71 + 0.84 = 1.55, which is more than 1. This indicates increasing returns to scale, meaning if all inputs are increased by a certain percentage, output increases by a larger percentage.
In the context of a long-run average cost (LRAC) curve, increasing returns to scale occurs when the average cost of production decreases as the scale of production increases. This is typically seen in the downward-sloping part of the LRAC curve. On the other hand, constant returns to scale, as described in your question, would be indicated by a sum of exponents equal to 1, where average costs do not change as production scale changes. Since the sum of the exponents in this function is greater than 1, constant returns to scale do not apply here.