Final answer:
The production function Q=5L2/3K1/3 exhibits constant returns to scale, as scaling inputs by a constant factor results in output increasing by the same factor. This is demonstrated mathematically by the sum of the exponents equaling 1, and supported by economic principles related to the long-run average cost curve.
Step-by-step explanation:
The production function given is Q=5L2/3K1/3. To determine whether it exhibits constant, increasing, or decreasing returns to scale, we scale up the inputs of labor (L) and capital (K) by some constant factor α. The new production level would be Q' = 5(αL)2/3(αK)1/3 = 5α2/3+1/3L2/3K1/3 = 5αL2/3K1/3. Because the exponents add up to 1 (2/3 + 1/3 = 1), the factor α comes out to the power of 1, which means that the new production Q' will be exactly α times the original production Q, which implies constant returns to scale.
An example from a secretarial firm indicates that in the short run, with fixed capital, such as having only one personal computer, the firm cannot achieve a proportional increase in output with a proportional increase in labor alone. This practical scenario aligns with the economic principle that in the long run, where all factors can vary, a flat long-run average cost curve (LRAC) around Q3 indicates constant returns to scale because average cost doesn't change significantly as scale increases or decreases. Thus, the production function given would reflect constant returns to scale in the long run.