Final answer:
The elasticity of substitution for the given production function q = lk² with marginal products mpl = k² and mpk = 2lk is equal to 1, indicating a fixed proportional change in input ratios to the marginal rate of technical substitution.
Step-by-step explanation:
The question is asking to demonstrate that the elasticity of substitution for the production function with the equation q = lk², which has marginal products mpl = k² and mpk = 2lk, is exactly equal to 1. To show this, we would typically utilize calculus and economic theory to find the elasticity of substitution which measures how easily inputs such as labor (L) and capital (K) can be substituted for one another without affecting the output level (Q).
The production function provided suggests a specific functional form where the elasticity of substitution is constant. This form is characteristic of the Cobb-Douglas production function, which is widely known to have an elasticity of substitution equal to 1. While the question does not require the calculation steps, it is based on the proportional change in the ratio of input factors to the proportional change in the marginal rate of technical substitution (MRTS), which in the case of the Cobb-Douglas function remains constant.