Final answer:
To maximize the output of the production function Y = X1^α * X2^(1-α), the resources need to be allocated according to the value of α, reflecting their elasticity of substitution.
Step-by-step explanation:
The equation Y = X1^α * X2^(1-α) represents a production function often used in economics. To maximize the output Y, we need to consider the allocative efficiency of resources X1 and X2, which are raised to the powers of α and 1-α, respectively. The fraction that maximizes output is crucially dependent on the value of α, which reflects the elasticity of substitution between the two inputs.
In the context of utility maximization, the general rule regarding marginal utility suggests that the ratio of the marginal utilities of the goods should be equal to the ratio of their prices. However, this information is more related to consumer choice theory than to directly identifying the fraction that maximizes output in the given production function.
Without additional constraints or information on X1 and X2, we cannot give a specific fraction that maximizes Y. Instead, we can say that allocation according to the value of α ensures that resources are used efficiently to maximize production output.