Question

For each of the

following document if the function has increasing/decreasing or
constant returns to scale, explain why:
y=x1+x2
y=2x1+3x2"

Answer 1

The first function demonstrates constant returns to scale as doubling inputs doubles the output. The second function exhibits increasing returns to scale because doubling the inputs more than doubles the output.

Step-by-step explanation:

The question is considering the concepts of increasing, decreasing, or constant returns to scale in the context of production functions. These are mathematical expressions used in economics to represent the relationship between input quantities and the resulting output.

Looking at the first function y = x1 + x2, if we were to double inputs (2x1, 2x2), the output would double (2y). This indicates constant returns to scale, as increasing the input by a certain proportion results in the same proportion of increase in the output.

The second function y = 2x1 + 3x2 shows that if inputs are doubled, the output more than doubles (2(2x1) + 3(2x2) = 4x1 + 6x2). This exemplifies increasing returns to scale, as the proportionate increase in output is greater than the proportionate increase in inputs.

It's important to note that these calculations assume that inputs are scaled up evenly and that the functions capture all dimensions of the production process which might not always be the case in real-world scenarios.