If the production function is f(x, y) = min{ 2x + y, x + 2y}, then there are constant returns to scale.

Question

Quizplus · Accepted Answer

To test for constant returns to scale, we need to check if doubling the inputs, x and y, results in a doubling of the output, f(x,y). Let's see:
f(2x, 2y) = min{2(2x) + 2y, 2x + 2(2y)} = min{4x + 2y, 2x + 4y}
Now, let's look at f(x,y):
f(x, y) = min{2x + y, x + 2y}
If we double both x and y, then we get:
f(2x, 2y) = min{4x + y, x + 4y}
Notice that this is the same as min{2(2x) + 2y, 2x + 2(2y)}, which means that f(2x, 2y) = 2f(x,y). Therefore, there are constant returns to scale.

If the Production Function Is F(x, Y) = Min{ 2x