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What does it mean that a production function is homogeneous of degree r?If a production function...

What does it mean that a production function is homogeneous of degree r?If a production function is homogeneous of degree r=0.5,can we conclude that it has decreasing returns to scale?

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Answer #1

If a production function is homogeneous of degree 1, it means that if we multiply all the inputs by a constant number to the power 1 or 1 , the output will also be that constant number times output or Y.

For eg. If Y=X+Z

Then multiplying X and Z by will give us X+Z= (X+Z)= Y

If we could transform the equation similar to above except with a power more than 1, then the function will be said to be homogenous but with a degree of that number greater than 1.

If the production function is homogeneous of degree r=0.5, then it is said that the function inhibits the decreasing returns to scale. Degree 1 corresponds to constant returns whereas degree greater than 1 means increasing returns to scale.

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