Homogeneous & Homothetic Functions
نویسنده
چکیده
It should now become obvious the our profit and cost functions derived from production functions, and demand functions derived from utility functions are all homogeneous functions. Using these functions offers us ease of interpretation of key economic ideas. Consider the following idea related to production functions, the returns to scale. Let f(x) be the production function. Then if it were homogeneous of degree α = 1, it would be associated with constant returns to scale. If α > 1, then the firm would be experiencing increasing returns to scale. On the other hand, if α < 1, the firm would be experiencing decreasing returns to scale. It should become clear why the Cobb-Douglas function is so popular in undergraduate economics. Some of the key properties of a homogeneous function are as follows,
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