The Cobb-Douglas production function is given by

Show that is production function is homogeneous of degree 3 (i. e. exhibits increasing returns to scale) and verify the Euler’s theorem

If the Cobb Douglas production funtion is

This function is homogeneous of degree 3: To understand that, we first must know that a function f(K,L)  is homogeneous of degree "m" if . Intuitively, this means that, when you increase your productive factors (in this case, we are talking about a production function), by a factor "", your output increases by . Depending on the value of m, the function will exhibit increasing returns to scale (m>1), decreasing returns to scale (m<1) or returns to scale equal to 1 (when m=1).

Euler's Theorem: this theorem states that, if a function is homogeneous of degree "m", the following must hold: .

c

explanation: