Question

Is the production function a constant return to scale/homogeneous of degree 1? Y = function of capital (labor)

Answer 1

If the production function is homogeneous of degree 1 then if all inputs are multiplied by t then output is multiplied by t . A production function with this property is said to have “constant returns to scale” .

Let us assume that the production function is : Q = 2K + 3L ( K = capital . L= labor . Q = output )

We will increase both K and L by t and create a new production function Q’.

Q’ = 2(K*t) + 3(L*t) = 2*K*t + 3*L*t = t(2*K + 3*L) = t*Q

This is homogeneous of degree 1 .

Since Q’ = t*Q we see that by increasing all of our inputs by the multiplier t we've increased production by exactly t . So we have constant returns to scale .